Jean's Palace

Welcome back

Jean's Palace — jump to any section

Four subjects, every section one click away. Pick a card below, or use the tabs up top.

📈 Macroeconomics

Overview 1 · Introduction 2 · GDP 3 · Equilibrium Income 4 · Fiscal Policy ★ Worked Examples ❓ Quiz Cheat-Sheet

∫ Calculus I

Overview 1 · Limits & Continuity 2 · Differentiation 3 · L'Hôpital 4 · Linear Approx. ★ Practice + Solutions ❓ Quiz Formulas & Midterm

🅰 Econ English

Exam Overview Vocabulary ★ Grammar (Tenses) Author's Purpose Formal Writing Reading Tips ❓ Quiz

🧠 Influence

Overview & Ethics 1 · Franklin Effect 2 · Funnel Technique 3 · IKEA Effect 4 · Ericksonian 5 · Door-in-Face 📚 Concepts ★ The Stack 🛡 Defense ❓ Quiz

Study Hub · Rebuilt for teaching

Principles of Macroeconomics — your complete study companion

This hub rebuilds the EE212 lecture slides into a teaching format: every key idea is explained in plain language (often beyond the slide), every important formula is boxed, the blanks your professor left are filled in and marked with a green tag, and the hard ideas come with clean graphs. Four units, then fully-worked assignments.

How to use this Read a unit top-to-bottom. Watch for filled-in answers, blue Key boxes (must-know), red Careful boxes (common exam traps), and gold Exam boxes (likely to be tested). Use the search bar to jump to any term.

Introduction to Macroeconomics

What economics is · micro vs macro · goals & policies · types of variables · key indicators · schools of thought.

1.1 What economics is

Economics = the science of scarcity and choice

Economics studies how individuals and societies choose to use the scarce resources that nature and previous generations provided. Because resources are limited but wants are unlimited, choice is unavoidable.

Scarcity — we "cannot have it all", so we must decide what to have and what to forgo.

Trade-off — to get one thing you give up another.

Opportunity cost — the value of the next best alternative you gave up. This is the single most important idea in the whole course.

Intuition“There is no such thing as a free lunch.” Even a “free” hour of Netflix costs you the study (or sleep) you could have done instead — that forgone best option is its true cost.

The three basic questions every society answers

What to produce?
How to produce it?
For whom — who gets the goods and services?

Micro vs. Macro

Microeconomics zooms in — individual industries, firms and households (one market's price & quantity).

Macroeconomics zooms out — the whole nation's aggregates: total income, employment, output, the price level.

Positive vs. Normative

Positive = facts & cause-effect, no value judgment (“what is”). e.g. “A tax cut raised spending 2%.”

Normative = value judgments (“what should be”). e.g. “The government ought to cut taxes.” Policy debates are normative.

1.2 Objectives & policies

The four goals — and the two big policy levers

Economists judge outcomes against four criteria:

Efficiency (allocative) — produce what people want at the least possible cost.

Equity — fairness in how output is shared.

Growth — an increase in the economy's total output over time.

Stability — output grows steadily, with low inflation and full employment.

The two policies (memorise the split) Fiscal policy = the Government's taxing & spending (Chapter 4).
Monetary policy = the Central Bank's tools to control the quantity of money.

1.3 Types of variables

Stock vs. Flow, and Nominal vs. Real

Stock vs. Flow

Stock = measured at an instant (a photograph). Flow = measured over a period (a video).

Test yourself “FDI during 2016–2020” is a flow. “Total FDI held on 31 Dec 2020” is a stock. Wealth = stock; income & saving = flows.

Nominal vs. Real

Nominal = not adjusted for price changes. Real = adjusted for prices (divide out inflation).

Real income = YP · Real interest rate r = i − inflation

Why it mattersOnly real variables tell you about actual purchasing power. A 5% raise with 8% inflation makes you poorer in real terms.

1.4 Key indicators

The dashboard of the economy

Macro health is read from three groups of indicators:

Level & growth of output — GDP and its growth rate.
Internal stability — inflation, unemployment, interest rates, income distribution.
External stability — balance of payments, international reserves, external debt, exchange rate.

① Output & the business cycle

Aggregate output = total goods & services produced in a period. The business cycle is its short-run ups and downs around a rising long-run trend.

Definitions to nail Recession = output falls for two consecutive quarters. Depression = a prolonged, deep recession.

The cycle oscillates around a rising trend: peak → recession (down) → trough → recovery (up).

② Prices & inflation

Inflation — a rise in the overall price level. Deflation — a fall. Hyperinflation — very rapid inflation.

CPI (Consumer Price Index) & PPI (Producer Price Index) measure the price level.

Core inflation strips out volatile items (energy, fresh food) to reveal the underlying trend.

Inflation rate_{year t} = CPI_t − CPI_t−1CPI_t−1 × 100

③ Unemployment

Population = Labour force + Non-labour force
Labour-force participation rate = Labour forceWorking-age population × 100
Unemployment rate = UnemployedLabour force × 100 ← the blank: divide by the labour force, not population

Three types of unemployment Frictional — normal short-run job search / people between jobs (always exists).
Structural — skills/industries no longer match the economy (e.g. automation).
Cyclical — caused by recessions (demand falls).

Natural rate of unemployment = Frictional + Structural. It's the unemployment that remains even at "full employment" — cyclical unemployment is zero at the natural rate.

④ Interest rates

Real interest rate = Nominal interest rate − Inflation rate

Creditors (lenders/savers) want the real rate high; debtors (borrowers) want it low. Loan rate > deposit rate — the spread is the bank's margin.

⑤ Income distribution — Lorenz curve & Gini

The further the Lorenz curve bows away from the 45° line, the more unequal the distribution.

Gini coefficient = Area AArea A + Area B

Read the number Gini ranges 0 → 1. 0 = perfect equality (everyone the same), 1 = perfect inequality (one person has everything). Higher Gini = more unequal income distribution.

1.5 History of macroeconomic thought

From Classical to Keynesian — the big argument that runs through this course

Classical (Adam Smith, 1776) — the market's “invisible hand” coordinates self-interest into social good; division of labour raises output. Reaction against mercantilism.

Marx — focused on the unfair distribution of industrial gains; history as “class struggle” between owners of capital and labour.

Neo-classical (Marshall) — “father of modern economics”; markets are efficient & self-regulating; introduced homo economicus (rational self-interested agent).

Keynes (1936, Great Depression) — markets do not always self-correct; in slumps the government should boost aggregate demand (spend, cut interest rates, invest).

Monetarists (Friedman) — crises come from bad monetary policy; government should control the money supply and leave goods markets alone. Led to neo-liberalism (privatise, free trade).

The distinction you must remember all term Classical = the long run: prices & wages are flexible, economy sits at full employment.
Keynesian = the short run: prices & wages are sticky, economy can sit below full employment — so policy has room to work.
Keynes: “In the long run we are all dead.”

National Income & Product Accounts (GDP)

Circular flow · what GDP is · GDP vs GNP · the three ways to measure it · nominal vs real & the deflator · limitations.

2.1–2.2 The players & the circular flow

Five sectors, one loop of money

Macro tracks five groups: (1) Households + (2) Firms = the private sector, (3) Government, (4) Rest of the world, and (5) Financial institutions.

The circular flow shows income and payments moving between them. Two forces act on the loop:

Injections (money in) Investment I, Government spending G, Exports X.

Withdrawals / Leakages (money out) Saving S, Taxes T, Imports M.

Households supply factors & earn income; they spend it on firms' output. Injections add to the loop; leakages drain it.

2.3 What GDP is

Gross Domestic Product — read the definition word-by-word

GDP = total market value of all final goods & services produced within a period by factors of production located within a country.

Final goods = for final use. Intermediate goods = used up in producing something else — not counted directly (avoids double counting).

Value added = value of output leaving a stage − cost of inputs entering it. Summing value added = summing final value.

Located within the country — GDP is about where production happens, not who owns the factors.

What GDP excludes Used goods & pure paper transactions (a house built 3 years ago is not in this year's GDP). But the agent's commission on selling it is — that's a new service produced this year. Only new, current production counts.

2.4 GDP vs GNP

Where vs. Whose

GDP — output produced inside the country (any owner).

GNP — output produced by a country's citizens/factors (anywhere in the world).

GNP = GDP + income of Thai factors used abroad − income of foreign factors used in Thailand
The correction term is called Net Factor Income from Abroad (NFIEA).

ExampleProfit of a Thai-owned factory in Laos → adds to Thai GNP (not Thai GDP). A Japanese-owned factory in Bangkok → adds to Thai GDP (not Thai GNP).

2.5 Three ways to measure GDP

Same number, three doors — they must all agree

(a) Production (value-added) approach

Sum the value added at every stage. Worked from the slide (orange-juice example):

Stage	Sales value	Value added
Oranges (farm)	500	500
Orange juice	650	150
Juice bottled (factory)	900	250
Retail sale (supermarket)	1,200	300
Total value added	—	1,200

The pointTotal value added (1,200) = the final retail value (1,200). That's why we don't add up all the sales (500+650+900+1200) — that would double-count the oranges four times.

(b) Expenditure approach — the one you'll use most

GDP = C + I + G + (X − M)

C — Consumption: household spending. Durable goods, non-durables, and services.

I — Gross private investment: new capital by firms/households = non-residential (machines/plant) + residential (new housing) + change in inventories.

G — Government consumption & investment (excludes transfer payments like welfare — no new output).

X − M — Net exports: exports minus imports (can be negative).

Inventories — filled-in example Begin: 2 units. Produce: 7. Sell: 6. End: 3 units (×10฿).
Change in inventories = end − beginning = 3 − 2 = 1 unit = 10 ฿. This counts as investment even though it wasn't sold — it was produced this year.
GDP = final sales + change in inventories + other components.

Gross vs Net Net investment = Gross investment − Depreciation.
NDP = GDP − Depreciation. So NDP = C + (I − Depreciation) + G + (X − M).

(c) Income approach

National income = Factor incomes + (indirect taxes − subsidies) + net business transfers + surplus of gov. enterprises
Factor incomes = compensation of employees + proprietors' income + corporate profits + net interest + rental income.

The full ladder (very exam-friendly) GDP → + NFIEA → GNP → − Depreciation → NNP → − Statistical discrepancy → NI → − (retained earnings + other non-household parts) → PI → − personal income tax → DI.
And disposable income splits: DI = C + S (if no personal interest/transfer payments).

2.6 Nominal vs Real GDP & the deflator

Separating "more stuff" from "higher prices"

Nominal GDP = Σ (P_current × Q_current) — uses this year's prices
Real GDP = Σ (P_{base year} × Q_current) — holds prices fixed at the base year

GDP deflator = Nominal GDPReal GDP × 100

Why we bother Nominal GDP can rise just because prices rose. Real GDP strips prices out, so it measures genuine growth in output. The deflator is the economy-wide price level implied by that comparison. In the base year, Real = Nominal, so the deflator = 100.

→ Full numeric solution (base year = Year 3) is in Worked Example A2.

2.7 Limitations of GDP

GDP is not the same as well-being

GDP & welfareIgnores crime, leisure, pollution and how income is distributed (use GDP per capita + Gini for that).

GDP & measurementMisses the underground economy and non-market work (housework, volunteering) — real production that never shows up.

National Income & Equilibrium Determination

The Keynesian core: consumption & saving · investment · the DAE line · equilibrium (two methods) · the multiplier · paradox of thrift · GDP gaps.

3.1 The key idea

Desired vs. Actual — the engine of Keynesian economics

Keynes built the model on desired (planned) spending, not actual spending. The gap between them is unplanned inventory, and it's what pushes the economy toward equilibrium.

Actual Aggregate Expenditure = Actual C + Actual I (always = output, by accounting)
DAE (Desired Aggregate Expenditure) = Desired C + Desired I + G + (X − M)

The crucial split — investment Actual I = Planned I + Unplanned inventory investment. When firms can't sell what they made, goods pile up as unplanned inventory (actual > planned). When they sell more than expected, inventories fall below plan (actual < planned). This mismatch is the signal to change production.

3.2.1 Consumption & saving

The consumption function C = C_a + bY_d

Keynes: the main driver of consumption is disposable income Y_d = Y − T. Using the slide's numbers, C = 100 + 0.6Y_d.

C_a = autonomous consumption (spending even at zero income = 100)
b = MPC = ΔCΔY_d = slope = 0.6 → of each extra ฿, 60 satang is spent
APC = CY_d (average) MPC = marginal (the slope)

Golden rule MPC + MPS = 1. Every extra baht is either spent or saved. Here MPC = 0.6, so MPS = 0.4.

Saving is just the mirror image

S = Y_d − C = Y_d − (C_a + bY_d) = −C_a + (1 − b)Y_d
S = −100 + 0.4Y_d → intercept −C_a, slope = MPS = 0.4

Break-even income (where C = Y_d, S = 0) 100 + 0.6Y_d = Y_d → 0.4Y_d = 100 → Y_d* = 250. Below it households dissave (borrow / sell assets); above it they save.

Where the C-line meets the 45° line, C = Y_d and saving = 0. Left of it C > Y_d (dissaving); right of it households save.

Move ALONG vs. SHIFT (classic exam question) A change in Y_d → move along the C (or S) curve. A change in any other factor (interest rate, expectations, wealth, population) → the whole curve shifts.

Two rival theories (know the one-liners) Permanent Income (Friedman): consumption depends on permanent (expected long-run) income, not this year's. A one-off bonus is mostly saved.
Life-Cycle (Ando & Modigliani): people smooth consumption over a lifetime — borrow when young, save in middle age, dissave in retirement.

3.2.2–3.2.4 The other components

Investment, Government & Net exports

Investment I

Driven by the real interest rate (↑r → ↓I) and income (↑Y → ↑I), plus technology, existing capital, taxes, expectations.

Autonomous: I = I_a
Induced: I = I_a + dY

Invest when… NPV > 0, or equivalently MEC (IRR) > i — the project's return beats the market interest rate.

Accelerator principle: investment demand is derived from the change in output — a rising ΔY accelerates net investment.

Government G & Net exports (X−M)

G is set by policy, planned in advance → treated as autonomous (G = G_a, flat line vs. Y). Expansionary policy shifts it up; contractionary shifts it down.

Exports X depend on foreign demand → autonomous (X = X_a).

Imports rise with income: M = M_a + mY
m = MPM = ΔMΔY

3.2 The DAE line

Add it all up

DAE = C + I + G + (X − M)
= (C_a − bT_a + I_a + G_a + X_a − M_a) + (b + d − m)Y
↑ autonomous part (the intercept) ↑ slope of the DAE line

Slope of DAE = MPC + MPI − MPM = (b + d − m). Every extra ฿ of income induces this much extra spending. It's always < 1, which is what makes equilibrium stable and the multiplier finite.

3.3 Equilibrium — Method 1

Y = DAE (the "Keynesian cross")

Equilibrium = no tendency to change. In the goods market that means output equals desired spending:

Y = DAE

Left of Y_E, desired spending exceeds output → inventories fall unexpectedly → firms raise output. Right of it, the reverse. Only at Y_E is there no pressure.

Equilibrium formulas (memorise the pattern) Closed, no gov: Y_E = 11 − b(C_a + I_a)
Closed, with gov: Y_E = 11 − b(C_a − bT_a + I_a + G_a)
Open, with gov: Y_E = 11 − b + m(C_a − bT_a + I_a + G_a + X_a − M_a)

Worked (closed, with gov) C=100+0.6Y_d, I=40, T=10, G=60 → Y_E = 2.5 [100 − 0.6(10) + 40 + 60] = 2.5(194) = 485.

3.3 Equilibrium — Method 2

Injection = Leakage (must give the same Y_E)

At equilibrium the money added to the loop equals the money drained from it:

Closed, no gov: I = S
Closed, with gov: I + G = S + T
Open, with gov: I + G + X = S + T + M

When injection > leakage the economy expands; when leakage > injection it contracts. Equal at Y_E.

→ Both methods solved on the same numbers in A3 & A4 — and they agree (Y_E = 880).

3.3 The multiplier

Why a small push moves income a lot

Spend 1,000฿ building a factory. The builders earn 1,000฿; they spend MPC of it (600฿); those receivers spend 600×0.6 = 360฿; and so on — an infinite but shrinking chain:

ΔY = 1000(1 + 0.6 + 0.6² + …) = 1000 × 11 − 0.6 = 1000 × 2.5 = 2,500

Multiplier formulas Simple spending multiplier k = 11 − MPC = 1MPS.
More leakages → smaller multiplier. Adding an income tax and imports changes the denominator to (1 − slope of DAE). Higher MPC (or lower MPS) → bigger multiplier.

Tax & balanced-budget multipliers (closed economy) Government-spending multiplier = 11−b. Tax multiplier = −b1−b (smaller & negative — a tax cut is weaker than equal spending, because part is saved).
Balanced-budget multiplier = 1: raise G and T by the same amount and Y rises by exactly that amount.

3.4 Paradox of thrift

If everyone saves more, everyone earns less

An individual saving more is prudent. But if everyone tries to save more at once, aggregate demand falls → firms cut output → income falls → and society may end up saving the same (or less). This is a fallacy of composition: what's true for one isn't true for all.

The S curve shifts up (more thrift). With I fixed, the new intersection sits at a lower Y — and saving is unchanged. If investment is induced (I=I_a+dY), income falls even further.

Policy takeawayShort run (fight a slump): encourage spending (↓S, ↑C). Long run (fund growth): encourage saving (↑S) so there are funds for investment.

3.5 GDP gaps

Inflationary vs. Deflationary gap

Compare equilibrium output Y_E with full-employment (potential) output Y_F.

The gap is the vertical distance between the DAE line and the 45° line, measured right at Y_F.

At Y_F, desired spending exceeds output (DAE above the 45° line). Equilibrium Y_E sits beyond full employment → demand-pull inflation. Fix: reduce DAE (↑T or ↓G).

At Y_F, desired spending falls short of output (DAE below the 45° line). Equilibrium Y_E sits below full employment → unemployment. Fix: raise DAE (↓T or ↑G).

3.6 Keynes vs Classical vs in-between (the multiplier's size depends on prices) Keynesian: below full employment, prices sticky → when DAE rises, only Y rises → biggest multiplier.
Classical: at full employment, prices flexible → DAE↑ mostly raises P, not Y → smallest multiplier.
Non-Keynes non-classic: below full employment but prices do move → in between.
So ΔY: Keynes > in-between > Classical.

Fiscal Policy

Government spending & taxing · tools · tax structures · public debt · budget types · automatic vs discretionary · policy problems.

4.1–4.3 Meaning & tools

Fiscal policy = the government's spending & taxing choices

Its objectives mirror the four macro goals: efficient allocation, fair distribution, growth, and stability. Four tools:

Government expenditure (G) — consumption, investment, and loan/interest payments.

Transfer payments (R) — welfare, unemployment benefits, pensions, veterans' benefits. Not counted in G/GDP — no new output, just redistribution.

Revenue (T) — mostly taxes (below), plus non-tax revenue (state enterprises, fees, fines).

Public debt — borrowing to finance a deficit.

Direct vs Indirect tax Direct — the payer cannot shift the burden (personal & corporate income tax, inheritance, property tax).
Indirect — the payer can shift it onto others (VAT/sales tax, excise, customs duties).

4.3.3 Tax structures — with the blanks filled & checked

Progressive · Proportional · Regressive

Compare the average tax rate (T/Y) and marginal tax rate (ΔT/ΔY) as income rises. Same three income bands (each 1,000 wide) in every table.

① Progressive — rate rises with income

Income band	Rate	Cumulative Y	Tax paid T	Avg rate T/Y	Marginal ΔT/ΔY
0–1,000	10%	1,000	100	0.100	0.10
1,001–2,000	12%	2,000	220	0.110	0.12
2,001–3,000	15%	3,000	370	0.123	0.15

T at 2,000 = 100 + (1,000×0.12) = 220; T at 3,000 = 220 + (1,000×0.15) = 370.

SummaryIncome ↑ → tax rate rises. And marginal > average at every step. This is Thailand's personal-income-tax design.

② Proportional (constant)

Y	T (10%)	T/Y	ΔT/ΔY
1,000	100	0.10	0.10
2,000	200	0.10	0.10
3,000	300	0.10	0.10

SummaryRate is constant; marginal = average.

③ Regressive — rate falls with income

Y	T	T/Y	ΔT/ΔY
1,000	150 (15%)	0.150	0.15
2,000	270 (12%)	0.135	0.12
3,000	370 (10%)	0.123	0.10

SummaryRate falls; marginal < average.

Exam shortcutCompare marginal vs average: MTR > ATR → progressive · MTR = ATR → proportional · MTR < ATR → regressive.

4.3.4 Public debt & budgets

Borrowing and the budget balance

Public debt is classified by term (short < 1 yr, long > 5 yr) and source (domestic vs. international). It affects price stability, resource allocation, income distribution, and the state's ability to run projects.

Three budget types (G + R vs T) Deficit: G + R > T (spend more than you take) · Surplus: G + R < T · Balanced: G + R = T.
In accounting terms total spending is financed by revenue + public debt + treasury reserves.

4.4 Types of fiscal policy

Automatic vs. discretionary — and expansion vs. contraction

Non-discretionary = Automatic stabilisers Work by themselves, no new law needed. Boom → tax take rises & welfare falls automatically → cools the economy. Slump → taxes fall & welfare rises automatically → cushions the fall.
Tools: income tax (T = T_a + tY) and transfer payments (R = R_a − gY).

Discretionary Deliberate changes to tax types, tax rates, or G when automatic stabilisers aren't enough. Slump → ↑G / ↓T (expansionary). Overheating → ↓G / ↑T (contractionary).

Match the disease to the cure Recession / deflationary gap → Expansionary: ↑G, ↓T → DAE↑ → Y↑.
Inflation / inflationary gap → Contractionary: ↓G, ↑T → DAE↓ → Y↓.

4.4 Why fiscal policy is hard

Six real-world problems

Lags — recognition → decision → execution → response. By the time it acts, the problem may have changed.
Irreversibility — programmes are hard to switch off once the crisis passes.
Expectations — if people think a stimulus is temporary, they don't change behaviour.
Political goals can conflict with economic stability (spending before elections).
Extra saving — an expansion fails to stimulate if households just save the extra income (paradox of thrift again).
Crowding-out — government borrowing pushes up interest rates and displaces private investment.

Thailand's Sustainable Fiscal Framework (targets) Public debt / GDP < 60% ✓ · Debt / budget < 15% ✓ · Balanced budget ✗ (government chose to stimulate) · Investment share of spending > 25% ✗.

★

Worked Examples (Assignments, fully solved)

Every step shown, so you can reproduce these under exam conditions. Numbers taken from your assignment sheets.

Assignment 2 · GDP calculation

Nominal & Real GDP, deflator, inflation — base year = Year 3

Three goods: Books (B), Rulers (R), Erasers (E).

Year	P_B	Q_B	P_R	Q_R	P_E	Q_E
1	100	80	20	300	5	250
2	120	60	30	250	6	150
3 (base)	130	90	35	400	7	450

Nominal GDP = Σ (current P × current Q)

Year 1 = 100·80 + 20·300 + 5·250 = 8,000 + 6,000 + 1,250 = 15,250
Year 2 = 120·60 + 30·250 + 6·150 = 7,200 + 7,500 + 900 = 15,600
Year 3 = 130·90 + 35·400 + 7·450 = 11,700 + 14,000 + 3,150 = 28,850

Real GDP = Σ (Year-3 P × current Q) — prices fixed at 130 / 35 / 7

Year 1 = 130·80 + 35·300 + 7·250 = 10,400 + 10,500 + 1,750 = 22,650
Year 2 = 130·60 + 35·250 + 7·150 = 7,800 + 8,750 + 1,050 = 17,600
Year 3 = 130·90 + 35·400 + 7·450 = 28,850 (= nominal, because Year 3 is the base year ✓)

GDP deflator = (Nominal ÷ Real) × 100

Year 1 = 15,250 / 22,650 × 100 = 67.33
Year 2 = 15,600 / 17,600 × 100 = 88.64
Year 3 = 28,850 / 28,850 × 100 = 100.00

Growth rates

Nominal growth Y2 = (15,600−15,250)/15,250 = +2.30%
Nominal growth Y3 = (28,850−15,600)/15,600 = +84.94%
Real growth Y2 = (17,600−22,650)/22,650 = −22.30%
Real growth Y3 = (28,850−17,600)/17,600 = +63.92%

Inflation (from the deflator)

Year 2 = (88.64−67.33)/67.33 = +31.65%
Year 3 = (100−88.64)/88.64 = +12.82%

Read the storyIn Year 2, nominal GDP barely moved (+2.3%) but real GDP fell sharply (−22.3%) — output actually shrank; prices masked it. That's exactly why we compute real GDP.

Assignment 3 · Equilibrium (Y = DAE)

Open economy with government — every step

Given: C = 80 + 0.4Y_d, I = 50 + 0.6Y, G = 30, T = 10 + 0.1Y, X = 40, M = 20 + 0.16Y, with Y_d = Y − T.

Step 1 — substitute to get C in terms of Y

Y_d = Y − T = Y − (10 + 0.1Y) = −10 + 0.9Y
C = 80 + 0.4(−10 + 0.9Y) = 80 − 4 + 0.36Y = 76 + 0.36Y

Step 2 — build DAE

DAE = C + I + G + X − M
= (76 + 0.36Y) + (50 + 0.6Y) + 30 + 40 − (20 + 0.16Y)
= (76+50+30+40−20) + (0.36+0.6−0.16)Y = 176 + 0.80Y

Step 3 — set Y = DAE (Question 1)

Y = 176 + 0.8Y → 0.2Y = 176 → Y_E = 880

Question 3 — multipliers (the important, subtle part)

The DAE slope is k = b(1−t) + d − m = 0.4(0.9) + 0.6 − 0.16 = 0.80, so the common multiplier is:

11 − k = 11 − 0.8 = 5

Autonomous variable	Multiplier (∂Y/∂·)
C_a, I_a, G_a, X_a (spending)	+5
M_a (imports — a leakage)	−5
T_a (autonomous tax) = −b/(1−k)	−0.4/0.2 = −2

Meaning: +1 unit of autonomous G raises equilibrium income by 5 units; +1 unit of autonomous tax lowers it by 2 units.

Careful — a genuine inconsistency in the lecture slides Some slides compute these multipliers with the shortcut 1/(1−b+m) = 1/0.76 ≈ 1.32. That shortcut is only valid when investment and taxes are purely autonomous. Here investment has an induced part (+0.6Y) and tax is induced (+0.1Y), which is exactly why Y_E came out as 880 (using slope 0.8). To stay consistent with that same Y_E, the correct multiplier is 1/(1−0.8) = 5, and the tax multiplier is −2. Use the reduced-form (slope) method and you can't go wrong.

Question 4 — ΔG_a = +4 and ΔT_a = +20

ΔY = (G-multiplier)ΔG_a + (T-multiplier)ΔT_a = (+5)(4) + (−2)(20) = 20 − 40 = −20
New Y_E = 880 − 20 = 860

Check by re-deriving: new G=34, T=30+0.1Y → C=68+0.36Y → DAE=172+0.8Y → Y_E=172/0.2=860 ✓

Question 5 — if current income is 700 (below Y_E)

At Y = 700, DAE = 176 + 0.8(700) = 736 > 700. Desired spending exceeds output → inventories fall unexpectedly → firms raise production → income rises. The process continues until Y = 880, the equilibrium.

Assignment 4 · Equilibrium (Injection = Leakage)

Same economy, second method — should give Y_E = 880 again

Step 1 — saving function

S = Y_d − C = Y_d − (80 + 0.4Y_d) = −80 + 0.6Y_d
with Y_d = −10 + 0.9Y → S = −80 + 0.6(−10 + 0.9Y) = −86 + 0.54Y

Step 2 — set Injection = Leakage (Question 1)

Injection: I + G + X = (50 + 0.6Y) + 30 + 40 = 120 + 0.6Y
Leakage: S + T + M = (−86 + 0.54Y) + (10 + 0.1Y) + (20 + 0.16Y) = −56 + 0.8Y
120 + 0.6Y = −56 + 0.8Y → 176 = 0.2Y → Y_E = 880 ✓ (matches Method 1)

Question 4 — autonomous saving rises 7 units (Paradox of Thrift)

More autonomous saving = less autonomous consumption (C_a effectively ↓7). Saving is a leakage, so with multiplier 5:

ΔY = −5 × 7 = −35 → New Y_E = 880 − 35 = 845

LessonTrying to save more made national income fall — the paradox of thrift in one calculation.

Question 5 — if current income is 950 (above Y_E)

At Y = 950, leakage (−56 + 0.8·950 = 704) > injection (120 + 0.6·950 = 690). Output exceeds desired spending → goods pile up as unplanned inventory → firms cut production → income falls until Y = 880.

❓

Quiz Yourself — Macro

Tap an answer to check it instantly and see why. Your score updates as you go.

Score: 0 / 0

1. In the goods market, equilibrium national income occurs where…

Equilibrium = no tendency to change: what's produced (Y) exactly matches what people want to spend (DAE). Equivalently, injections = leakages.

2. If MPC = 0.8 (closed economy, no tax), the simple spending multiplier is…

k = 1/(1 − MPC) = 1/(1 − 0.8) = 1/0.2 = 5. Higher MPC ⟹ bigger multiplier.

3. An increase in autonomous taxes will make equilibrium income…

Taxes are a leakage → they reduce disposable income and spending. The tax multiplier is negative (−b/(1−b)), so ↑T lowers Y.

4. Which is counted in this year's GDP?

GDP counts new, final production this year. Used goods and pure financial transactions aren't new output; flour is an intermediate good (counted inside the bread's value).

5. When current output is below equilibrium (DAE > Y), what pushes the economy back up?

Desired spending exceeds output → firms sell more than they made → unplanned inventory fall → they produce more → Y rises to Y_E.

6. The paradox of thrift says that if everyone tries to save more at once…

More saving = less spending = lower DAE → output and income fall. A fallacy of composition: good for one person, harmful if everyone does it at once.

7. Real GDP differs from nominal GDP because real GDP…

Real GDP holds prices fixed at a base year, so changes reflect genuine output growth — not inflation. Nominal uses current prices.

8. To close an inflationary gap, contractionary fiscal policy would…

An inflationary gap = too much demand. Reduce DAE by ↓G or ↑T to bring Y back to full-employment output.

Score: 0 / 0

Formula Cheat-Sheet

One-page revision

National accounts

GDP = C + I + G + (X − M)
Deflator = (Nominal ÷ Real) × 100
GNP = GDP + NFIEA
NNP = GNP − Depreciation
DI = C + S

Consumption & saving

C = C_a + bY_d ; S = −C_a + (1−b)Y_d
MPC + MPS = 1
Break-even: C = Y_d (S = 0)

Equilibrium (open, with gov)

Y_E = C_a − bT_a + I_a + G_a + X_a − M_a1 − b + m
or solve Y = DAE directly (safest)

Multipliers

Spending k = 11 − slope of DAE = 1MPS (simplest case)
Tax = −b1 − b ; Balanced-budget = 1

Rates

Real r = i − inflation
Unemployment = (Unemployed ÷ Labour force) × 100
Gini = A ÷ (A + B)

Exam survival kit ① Always write Y_d = Y − T first. ② Collect the autonomous intercept and the Y-slope separately. ③ Solve Y = DAE. ④ Multiplier = 1/(1 − slope). ⑤ Sign-check: spending & exports +, imports & taxes −. ⑥ Below Y_E → produce more; above Y_E → produce less.

Calculus I · Midterm focus

Calculus I — limits, derivatives & their applications

Simplified straight from your professor's notes: every rule is stated as a clean formula, and the hard ones are shown worked out step-by-step exactly the way you'd write them on paper.

What the midterm actually tests Limits & asymptotes · continuity (find the constants that make f continuous) · L'Hôpital's rule · implicit & logarithmic differentiation · linear approximation.
Note from the slides: inverse-trig derivatives are on the FINAL, not the midterm — don't waste time there now.

Limits & Continuity

What a limit is · one/two-sided · limit laws · 0/0 tricks · trig limits · limits at infinity & asymptotes · continuity.

1.1 The idea

A limit is where a function is heading — not where it lands

Definition. lim_x→a f(x) = L means we can make f(x) as close to L as we like by taking x close enough to a (from both sides) — without ever letting x = a.

The golden existence rule The two-sided limit exists only if both one-sided limits exist AND are equal:

lim_x→a f(x) = L ⟺ lim_x→a⁻ f(x) = lim_x→a⁺ f(x) = L

If the left and right sides disagree, the limit does not exist (DNE). The value f(a) itself is irrelevant to the limit.

A "jump": the two sides head to different heights, so the two-sided limit doesn't exist.

1.2 Computing limits

Step 1: just plug in. Step 2: if you get 0/0, fix it.

Direct substitution works for polynomials, sin, cos, eˣ, and (on their domains) tan, ln, roots, etc. — just compute f(a).

The three outcomes of a fraction lim f/g ① g(a) ≠ 0 → answer is just f(a)/g(a).
② f(a) ≠ 0, g(a) = 0 → limit is infinite → DNE (a vertical asymptote).
③ f(a) = 0, g(a) = 0 → indeterminate 0/0 — you must rearrange (factor or rationalize) before the limit means anything.

0/0 trick A — factor & cancel

Ex. lim_x→2 (x²−4)/(x−2). Sub gives 0/0. Factor: (x−2)(x+2)/(x−2) = x+2 → limit = 4.

0/0 trick B — rationalize (multiply by the conjugate)

Ex. lim_x→0 (√(x²+4) − 2)/x². Multiply top & bottom by (√(x²+4)+2):

= lim_x→0 (x²+4) − 4x²(√(x²+4)+2) = lim_x→0 1√(x²+4)+2 = 12+2 = ¼

Handy algebra p²−q² = (p−q)(p+q) · p³±q³ = (p±q)(p²∓pq+q²). These are what let you cancel the troublesome factor.

1.3 Trig limits

Memorise two, derive the rest

lim_x→0 sin(x)x = 1 lim_x→0 1 − cos(x)x = 0

Ex. lim_x→0 sin(2x)/(5x). Force a matching "sin(2x)/(2x)": multiply/divide by 2 → (2/5)·[sin(2x)/(2x)] → (2/5)(1) = 2/5. General: lim sin(kx)/(mx) = k/m.

Squeeze (sandwich) theorem If f(x) ≤ h(x) ≤ g(x) and both outer limits equal L, then lim h(x) = L too. Classic: since −x² ≤ x²sin(1/x) ≤ x² and both ends → 0, we get lim_x→0 x²sin(1/x) = 0 (even though sin(1/x) alone has no limit).

1.4 Limits at infinity & asymptotes

End behaviour of a function

Rational functions: compare the top & bottom degrees For lim_x→±∞ p(x)/q(x), keep only the highest-power term on top and bottom:

deg(top) < deg(bottom) → limit = 0 (horizontal asymptote y = 0).
deg(top) = deg(bottom) → limit = ratio of leading coefficients (that's the H.A.).
deg(top) > deg(bottom) → limit = ±∞ (no horizontal asymptote).

Ex. lim_x→∞ (1+2x²−3x³)/(2x³+3x) → keep −3x³/2x³ = −3/2 (equal degrees).

"∞ − ∞" → rationalize lim_x→∞ (√(x²+5x) − x) ×conjugate → 5x/(√(x²+5x)+x) → 5/2 = 5/2. (Use √(x²)=|x|=x since x→∞.)

Vertical asymptote at x=a when the denominator → 0 (and top ≠ 0).

Horizontal asymptote y=L when lim_x→±∞ f(x)=L.

1.5 Continuity

Continuous = "you can draw it without lifting your pen"

f is continuous at x = a if ALL three hold ① f(a) is defined · ② lim_x→a f(x) exists · ③ they're equal: lim_x→a f(x) = f(a).

Exam-style: find the constants that make `f` continuous

Let f(x) = { (x−2)²/(x²−4) + 2k, x>2 ; h, x=2 ; 2x+k, x<2 }. Find h, k so f is continuous at x=2.

Left limit (x→2⁻): 2x+k → 4+k.

Right limit (x→2⁺): simplify (x−2)²/[(x−2)(x+2)] = (x−2)/(x+2) → 0, so → 0 + 2k = 2k.

Value: f(2) = h.

Set all three equal: 4+k = 2k = h → from 4+k=2k get k = 4, then h = 2k = 8. ✔

Discontinuity types & IVT Removable (a hole — limit exists but ≠ f(a)) · Jump (sides differ) · Infinite (vertical asymptote).
Intermediate Value Theorem: if f is continuous on [a,b] and takes opposite signs at the ends, it has a root in between — the standard way to "show an equation has a solution."

Differentiation

The derivative · the rule toolbox · implicit differentiation · log & exp · logarithmic differentiation.

2.1 Meaning

The derivative = slope of the tangent line = instantaneous rate of change

f′(x) = lim_h→0 f(x+h) − f(x)h

Tangent line at x=a: y = f(a) + f′(a)(x−a). Differentiable ⟹ continuous (but not the reverse — |x| is continuous yet has a corner at 0, so no derivative there).

2.2 The rule toolbox

The rules you apply on autopilot

Power: d/dx xⁿ = n·xⁿ⁻¹
Constant: d/dx c = 0 · Constant×: (c·f)′ = c·f′
Sum: (f ± g)′ = f′ ± g′
Product: (fg)′ = f′g + fg′
Quotient: (f/g)′ = (g·f′ − f·g′)/g²
Chain: d/dx f(g(x)) = f′(g(x))·g′(x)

Trig, exp & log derivatives (know cold) (sin)′=cos · (cos)′=−sin · (tan)′=sec² · (cot)′=−csc² · (sec)′=sec·tan · (csc)′=−csc·cot
(eˣ)′=eˣ · (bˣ)′=bˣ·ln b · (ln x)′=1/x · (log_b x)′=1/(x·ln b). With chain rule, multiply by du/dx.

Where a derivative fails to exist at a discontinuity, a corner (like |x| at 0), or a vertical tangent (like ∛x at 0).

2.3 Implicit differentiation ★

When you can't (or don't want to) solve for `y`

Two-step recipe ① Differentiate both sides w.r.t. x, treating y as a function of x (so every y gets a ·dy/dx by the chain rule). ② Solve algebraically for dy/dx.

Ex. x² + y² = 2 → differentiate: 2x + 2y·(dy/dx) = 0 → dy/dx = −x/y.

Tangent line at (1,1): slope = −1/1 = −1 → y − 1 = −1(x−1) → y = −x + 2.

Harder. x⁴ + x²y³ − y⁵ = 2x + 1. Differentiate (product rule on x²y³): 4x³ + (2x·y³ + x²·3y²y′) − 5y⁴y′ = 2. Collect y′:

dy/dx = 2 − 4x³ − 2xy³3x²y² − 5y⁴

2.4 Logarithmic differentiation ★

The trick for "variable to a variable power", like `xˣ`

Three steps ① Take ln of both sides & use log laws to break it up. ② Differentiate implicitly (left side becomes (1/y)·y′). ③ Solve for y′ and replace y with the original f(x).

Ex. y = xˣ. Take ln: ln y = x·ln x.

Differentiate: (1/y)y′ = ln x + x·(1/x) = ln x + 1.

Solve: y′ = y(1 + ln x) → y′ = xˣ(1 + ln x).

Log laws that do the heavy lifting ln(AB)=ln A+ln B · ln(A/B)=ln A−ln B · ln(Aᴮ)=B·ln A. Also great for messy products/quotients like ln( x²√((x−1)³(2x+1)⁷) ) — take ln first, then it's just sums.

L'Hôpital's Rule

Using derivatives to crack indeterminate limits.

3.1 The rule

When you hit 0/0 or ∞/∞, differentiate top and bottom separately

If lim f/g is 0/0 or ∞/∞, then lim_x→a f(x)g(x) = lim_x→a f′(x)g′(x)

Check the form FIRST L'Hôpital is only valid for 0/0 or ∞/∞. Applying it to something like 1/0 or 2/1 gives a wrong answer. You may apply it repeatedly if the form stays indeterminate.

Ex. lim_x→0 sin x / x = cos x / 1 → cos 0 = 1.

Ex. lim_x→∞ ln x / eˣ (∞/∞) = (1/x)/eˣ → 0 = 0.

3.2 Other indeterminate forms

Convert them to 0/0 or ∞/∞ first

The disguised forms: ∞−∞, 0·∞, 0⁰, ∞⁰, 1^∞. Reshape, then apply L'Hôpital.

0·∞ → make a fraction

Ex. lim_x→∞ x·sin(1/x) = sin(1/x)/(1/x) (now 0/0) → 1.

1^∞, 0⁰, ∞⁰ → take ln, solve, then exponentiate

Recipe Let y = f(x)^{g(x)}. Then ln y = g(x)·ln f(x) (a 0·∞ form). Find L = lim ln y, and the answer is e^L.

Ex. lim_x→∞ (1 − 3/x)^2x (form 1^∞). ln y = 2x·ln(1−3/x) → −6, so limit = e⁻⁶.

Ex. lim_x→0 x^{1/ln x} (form 0⁰). ln y = (1/ln x)·ln x = 1, so limit = e.

Linear Approximation & Differentials

Using the tangent line to estimate hard values by hand.

4.1 Linearization

Near `x=a`, a curve looks like its tangent line

L(x) = f(a) + f′(a)(x − a) and f(x) ≈ L(x) (for x near a)

How to pick a Choose an a close to your target where f(a) and f′(a) are easy (a perfect square/cube, or 1).

Ex. Approximate √4.01

f(x)=√x, a=4: f(4)=2, f′(x)=1/(2√x) so f′(4)=¼.

L(x)=2+¼(x−4) → √4.01 ≈ 2+¼(0.01) = 2.0025. (and √3.95 ≈ 2−¼(0.05)= 1.9875)

Ex. ln(1.1): f=ln x, a=1 → L(x)=0+1·(x−1)=x−1 → ln(1.1)≈ 0.1.

Ex. ∛0.97: f=x^{1/3}, a=1, f′(1)=⅓ → 1+⅓(−0.03)= 0.99.

4.2 Differentials

Estimating error

dy = f′(x)·dx ≈ Δy (the small change in f when x changes by dx)

Ex. A cube side is 30 cm ± 0.02. V=x³, dV=3x²·dx = 3(30²)(±0.02) = ±54 cm³. Relative error dV/V = 54/27000 = 1/500.

★

Practice Exam Problems — with full solutions

Modeled on your past midterms. Try each one first, then click "Show solution". Grouped by the topics that actually appear on the exam.

Set 1 · One-sided & piecewise limits

1. Let f(x) = { (x²+3x+2)/|x+1|, x<−1 ; 2−x², x≥−1 }. Find lim_x→−1⁻f, lim_x→−1⁺f, and lim_x→−1f.

Left (x<−1, so x+1<0 ⟹ |x+1| = −(x+1)): factor x²+3x+2=(x+1)(x+2) → (x+1)(x+2)/[−(x+1)] = −(x+2) → −(−1+2) = −1.

Right (x≥−1): 2−x² → 2−1 = 1.

Left (−1) ≠ Right (1), so lim_x→−1f does not exist. The absolute value is the trap — it flips the sign on the left side.

2. Evaluate (a) lim_x→3 (x−3)/(x²−9) (b) lim_x→0 (√(x+9)−3)/x.

(a) 0/0. Factor x²−9=(x−3)(x+3) → 1/(x+3) → 1/6 = 1/6.

(b) 0/0. Multiply by conjugate (√(x+9)+3): (x+9−9)/[x(√(x+9)+3)] = 1/(√(x+9)+3) → 1/(3+3) = 1/6.

Set 2 · Trig limits & squeeze theorem

3. Find lim_x→0 tan(3x)/sin(5x).

Rewrite tan(3x)=sin(3x)/cos(3x) and force the sin(kx)/(kx)→1 pattern:

= [sin(3x)/(3x)]·(3x) / { cos(3x)·[sin(5x)/(5x)]·(5x) } = (1·3x)/(1·1·5x) → 3/5.

4. Show lim_x→0 x²·sin(1/x) = 0, and use it to decide continuity of g(x)={ x²sin(1/x), x≠0 ; 0, x=0 } at 0.

Since −1 ≤ sin(1/x) ≤ 1, multiply by x²≥0: −x² ≤ x²sin(1/x) ≤ x².

Both lim_x→0(−x²)=0 and lim_x→0x²=0, so by the squeeze theorem the middle → 0.

Now check continuity: ① g(0)=0 defined; ② lim_x→0g=0 exists; ③ they're equal → g is continuous at 0. ✔

Set 3 · Limits at infinity & asymptotes

5. Find all vertical and horizontal asymptotes of f(x) = (3x²+1)/(x²−4).

Vertical: denominator zero where numerator isn't: x²−4=0 → x=±2 → x=2 and x=−2.

Horizontal: equal degrees (2 and 2) → ratio of leading coeffs 3/1 → y=3.

6. Evaluate (a) lim_x→∞ (√(x²+5x) − x) (b) lim_x→−∞ √(x²−8)/(1+2x).

(a) ∞−∞. Conjugate: (x²+5x−x²)/(√(x²+5x)+x) = 5x/(x√(1+5/x)+x) → 5/(1+1) = 5/2.

(b) As x→−∞, √(x²)=|x|=−x. Divide by x: [−x·√(1−8/x²)]/[x(1/x + 2)] → (−1·1)/(0+2) = −1/2. (sign flip because x is negative — the classic trap)

Set 4 · Continuity — find the constants ★

7. Find m so that f(x) = { x/sin(mx), x≠0 ; 3, x=0 } is continuous at 0.

Need lim_x→0 x/sin(mx) = f(0)=3. Write x/sin(mx) = (1/m)·[mx/sin(mx)] → (1/m)·1 = 1/m.

So 1/m = 3 → m = 1/3.

8. Find a, b so that f(x) = { ax+1, x≤2 ; x²−b, x>2 } is both continuous and differentiable at x=2.

Differentiable ⟹ slopes match: left slope a, right slope 2x|₂=4 → a = 4.

Continuous ⟹ pieces meet: a(2)+1 = 2²−b → 8+1 = 4−b → b = 4−9 = −5.

Check: left 4x+1 and right x²+5 both give 9 at x=2, slopes both 4. ✔

Set 5 · Product / quotient / chain

9. Differentiate (a) y=(2+√x+x)(x³−3x+1) (b) F(x)=cos³(sin x) (c) y=sin¹⁰(2x+1).

(a) Product rule (fg)′=f′g+fg′ with f′ = 1/(2√x)+1: y′ = (1/(2√x)+1)(x³−3x+1) + (2+√x+x)(3x²−3).

(b) Chain, 3 layers (outer cube · cos · inner sin): F′ = 3cos²(sin x)·(−sin(sin x))·cos x.

(c) y=[sin(2x+1)]¹⁰ → y′ = 10 sin⁹(2x+1)·cos(2x+1)·2.

10. Differentiate y = (2 + x√x)/(x³+1).

Quotient rule (f/g)′=(g f′ − f g′)/g², with f = 2 + x^{3/2}, f′ = (3/2)x^{1/2}, g = x³+1, g′=3x²:

y′ = [ (x³+1)(3/2)√x − (2+x√x)(3x²) ] / (x³+1)².

Set 6 · Implicit differentiation ★

11. For x³ + y³ = 6xy (the folium), find dy/dx.

Differentiate (product rule on 6xy): 3x² + 3y²y′ = 6y + 6xy′.

Collect y′: y′(3y² − 6x) = 6y − 3x² → dy/dx = (6y−3x²)/(3y²−6x) = (2y−x²)/(y²−2x).

12. For y² = x³ + 3x²: find the slope at (1, 2) and the tangent line.

2y·y′ = 3x² + 6x → y′ = (3x²+6x)/(2y). At (1,2): (3+6)/(4) = 9/4.

Tangent: y − 2 = (9/4)(x − 1) → y = (9/4)x − 1/4.

13. For x² + y² = 2, find the second derivative d²y/dx².

First: 2x+2yy′=0 → y′=−x/y. Differentiate y′=−x/y with the quotient rule (remember y′=−x/y):

y″ = −[ y·1 − x·y′ ]/y² = −[ y − x(−x/y) ]/y² = −(y²+x²)/y³. Since x²+y²=2: y″ = −2/y³.

Set 7 · Logarithmic differentiation ★

14. Differentiate y = x^{\,sin x}.

Take ln: ln y = sin x · ln x. Differentiate (product rule on the right):

(1/y)y′ = cos x·ln x + sin x·(1/x) → y′ = x^{sin x}( cos x·ln x + sin x / x ).

15. With a,b,c,d constants, differentiate f(x) = (x−2)ᵃ(x−3)ᵇ / [ (x+4)ᶜ(x+5)ᵈ ].

Take ln and split with log laws: ln f = a·ln(x−2)+b·ln(x−3)−c·ln(x+4)−d·ln(x+5).

Differentiate: f′/f = a/(x−2)+b/(x−3)−c/(x+4)−d/(x+5), so

f′ = f·[ a/(x−2)+b/(x−3)−c/(x+4)−d/(x+5) ] (a nightmare with the quotient rule, trivial with logs).

Set 8 · L'Hôpital — every form

16. lim_x→0 (eˣ − 1 − x)/x²

0/0 → (eˣ−1)/(2x) still 0/0 → eˣ/2 → 1/2 = 1/2 (applied twice).

17. lim_x→0⁺ x·ln x (form 0·∞)

Rewrite as a fraction: ln x/(1/x) (form −∞/∞) → L'Hôpital (1/x)/(−1/x²) = −x → 0 = 0.

18. lim_x→∞ (1 + 3/x)ˣ (form 1^∞)

Let y=(1+3/x)ˣ, so ln y = x·ln(1+3/x). Sub t=1/x→0⁺: ln(1+3t)/t (0/0) → 3/(1+3t) → 3.

So lim ln y = 3 ⟹ answer e³.

19. lim_x→0 ( 1/x − 1/sin x ) (form ∞−∞)

Common denominator: (sin x − x)/(x sin x) (0/0). L'Hôpital: (cos x − 1)/(sin x + x cos x) (still 0/0).

Again: (−sin x)/(2cos x − x sin x) → 0/2 = 0.

Set 9 · Linear approximation & error

20. Use linearization to approximate (a) √50 (b) (8.06)^{1/3}.

(a) f=√x, a=49: f(49)=7, f′(49)=1/(2·7)=1/14. √50 ≈ 7 + (1/14)(1) ≈ 7.0714.

(b) f=x^{1/3}, a=8: f(8)=2, f′(8)=(1/3)·8^{−2/3}=1/12. (8.06)^{1/3} ≈ 2 + (1/12)(0.06) = 2.005.

21. A circle's radius is measured as 10 cm ± 0.1. Use differentials to estimate the maximum error in its area.

A=πr², dA = 2πr·dr = 2π(10)(0.1) = 2π ≈ 6.28 cm². Relative error dA/A = 2πr dr/(πr²) = 2dr/r = 0.02 = 2%.

Set 10 · Abstract chain rule (the signature hard one) ★

22. Let h(x) = f(sin(2x) + f(2x)) where f(0)=0 and f′(0)=2. Find h′(0) and the tangent line to y=h(x) at x=0.

Chain rule — outer f′ at the inside, times the derivative of the inside:

h′(x) = f′( sin 2x + f(2x) ) · ( 2cos 2x + 2f′(2x) ).

At x=0: inside = sin 0 + f(0) = 0, so the outer factor is f′(0)=2. Bracket = 2cos0 + 2f′(0) = 2 + 4 = 6.

h′(0) = 2·6 = 12. And h(0)=f(sin0+f(0))=f(0)=0, so the tangent line is y = 12x.

On the real exam they push this further to h″(0) — same idea, differentiate h′ again with the product + chain rule and plug in the given f″(0).

Set 11 · Exponential & logarithmic equations + growth

Toolkit Same base ⟹ equate exponents. Hidden quadratic ⟹ let u=eˣ (or 5ˣ). Log rules: ln A + ln B = ln(AB), ln A − ln B = ln(A/B). Continuous growth: A=A₀e^{kt}; rate A′=kA; doubling time t=ln2/k.

23. Solve 2^{x+1} + 2^x + 2^{x−1} = 56.

Factor out 2^{x−1}: 2^{x−1}(4 + 2 + 1) = 56 → 7·2^{x−1} = 56 → 2^{x−1} = 8 = 2³.

So x−1 = 3 → x = 4.

24. Solve e^{2x} − 7eˣ + 12 = 0.

Let u=eˣ: u²−7u+12=0 → (u−3)(u−4)=0 → u=3, 4.

So eˣ=3 or eˣ=4 → x = ln 3 or x = ln 4.

25. An investment grows as A = 10000·e^{0.05t}. Find the time to double. Also, for N(t)=200e^{0.3t} find the growth rate at t=4.

Double: e^{0.05t}=2 → 0.05t = ln 2 → t = ln2/0.05 ≈ 13.86 years.

Rate: N′(t)=200·0.3·e^{0.3t}=60e^{0.3t}. At t=4: 60e^{1.2} ≈ 60(3.320) ≈ 199.3 per unit time.

❓

Quiz Yourself — Calculus

Quick concept checks. Tap to reveal correct/incorrect + the reason.

Score: 0 / 0

1. lim_x→0 sin(x)/x = ?

One of the two must-know trig limits: sin(x)/x → 1 as x→0. (The other: (1−cos x)/x → 0.)

2. A two-sided limit lim_x→af(x) exists only if…

Left limit = right limit (both finite). f(a) itself is irrelevant to whether the limit exists.

3. When lim f/g gives the form 0/0, L'Hôpital's rule says it equals…

Differentiate top and bottom separately: lim f/g = lim f′/g′. Only valid for 0/0 or ∞/∞.

4. For f to be continuous at x=a, we need f(a) defined, the limit to exist, and…

All three: defined, limit exists, and they're equal. (Differentiable ⟹ continuous, but continuous does NOT ⟹ differentiable — think |x| at 0.)

5. The horizontal asymptote of f(x)=(3x²+1)/(x²−4) is…

Equal degrees (2 and 2) → H.A. = ratio of leading coefficients = 3/1 = 3. (x = ±2 are the vertical asymptotes.)

6. d/dx (xˣ) = ?

Variable base and exponent → logarithmic differentiation: ln y = x ln x → y′/y = ln x + 1 → y′ = xˣ(1+ln x).

7. Using implicit differentiation on x² + y² = 2, dy/dx = ?

2x + 2y·y′ = 0 → y′ = −x/y. Every y picks up a ·y′ from the chain rule.

8. The linearization of f at a is L(x) = ?

It's just the tangent line at a: L(x) = f(a) + f′(a)(x−a), used to approximate f(x) ≈ L(x) near a.

9. lim_x→∞ (1 + 3/x)ˣ = ?

Form 1^∞. Take ln: x·ln(1+3/x) → 3, so the limit is e³. (General: (1+a/x)ˣ → eᵃ.)

Score: 0 / 0

Formulas & Midterm Checklist

Must-know limits

lim_x→0 sin(x)/x = 1
lim_x→0 (1−cos x)/x = 0
Rational at ∞: compare degrees
0/0 → factor or rationalize

Derivative rules

Power · Product · Quotient · Chain
Trig: (sin)′=cos, (tan)′=sec²…
(eˣ)′=eˣ, (ln x)′=1/x

L'Hôpital

0/0 or ∞/∞ → f′/g′
others → reshape (0·∞, ∞−∞)
powers → ln then e^L

Linearization

L(x)=f(a)+f′(a)(x−a)
dy=f′(x)dx

Midterm checklist — can you do each? ☐ Evaluate one/two-sided limits & say if DNE ☐ 0/0 by factoring/rationalizing ☐ trig limits ☐ find vertical & horizontal asymptotes ☐ find constants that make f continuous ☐ product/quotient/chain derivatives ☐ implicit dy/dx + tangent line ☐ logarithmic differentiation (xˣ) ☐ L'Hôpital incl. 1^∞/0⁰ ☐ linear approximation.

Academic English for Economists · Midterm

Econ English — everything on the midterm, in one place

Tailored to your MT Vocabulary Review and exam overview. The vocabulary below is the exact list that's coming up — learn these cold.

Midterm structure — 40 points I · Vocabulary (10) — 10 multiple-choice + 10 fill-in-the-blank in 2 paragraphs (word box).
II · Reading (15) — 1 "seen" passage (5 MC) + 1 "unseen" passage (5 MC + 5 fill-in from the text).
III · Grammar (5) — Present Continuous (pp.10–12) & Present Perfect (pp.31–32).
IV · Academic Writing (5) — rewrite an informal paragraph in formal style (pp.33–38).
V · Author's Purpose (5) — label 5 paragraphs: inform / persuade / entertain (p.23).

★

Vocabulary — the exact midterm list

From the official MT Vocabulary Review (Units 1–2). Meaning + how it's used in economics + an example. Watch the word-family forms — the exam tests those too.

How it's tested10 multiple-choice + 10 fill-in-the-blank (words given in a box, used inside 2 paragraphs). So you need the meaning and which form (noun/verb/adjective) fits the sentence.

Word (part of speech)	Meaning	Economics example
Aggregate (adj/n)	total; combined sum of all parts	"Aggregate demand is total spending in the economy."
Asset (n)	something valuable that you own	"A house and shares are assets."
Collateral (n)	property pledged to secure a loan (the lender can seize it if you default)	"She put up her car as collateral."
Contraction (n)	a period when the economy shrinks / output falls (opposite of expansion)	"During a contraction, GDP declines."
Deficit (n)	a shortfall — spending exceeds income	"The budget deficit widened."
Deflation (n)	a general fall in prices (opposite of inflation)	"Deflation can make people delay purchases."
Entertain (v)	to amuse; (also: to consider an idea)	"A column written to entertain readers." (see Author's Purpose)
Emotional (adj)	based on feelings, not facts	"An emotional appeal rather than data."
Empirical (adj)	based on observation/data, not just theory	"Empirical evidence supports the model."
Exorbitant (adj)	unreasonably high (price/cost)	"Exorbitant interest rates."
Expansion (n)	a period when the economy grows	"An economic expansion creates jobs."
Forecast (n/v)	a prediction of future events	"The forecast is for 3% growth."
Fragile (adj) → fragility (n)	weak, easily damaged, unstable	"A fragile recovery."
Indebted (adj)	owing money; in debt	"Heavily indebted households."
Indicator (n)	a measurement showing an economy's state	"Unemployment is a key indicator."
Inflation (n)	a general rise in prices	"High inflation erodes purchasing power."
Inform (v) → informative	to give facts/information	"The report aims to inform." (Author's Purpose)
Informal (adj)	casual, relaxed (not formal)	"Informal writing uses contractions."
Intervene (v) → intervention (n)	to step in to change an outcome	"The central bank intervened to support the currency."
Mandate (n/v)	official authority or order to do something	"Price stability is the bank's mandate."
Measure (n/v)	a step/action taken; also to assess a size	"The government took measures to curb inflation."
Obligation (n)	a duty; something you must do	"A debt obligation."
Obtain (v)	to get / acquire	"Obtain a loan / a licence."
Prospect (n)	the likelihood/expectation of a future outcome	"Prospects for growth improved."
Prosperity (n) → prosper (v)	the state of being wealthy/successful	"A decade of prosperity."
Prudent (adj) → prudence (n)	careful, sensible, wise (esp. with money)	"Prudent fiscal management."
Recovery (n)	return to growth after a downturn	"An economic recovery followed the recession."
Severe (adj)	very serious or harsh	"A severe recession."
Stagnation (n)	little or no growth/activity	"Years of economic stagnation."
Stellar (adj)	outstanding, excellent	"Stellar quarterly results."
Stimulate (v) → stimulus (n)	to encourage growth/activity	"Rate cuts stimulate spending."
Systematic (adj)	done to a plan; methodical, organized	"A systematic approach to reform."
Temptation (n)	a strong urge to do something (often unwise)	"The temptation to overspend."
Unanimous (adj)	agreed by everyone	"A unanimous vote by the committee."

Fast pairs to not confuse Inflation ↔ Deflation (prices up ↔ down) · Expansion ↔ Contraction (economy grows ↔ shrinks) · Stagnation (flat) vs Recovery (bouncing back) · Prospect (future outlook) vs Prosperity (being wealthy) · Empirical (data-based) vs Emotional (feeling-based).

III

Grammar — Verb Tenses (5 pts)

Two sentences to write + 6 multiple-choice. Only two tenses are tested.

Present Continuous (pp.10–12)

am / is / are + verb-ing

Use it for: actions happening now or around now, temporary situations, and current trends (very common in economics).

Signal words now, right now, at the moment, currently, these days, today.

"The Prime Minister is sleeping right now."
"Prices are rising at the moment."
"Unemployment is falling this year."

Watch out Stative verbs (know, want, believe, own) normally aren't used in the continuous.

Present Perfect (pp.31–32)

have / has + past participle

Use it for: a past action with a present result/relevance, or something that started in the past and continues now (with since / for).

Signal words since, for, already, yet, ever, never, just, recently, so far.

"The war has caused prices to rise since March."
"GDP has grown for three years."
"The bank has already cut rates."

since vs for since + a point in time (since March, since 2020). for + a duration (for 3 years, for a decade).

Exam tip — how to choose Ask: is it happening right now / a current trend? → Present Continuous. Did it start in the past and still matter now (esp. with since/for)? → Present Perfect. The prompt words (now vs since) are your biggest clue.

Author's Purpose (5 pts, p.23)

Label 5 short paragraphs: is the writer trying to inform, persuade, or entertain?

INFORMGives facts neutrally — explains, teaches, reports. Objective tone, data, definitions. "The CPI rose 2% in June."

PERSUADETries to convince you of an opinion or push an action. Look for opinion words, "should/must", emotive or loaded language, one-sided arguments. "The government must act now."

ENTERTAINAims to amuse or engage — stories, humour, vivid or playful language, personal anecdotes. "My wallet wept as I opened the electricity bill."

Decide by asking Facts only? → inform. Opinion + wants you to agree/act? → persuade. Fun / story / makes you smile? → entertain.

Academic Writing — Formal Style (5 pts, pp.33–38)

You'll rewrite an informal paragraph in formal academic English. Apply these rules.

The rewrite rules

No contractions: don't → do not, it's → it is, can't → cannot.
Replace phrasal verbs with single formal verbs: find out → discover, go up → increase, put off → postpone, cut down → reduce, look into → investigate.
No slang / vague words: "a lot of" → a significant amount / many, "kids" → children, "stuff" → items, "get" → obtain / receive.
Impersonal & objective: avoid "I think", "you"; use hedging (may, appears to, suggests) and often the passive.
No emotional language / exclamation marks / rhetorical questions.

Informal ✗"Prices have gone up a lot and it's really bad. I think the government should do something about it ASAP!"

Formal ✓"Prices have increased significantly, which appears to have had a negative effect. It may be advisable for the government to intervene promptly."

Reading Strategy (15 pts)

"Seen" passage (from the textbook)

Re-read the Unit 1–4 passages before the exam so the 5 MC questions are easy recall. Know the main idea and key facts of each.

"Unseen" (new) passage

Skim first for the main idea, then scan for details the questions ask about. For fill-in-the-blank, the answers are exact words or figures from the passage — copy them precisely.

Vocabulary in contextDon't panic at an unknown word — use the surrounding sentence (and the vocab list above) to infer meaning.

❓

Quiz Yourself — Econ English

Vocabulary, tenses, purpose & formal style — the four things the midterm tests. Tap to check.

Score: 0 / 0

1. Deflation means…

Deflation = prices fall (opposite of inflation). Don't confuse with contraction (economy shrinks).

2. Choose the best formal replacement for the informal phrasal verb “find out”.

Formal academic writing prefers single verbs over phrasal verbs: find out → discover, go up → increase, put off → postpone.

3. “Prices ______ rapidly at the moment.” Which tense fits?

“at the moment” signals a current trend → present continuous (am/is/are + -ing).

4. “The war ______ prices to rise since March.” Which tense?

“since March” = started in the past, still relevant now → present perfect (have/has + past participle). since + a point in time.

5. A paragraph that gives neutral facts to teach the reader has the purpose to…

Facts, neutral tone, no opinion → inform. Opinion + “should/must” → persuade. Humour/story → entertain.

6. Collateral is…

Collateral is an asset the lender can seize if you don't repay — e.g. a house or car backing a loan.

7. Prudent most nearly means…

Prudent = wise and cautious (noun: prudence). “Exorbitant” = too expensive; “stellar” = excellent; “unanimous” = agreed by all.

8. The central bank “intervened” in the currency market. To intervene is to…

Intervene = get involved to affect the result (noun: intervention).

Score: 0 / 0

Private · Influence & Persuasion

The psychology of influence — how four classic techniques actually work

Five well-studied mechanisms — the Franklin effect, the funnel technique, the IKEA effect, Ericksonian (indirect) suggestion, and the door-in-the-face — sit behind a huge amount of everyday sales, marketing, management and negotiation. Each is taught as a four-level module (recognise → understand → apply → critique) with the mechanism, the research it rests on, how it shows up in social and corporate settings, how they link together, and — most important — how to recognise and resist it. A wider Concepts library follows.

Influence vs. manipulation — the line Persuasion becomes manipulation when it is covert (you'd object if you saw the technique), exploitative (benefits one side by using your biases against you), and irreversible (engineered so you can't easily back out). The single best test: would this survive disclosure? If the other person would feel used the moment they understood what you did, it was manipulation. Learn these to defend yourself first.

Honesty noteThese effects are real and replicated — but the internet oversells them. "Covert hypnosis can control anyone against their will" is not supported by evidence, and most strong NLP claims have failed empirical tests. Where a claim is shaky, this page says so.

How this course is graded Each technique is taught as a four-level module (Recognise → Understand → Apply → Critique) and carries an evidence grade: A · replicated experiment B · single / contested study C · clinical or field lore Empirical claims are tagged Certain Likely Guessing, and SPOT-CHECK marks a citation to verify against the source. Track your progress on the course path below.

🗺

Course path — recognise → understand → apply → critique

Each technique climbs four levels, hardest last. Mark a level done to track progress (saved in your browser). Click an active cell to jump to it.

L1
Recognise

L2
Understand

L3
Apply

L4
Critique

📈 Franklin

🔻 Funnel

🪑 IKEA

🌀 Ericksonian

🚪 Door-in-Face

0 of 16 levels complete

How to work through itAll four techniques are fully leveled. Read a technique top-to-bottom (L1→L4), or take one level across all four before moving up. Mark each level complete to fill the bar — it's saved in your browser. Evidence claims carry Certain/Likely/Guessing tags, and SPOT-CHECK flags citations to verify against the paper.

The Ben Franklin Effect

Grade B

"He that has once done you a kindness will be more ready to do you another than he whom you yourself have obliged."

L1 · Recognise

What it is, and how to spot it

The effect: do someone a small favour and — counter-intuitively — they tend to like you more afterwards. We assume we help people we already like; here the liking runs the other way, following the help.

The origin: in his autobiography, Franklin defused a hostile rival legislator by asking to borrow a rare book from his library. Having done Franklin the favour, the man became a lifelong ally.

Spot it in the wildWatch for a small favour or "can you help me with…" that arrives just before warmth or a bigger request. The favour flows toward the asker, but it's the helper whose attitude shifts.

The favour flows toward the asker, yet it's the helper whose liking rises.

Source: Franklin, B. (1793). The Autobiography of Benjamin Franklin. — historical anecdote, the origin of the name, not itself evidence.

L2 · Understand

Why it works — and when it doesn't

The helper's mind holds two clashing thoughts: "I went out of my way for them" and "I don't especially like them." That clash is cognitive dissonance, and the cheapest way to resolve it is to revise the attitude: "I helped them → I must like them." By self-perception, we read our own behaviour to infer our feelings.

Parent principle: consistency — attitudes bend to line up with freely-chosen actions. Likely

Boundary conditions — it only fires when…

The favour feels freely chosen. Coerce it ("you had to") and there's no dissonance to resolve, so no attitude shift.
It's modest. Too large and the mind resolves the other way — resentment, not liking.
It isn't transparently instrumental. If the favour obviously sets up a sale, the helper concludes "I was used."

Sources: Festinger, L. (1957). A Theory of Cognitive Dissonance. Stanford Univ. Press. Certain · Bem, D. J. (1967). "Self-perception: An alternative interpretation of cognitive dissonance phenomena." Psychological Review, 74(3), 183–200. Certain

L3 · Apply

Use it — script, drill, guardrails

The move: ask for a small, genuine favour or piece of advice — then credit it sincerely. "Ask for advice, not approval."

"Can I borrow your read on something for two minutes? You know this space better than I do."

"Honestly, that helped more than the last three articles I read on it."

"Mind if I come back to you once I've tried it?"

Micro-favour → sincere, specific credit → permission for a next contact. No flattery, no ask attached.

Drill — 10 min, pass/failAsk one real person today for a small, genuine piece of advice in their domain, take it visibly, and thank them specifically. Pass = they volunteer a follow-up unprompted ("let me know how it goes" / offer more help) in the same conversation. Fail = they answer and disengage.

Ethical guardrailsThe favour must be real — you actually want and use the advice. A fake ask is a pretext, and it fails the disclosure test: would they feel used if they saw the technique? If yes, don't.

L4 · Critique & Master

Evidence limits, defense, and how it stacks

How solid is it? Grade B. The named "Ben Franklin effect" rests largely on one old, small study, with thin direct replication. It is best understood not as a standalone law but as a special case of the well-replicated dissonance / effort-justification family — which is Grade A. The catchy name is pop-psych packaging over Festinger and Bem.

Strongest objectionStrip the anecdote and you may just be seeing effort justification: people value what they worked for. "Favour → liking" might add nothing the parent theory doesn't already predict. Likely

How it stacksA favour is the first micro-commitment → it primes the Funnel (§2). Completed effort on your behalf is a cousin of the IKEA effect (§3). The unifying meta-principle across all four techniques is self-perception / consistency.

🛡 Adversarial defenseWhen a small favour precedes a bigger ask, decouple the two: "I helped them" does not mean "I trust this proposal." Judge the ask on its own merits, as if the favour never happened.

Source to verify: Jecker, J. & Landy, D. (1969). "Liking a person as a function of doing him a favour." Human Relations, 22(4), 371–378. SPOT-CHECK — confirm the citation and sample details against the paper; direct replications are sparse. Likely

The Funnel Technique

Grade Asales-script version: B

Start broad and easy; narrow to the commitment. Every small "yes" makes the next one cheaper.

L1 · Recognise

What it is, and how to spot it

A funnel is a sequenced escalation — you move from a trivial, easy agreement toward the real ask, one small step at a time. It wears two shapes:

Funnel questioning (sales discovery, interviews, UX research): open, broad questions first to build rapport and context, then closed, specific ones that pin down a decision.
Commitment funnel (foot-in-the-door): secure a trivial agreement, then escalate — each "yes" lowers resistance to the next.

Spot it in the wildWatch for a run of easy, agreeable questions or asks before the one that matters. If you've said "yes" three times before the real request lands, you're in a funnel.

Resistance drops band by band. By the real ask, refusing means breaking a chain of your own agreements.

Origin: the experimental version is the foot-in-the-door effect — Freedman & Fraser (1966): agreeing to a tiny request tripled later compliance with a large one.

L2 · Understand

Why it works — and when it doesn't

Once you've said yes, saying no next feels like contradicting yourself. Each agreement nudges your self-image ("I'm the kind of person who says yes to this"), and the next refusal would clash with it. That's commitment & consistency: we act consistently with what we've already said and done, so a "yes-set" builds behavioural momentum.

Parent principle: consistency (Cialdini), powered by self-perception.

Boundary conditions — it only fires when…

The first ask is the right size: big enough to shift self-image, small enough to get an easy yes. Too trivial → no self-perception change; too heavy → reactance.
No external incentive: if you paid for or pressured the first yes, the person attributes it to the reward, not to themselves — no consistency forms.
Similar requester / short delay help; a stranger weeks later gets far less carry-over.

Sources: Freedman, J. L. & Fraser, S. C. (1966). "Compliance without pressure: the foot-in-the-door technique." J. Personality & Social Psychology, 4(2), 195–202. SPOT-CHECK · Burger, J. M. (1999). "The foot-in-the-door compliance procedure: a multiple-process analysis and review." Personality & Social Psychology Review, 3(4), 303–325. SPOT-CHECK — meta-analysis, small-but-reliable effect. Likely

L3 · Apply

Use it — script, drill, guardrails

The move: two easy trues, then one small concrete ask that carries its own bind. Never open with the big request.

"Quick one — is saving your team a few hours a week something you'd even want right now?"

"And if a tool did that without a migration headache, worth a look?"

"Then the honest next step is fifteen minutes where I show you the two features that matter — Thursday or Friday?"

Two agreements, then a small ask with a built-in choice (Thu/Fri) — not "yes or no".

Drill — 10 min, pass/failThe four-yes ladder. Write four true, small pacing statements in advance, deliver them naturally, then one real lead. Pass = four agreements (nod / "yeah/right/mm") AND movement on the lead. Fail = any pacer draws a correction, or no action on the lead.

Corporate variantsSPIN (Situation → Problem → Implication → Need-payoff), the AIDA marketing funnel (Attention → Interest → Desire → Action), growth funnels (free → email → trial → paid). Each is the same escalation with different labels.

Ethical guardrailsThe small yeses must be honest questions, not manufactured traps, and the final ask must be one they'd accept on its own merits. If the funnel is the only reason they said yes, it fails the disclosure test.

L4 · Critique & Master

Evidence limits + advanced stacking

How solid is it? Grade A at its experimental core (foot-in-the-door is replicated and meta-analysed), but modest — effect sizes are small, and the sales "funnel questioning" packaging is B/C lore, not the experiment. It's a rebranding of commitment & consistency.

Strongest objectionMuch of what looks like a working funnel is actually attrition, not persuasion — a marketing funnel "converts 2%" by filtering out the 98%, which tells you nothing about whether the steps changed anyone's mind. Don't confuse a filter with influence. Likely

Advanced application — stack itThe funnel is the spine the other three hang on:

Open with a Franklin micro-favour (§1) — the favour is the first "yes".
Make one rung an effort step (sketch it together) so the IKEA effect (§3) inflates their ownership mid-ladder.
Deliver the rungs as an Ericksonian yes-set (§4) and close on a double bind ("Thursday or Friday?") — a funnel with the exit removed.

Contradicts: door-in-the-face (large ask first, concede down) — don't run both at once, they pull opposite directions.

🛡 DefenseOnly the last decision has real stakes. Decide it fresh, as if the earlier yeses never happened: "I agreed to those, but this one I'll judge on its own."

The IKEA Effect

Grade A

Labour leads to love: we over-value what we partly built ourselves.

L1 · Recognise

What it is, and how to spot it

The effect: people assign disproportionately high value to things they partially made — the self-assembled IKEA cabinet, the folded origami, the Lego set — compared with identical items they didn't build.

Spot it in the wildWatch for invitations to invest effort: "build your own", "customise it", "let's map this out together". The moment your hands are on it, your valuation starts to rise.

Self-made effort becomes felt ownership, and ownership inflates the value you place on the result above its market price.

Origin of the name: Norton, Mochon & Ariely (2012) — people paid ~63% more for IKEA boxes they assembled than identical pre-built ones, and rated their own origami nearly as highly as an expert's.

L2 · Understand

Why it works — and when it doesn't

Two well-established forces stack. Effort justification: "I worked on it, so it must be worth it" (the mind refuses to have wasted the effort). Ownership / endowment: we value what feels like ours more than the same thing owned by someone else — and building it makes it feel intensely ours. Add a quiet competence signal ("I made this, so I'm capable").

Parent principle: effort justification (with the endowment effect amplifying it).

Boundary condition — the one that mattersThe premium only appears when the build succeeds. Abandon it half-finished and the effect vanishes; a build that fails can flip negative — the frustration attaches to the object (and to whoever set the task).

Sources: Norton, M. I., Mochon, D. & Ariely, D. (2012). "The IKEA effect: when labor leads to love." J. Consumer Psychology, 22(3), 453–460. SPOT-CHECK · parents: Aronson & Mills (1959), effort justification Certain; Kahneman, Knetsch & Thaler (1990), endowment effect Certain.

L3 · Apply

Use it — script, drill, guardrails

The move: hand over the pen. Get the other person's fingerprints on the artifact — that's the whole point.

"Before I send a proposal, let's build the rough plan together on the whiteboard — you drive."

"Put your must-haves top-left; I'll only push where I think you're leaving value on the table."

"This is your plan now — I just typed it up."

Their contribution has to be real and visible, not a token gesture.

Drill — 10 min, pass/failCo-authorship test. In one real decision today, get the other person to physically add ≥2 elements to the plan (write on the doc, move a sticky, name a section). Pass = they later call it "ours/mine" or defend a part they added. Fail = they keep calling it yours.

Corporate variantsConfigurators ("build your own" cars, PCs, meal kits); management buy-in ("people support what they help build"); onboarding that makes users customise early → higher retention.

Ethical guardrailsThe effort must produce something they genuinely want and can use. Manufacturing busywork to fake ownership is a manipulation, and it backfires the moment it's noticed (see L2's negative-flip).

L4 · Critique & Master

Evidence limits + advanced stacking

How solid is it? Grade A — multiple experiments, replicated, resting on two A-grade parents.

Strongest objectionIt may be nothing new: endowment + effort justification already predict the whole result, so "IKEA effect" is a memorable label, not a distinct mechanism. Useful as a name, not as a discovery. Likely

Advanced application — stack itIKEA is the lock-in stage of a sequence:

A funnel (§2) rung asks them to do a small piece of the work — that step is both a "yes" and an investment.
The IKEA effect then inflates their ownership of the output.
Consistency makes them defend it afterwards, and a completed build is a big Franklin-style self-investment (§1) that warms them to you.

Contradicts: full-service "we'll handle everything" positioning — doing all the work removes the ownership lever.

🛡 Defense (works on you too)Separate the value of your labour from the market value of the thing: "If a stranger built this, what would I pay?" It's a close cousin of the sunk-cost trap — the effort you already spent is not a reason to keep going.

Ericksonian (Indirect) Suggestion

Grade Cunfalsifiable as sold

Milton Erickson's permissive, conversational style — match the person's reality first, then lead.

L1 · Recognise

What it is, and how to spot it

Grade C — field/clinical lore. Milton H. Erickson (1901–1980), a psychiatrist, rejected the authoritarian "you are getting sleepy" style for an indirect, permissive one that uses the person's own language and experience. The pop-culture "covert hypnosis" repackages his devices (the "Milton model") for sales and copywriting.

Core devices — spot these

Pacing & leading: state what's undeniably true now (pace) to build a "yes" rhythm, then append the suggestion (lead).
Presupposition: a claim smuggled in as a given — "When you start noticing improvements…" (assumes you will).
Double bind: two options that both lead where the speaker wants — "begin now, or after a coffee?"
Embedded command / artful vagueness: a directive nested in a sentence; language so unspecific the listener fills it in.

While the lines run together (pacing), trust builds; at the switch point the guide leads and the paced subject tends to follow.

L2 · Understand

Why it (sometimes) works — and the honest caveat

Strip away the mystique and the working parts are ordinary: consistency (each paced "yes" is a micro-commitment), response expectancy (people behave as they're led to expect they will), reduced scrutiny (agreeable vagueness gives nothing to argue against), and rapport → reciprocity. No altered state of consciousness is required.

Parent principle: consistency, riding on expectancy. Likely

Honesty note — real vs. hypeClinical hypnosis is a genuine, studied phenomenon (pain, anxiety), but it's trait-dependent and consent/context-bound. "Covert conversational hypnosis that controls people without consent" is not established science, and NLP's specific claims have largely failed controlled testing. Treat pacing/leading as rapport and framing, not mind control.

Sources: Sharpley, C. F. (1987), review of NLP SPOT-CHECK; Witkowski, T. (2010), review of NLP research base SPOT-CHECK — both find core claims unsupported. Kirsch, I. — response expectancy. Barnier & Oakley — hypnotic suggestibility as a trait. Certain that these critiques exist; Likely on exact scope.

L3 · Apply

Use it — script, drill, and a hard ethics ceiling

The move: three statements that are undeniably true (pace), then one suggestion (lead), with a soft choice that isn't really a choice.

"You're sitting here, you've read a bit about what I do, and part of you is still deciding whether this is worth your time — which is fair."

"Most people I talk to feel exactly that mix, curious and a little skeptical, and it's usually the skeptical part that ends up making this work for them."

"So you don't have to commit to anything right now — just notice, while we talk, which bits land and which don't."

"And when one lands, you'll feel it settle a bit — that's normally the point people realise they've already started."

Three trues (pace) → one presupposition ("already started"), with a soft bind ("which bits land and which don't").

Drill — 10 min, pass/failYes-Set Ladder. Write four statements undeniably true about the person's present state/context, deliver them spaced naturally, then one small lead. Pass = four agreements AND movement on the lead. Fail = any pacer draws a "no"/correction, or no action.

Ethics ceiling — this is the manipulation-adjacent oneOf the four, this sits closest to the line. Keep it clean: the pacing must be genuine rapport, the presuppositions must be things you'd state openly, and the "no" must stay genuinely available. If you'd hide the technique from the person, you've crossed into manipulation — don't.

L4 · Critique & Master

Evidence limits + advanced stacking

How solid is it? Grade C — the mechanism as sold is unfalsifiable. It's a rebranding of NLP's "Milton model," which abstracted patterns from Erickson's clinical work; the levers underneath are Cialdini consistency plus classic expectancy research.

Strongest objectionEverything that reliably works is already explained by compliance and response-expectancy — so "hypnosis" adds no falsifiable content. Worse: calling it hypnosis makes you worse at it, because you stop tracking the boring variables (rapport, timing, whether the person actually agreed) that predict a yes. Likely

Advanced application — it's the delivery layer of the stackEricksonian language is how you deliver the other three in conversation:

Pacing = the funnel's yes-set (§2) in spoken form.
The double bind = a two-band funnel with the exit removed.
Rapport = Franklin/reciprocity warmth (§1); an effort invitation delivered this way = IKEA (§3).

So a full sequence — favour → yes-set → co-build → framed close — is spoken in this register. That is also exactly why the ethics ceiling in L3 matters most here.

🛡 DefenseMake the implicit explicit. Hearing "now or after coffee?", say: "Those aren't my only two options — I might not start at all." Name presuppositions out loud, surface the hidden third choice, and slow the pace — indirect suggestion runs on momentum.

The Door-in-the-Face

Grade A

Ask for the moon, get refused, then ask for what you actually wanted — which now looks reasonable.

L1 · Recognise

What it is, and how to spot it

The technique: make a large request you expect to be refused, and when it is, immediately follow with the smaller request you wanted all along. The retreat from big to small makes the second ask feel like a concession — and the other person concedes back by saying yes. It is the mirror image of the Funnel: that one climbs up from small; this one steps down from big.

Spot it in the wildWatch for an opening ask that seems too big, a quick "no", and then a softened second ask that arrives before you've moved on. The first request was never the real one — it was the anchor.

Against the rejected large ask, the real request looks small — and your visible "retreat" pulls a matching concession: yes.

Origin: Cialdini et al. (1975) — students asked to mentor delinquents for two years (almost all refused) then asked for a single afternoon trip agreed at ~3× the rate of those asked only the small request.

L2 · Understand

Why it works — and when it doesn't

Three forces run together. Reciprocal concession: you visibly gave ground (big → small), so the norm of reciprocity presses the other person to give ground too — by accepting. Perceptual contrast: after the large ask, the small one looks smaller than it is. Self-presentation / guilt: refusing twice would make them feel unhelpful, so the second yes repairs their self-image.

Parent principle: reciprocity (of concessions), with contrast and guilt riding along.

Boundary conditions — it only fires when…

Same requester makes both asks. If a different person makes the second ask, there's no concession to reciprocate — the effect collapses.
No delay. The second ask must follow immediately; a gap lets the obligation fade.
The first ask is large but not absurd. An outrageous opener reads as manipulative or insincere and kills goodwill.
A prosocial or legitimate cause strengthens it; a purely self-serving retreat weakens it.

Sources: Cialdini, R. B. et al. (1975). "Reciprocal concessions procedure for inducing compliance: the door-in-the-face technique." J. Personality & Social Psychology, 31(2), 206–215. SPOT-CHECK · meta-analysed by O'Keefe & Hale (1998), confirming a small-to-moderate reliable effect. Likely

L3 · Apply

Use it — script, drill, guardrails

The move: lead with a bigger, genuine version of the ask; when it's declined, retreat—visibly—to the real one.

"Would you be open to owning the whole onboarding revamp this quarter?" — (they hesitate / decline)

"Totally fair, that's a lot. Then could you just review the first draft and give me 20 minutes of feedback?"

The big ask must be real (you'd have accepted a yes), the retreat immediate, and the small ask the one you actually wanted.

Drill — 10 min, pass/failThe concession test. In one real ask today, open one notch larger than you need; when it's declined, immediately step down to your true request. Pass = they accept the smaller ask and the whole exchange stays warm. Fail = they accept but feel cornered, or the big ask reads as a stunt.

Corporate variantsNegotiation openers (anchor high, then "concede"); budget/scope asks (request the full team, settle for two hires); fundraising ("monthly donor?… or a one-off £10?").

Ethical guardrailsThe first ask must be one you'd genuinely accept — a fake demand you never wanted is a manufactured concession, and it fails the disclosure test. Keep the opener reasonable enough that a "yes" wouldn't shock you.

L4 · Critique & Master

Evidence limits + advanced stacking

How solid is it? Grade A — Cialdini's original plus a meta-analysis (O'Keefe & Hale, 1998) confirm a reliable but small-to-moderate effect, heavily dependent on the boundary conditions in L2.

Strongest objectionThe effect is fragile: break same-requester or no-delay and it vanishes, and an over-large opener can backfire into distrust. It also fades for purely commercial (non-prosocial) asks. Treat it as a situational tool, not a reliable lever. Likely

Advanced application — stack it (carefully)

Never run it with the Funnel (§2) in the same breath — foot-in-the-door climbs up from small, door-in-the-face steps down from big; combined, they read as incoherent and expose the manoeuvre.
It pairs with anchoring (the big ask sets the reference point) and reciprocity/Franklin warmth (§1) — a concession lands softer once rapport exists.
Sequence choice: use DITF when you can open big and retreat once; use the Funnel when you need many small steps. Pick one per interaction.

🛡 DefenseWhen a request suddenly shrinks, notice it: "Am I saying yes to this because it's right, or just because it's smaller than the last thing?" Judge the real ask against zero, not against the rejected opener.

📚

Principles & Concepts — the wider map

A searchable map of the wider canon — rhetoric, strategy, social psychology, judgment, clinical, behaviourism, mentalism, propaganda, ideologies, philosophy and historical trend-frames. Empirical entries carry a grade — A replicated, B single/contested, C lore, MYTH false. Type any name into search to jump to it.

Cialdini's principles of influence from Influence, 1984 / rev. 2021

ReciprocityA — we feel obliged to repay what we're given; concessions count too (→ door-in-the-face).

Commitment & ConsistencyA — we act consistently with prior commitments. Parent of the Funnel (§2).

Social ProofA — under uncertainty we copy similar others ("5,000 sold").

AuthorityA — we defer to credible experts (titles, coats, credentials).

LikingA — we say yes to people we like: similarity, praise, cooperation. Cousin of Franklin (§1).

ScarcityA — rare or dwindling things feel more valuable; loss-framed ("last 2").

UnityB — shared identity ("one of us"); the newest, least-tested principle.

Core cognitive mechanisms

Cognitive dissonanceA — discomfort from clashing beliefs/acts drives attitude change (Festinger, 1957). Parent of Franklin.

Self-perceptionA — we infer our attitudes from our own behaviour (Bem, 1967).

Effort justificationA — we value what we suffered or laboured for (Aronson & Mills, 1959). Parent of IKEA (§3).

Endowment effectA — we over-value what we own (Kahneman, Knetsch & Thaler, 1990).

Loss aversionA — losses hurt roughly twice as much as equal gains (Kahneman & Tversky, 1979); powers scarcity & framing.

AnchoringA — the first number sets the reference point for everything after (pricing, negotiation).

FramingA — identical facts worded as a gain vs a loss flip the decision.

Peak–end ruleA — we judge an experience by its most intense moment and its ending, not its average (Kahneman).

Sequential-request techniques (the compliance family)

Foot-in-the-doorA — small yes → big yes (Freedman & Fraser, 1966). This is the Funnel (§2).

Door-in-the-faceA — an unreasonable ask first, then the real one looks reasonable (Cialdini, 1975). Runs opposite to the funnel.

Low-ballB — secure the commitment, then reveal the true (higher) cost; consistency keeps them in.

That's-not-allB — pile on a bonus before they answer, triggering reciprocity.

Disrupt-then-reframeB — a brief confusion, then a reframe, slips past scrutiny ("300 pennies… that's $3, a bargain").

Social & relational effects

Mere exposureA — repeated exposure to something breeds liking (Zajonc, 1968).

Halo effectA — one positive trait (e.g. attractiveness) bleeds into judgments of unrelated traits.

Pratfall effectB — a small, humanising blunder makes an otherwise competent person more likeable (Aronson).

Reciprocal self-disclosureB — sharing something personal invites the other to share back; builds rapport fast.

Biases persuasion exploits

BandwagonA — we adopt what the crowd adopts (social proof in motion).

Decoy effectA — adding a deliberately inferior third option steers choice between the other two.

Availability heuristicA — vivid or recent examples feel more probable than they are.

Confirmation biasA — we seek and weight evidence that fits what we already believe.

Primacy & recencyA — the first and last items in a sequence carry the most weight.

Authority biasA — a credible source's claim is under-scrutinised (Milgram's wider lesson).

⚠️ Commonly cited — but weak or false

Know these so you can call them out. Selling them is a tell that a "coach" hasn't checked their sources.

Subliminal advertisingFALSE — the 1957 "eat popcorn / drink Coke" study was fabricated by James Vicary; genuine subliminal-priming effects are tiny and unreliable.

"7-38-55" / 93% is body languageMYTH — a misquote of Mehrabian's narrow study on incongruent emotional messages; it is not a general law of communication.

Most of NLPC — "anchoring states", "eye-accessing cues", rep-systems: repeatedly failed controlled testing (Sharpley 1987; Witkowski 2010).

Lie detection by micro-expressionsC — untrained and most trained observers score barely above chance; confident "human lie detectors" are overselling.

Left-digit / "charm pricing" as mind-controlB — $9.99 vs $10 has a real but small effect; the dramatic claims around it are inflated.

Extended reference — the wider canon Broken into searchable entries on purpose: a reference list buried in a paragraph is one you'll never find anything in again. Grade pills (A/B/C/MYTH) mark empirical claims; the humanities domains (rhetoric, strategy, philosophy, ideology, history) are frameworks, not experiments, so they carry a gloss, not a grade. Attributions are solid; evaluative asides are flagged as opinion.

Rhetoric & persuasion

Ethos / Pathos / Logos — Aristotle's three proofs: credibility, emotion, logic.

Enthymeme — a rhetorical syllogism whose missing premise the audience supplies.

Five canons (Cicero) — invention, arrangement, style, memory, delivery.

Quintilian — Roman pedagogy of "the good man speaking well".

Gorgias — sophist on language's near-magical power to move (Encomium of Helen).

Protagoras — "man is the measure"; two sides to every case (dissoi logoi).

Schopenhauer, 38 Ways — eristic: winning the argument regardless of truth. cynical catalogue

Kenneth Burke — identification (become one with the audience) and dramatism.

Perelman, New Rhetoric — argument as winning the adherence of minds; the universal audience.

Toulmin model — claim, grounds, warrant, backing, qualifier, rebuttal.

Topoi (Aristotle) — "places": templates for generating arguments.

Stasis theory — locate the point at issue: fact, definition, quality, procedure.

Ramus — split logic from rhetoric, reducing rhetoric to style/delivery.

Blair & Campbell — 18th-c. belletristic rhetoric of taste and style.

Weaver's "god terms" — culturally charged words that command assent (and "devil terms").

Lakoff — framing and conceptual metaphor; "don't think of an elephant".

Luntz — poll-tested "words that work" ("death tax", "climate change").

Ogilvy & Hopkins — advertising copy: benefits, testing, "scientific advertising".

AIDA — Attention → Interest → Desire → Action.

Message framing — the same appeal as a gain vs a loss changes the response.

Self-persuasion (Aronson)A — arguments you generate yourself persuade you most.

Inoculation theory (McGuire)A — a weak counter-argument first builds resistance to later attack.

Sleeper effectB — a discounted message gains force as its source is forgotten.

Strategy & conflict

Sun Tzu — win without fighting; all warfare is deception.

Sun Bin — later Art of War: terrain, deception, the weak defeating the strong.

Thirty-Six Stratagems — Chinese deception schemes ("besiege Wei to rescue Zhao").

Clausewitz — friction, fog of war, the culminating point, war as politics by other means.

Jomini — geometric lines of operation; the rationalist counter to Clausewitz.

Machiavelli — Prince/Discourses: feared vs loved; virtù and fortuna.

Musashi, Five Rings — rhythm, the void, no fixed method.

Yagyū, Life-Giving Sword — winning by not killing; reading the opponent.

Hagakure — samurai ethic of decisiveness and death-acceptance.

Thucydides / Melian Dialogue — "the strong do what they can"; the Thucydides trap.

Kautilya, Arthashastra — ruthless statecraft, spies, economics. most cynical, least read in the West

Han Feizi (Legalism) — rule by law, incentives and fear; distrust of virtue.

Liddell Hart — the indirect approach: dislocate before you strike.

J.F.C. Fuller — mechanised, deep-operations warfare.

Boyd, OODA loop — observe-orient-decide-act; out-tempo the enemy ("destruction and creation").

Schelling — commitment, credible threats, focal points.

Nash equilibriumA — no player gains by deviating alone.

Prisoner's dilemmaA — individually rational, collectively worse.

Tit-for-tat (Axelrod)A — cooperate first, then mirror; robust in iterated games.

Signalling & cheap talkA — costly signals are credible; costless talk often isn't.

Lanchester laws — attrition math: concentration of force wins.

Manoeuvre vs attrition — dislocate the system vs grind it down.

Mao — protracted war's phases: guerrilla → mobile → positional.

Guevara, foco — a small vanguard sparks the wider revolution.

Galula & Kilcullen — counterinsurgency: the population is the prize.

Luttwak — the paradoxical logic of strategy ("si vis pacem…").

Greene, 48 Laws of Power — entertaining, historically loose; not scholarship

Porter's Five Forces — the market translation: rivalry, entrants, substitutes, buyer/supplier power.

Experimental social psychology (continued)

Asch conformityA — people echo an obviously wrong majority.

Milgram obedienceB — ordinary people shock a stranger on orders real, but the classic account is partly overstated

Stanford Prison (Zimbardo)DISPUTED — the received story is discredited: coaching, demand characteristics.

Robbers Cave (Sherif)B — competition breeds conflict; superordinate goals heal it.

Minimal groups (Tajfel)A — trivial categories alone create in-group bias.

Bystander effect (Latané & Darley)A — more onlookers, less help; diffusion of responsibility.

Placebic "because" (Langer)B — any reason-word lifts compliance ("because I'm in a rush").

Elaboration Likelihood Model (Petty & Cacioppo)A — central (argument) vs peripheral (cue) routes.

Heuristic-Systematic Model (Chaiken)A — shortcut vs effortful processing.

Balance theory (Heider)B — we seek consistent sentiment triangles.

Reactance (Brehm)A — threaten a freedom and people want it more.

Pique techniqueB — an odd request ("spare 37 cents?") disrupts the refusal script.

But-You-Are-Free (BYAF)A — affirming freedom to refuse ~doubles compliance strongest meta-analytic support of the small tricks

Chameleon effectB — unconscious mimicry builds rapport (Chartrand & Bargh).

Spotlight effectA — we overestimate how much others notice us.

Social comparison (Festinger)A — we evaluate ourselves against others.

Replication-crisis casualtiesWEAK — ego depletion, most social priming, power posing, facial-feedback: failed or badly weakened.

Judgment & decision (continued)

Prospect theory (Kahneman & Tversky)A — value is relative to a reference point; losses loom larger.

RepresentativenessA — judging by resemblance, ignoring base rates.

Planning fallacyA — we underestimate our own task times.

Mental accounting (Thaler)A — money is treated differently by mental "bucket".

Nudges / choice architectureA — defaults and layout steer choices (Thaler & Sunstein).

Arbitrary coherence (Ariely)B — a random anchor sets a whole price ladder.

Ecological rationality (Gigerenzer) — heuristics are smart in the right environment; rebuts "biases everywhere".

Bounded rationality / satisficing (Simon) — we settle for good-enough, not optimal.

Superforecasting (Tetlock) — foxes beat hedgehogs; calibrated probabilistic thinking.

Fat tails / narrative fallacy (Taleb) — rare events dominate; stories fool us.

Clinical vs actuarial (Meehl)A — simple formulas beat expert intuition.

Base-rate neglectA — ignoring prior probabilities.

Hindsight biasA — "I knew it all along".

Dunning–KrugerB — real but overstated, partly a statistical artefact

Clinical, hypnotic & therapeutic

Freud — the unconscious, transference, defence mechanisms.

Jung — archetypes, shadow, persona, individuation.

Adler — inferiority complex, striving for superiority.

Erickson — indirect suggestion, utilization, confusion technique, embedded commands. (→ §4)

Rogers — unconditional positive regard, reflective listening.

Beck (CBT) / Ellis (REBT)A — challenge distorted thoughts / irrational beliefs.

Frankl, logotherapy — meaning as the primary drive.

Perls, Gestalt — here-and-now awareness; the empty chair.

Bowlby & AinsworthA — attachment styles.

Motivational interviewing (Miller & Rollnick)A — evoke the person's own change talk most evidence-backed clinical persuasion; competitors ignore it

Satir — family systems, congruent communication.

Watzlawick — paradoxical intervention; "prescribe the symptom".

Bandler & Grinder (NLP)C — Milton model, meta-model, anchoring, rapport-matching potent-sounding, empirically unsupported

Behaviourism & habit

PavlovA — classical conditioning (bell → salivation).

Watson, Little Albert — conditioned fear in an infant ethically notorious

SkinnerA — operant conditioning; reinforcement shapes behaviour.

Variable-ratio schedulesA — unpredictable rewards drive slot machines and feeds.

Thorndike, law of effectA — rewarded behaviour recurs.

Premack principleA — a liked activity reinforces a disliked one.

BanduraA — social learning; self-efficacy; the Bobo doll.

SeligmanA — learned helplessness; later, positive psychology.

Fogg, B=MAP — behaviour = motivation × ability × prompt.

Eyal, Hook model — trigger → action → variable reward → investment.

Duhigg — the cue → routine → reward habit loop.

Clear, Atomic Habits — small habits; identity-based change.

Self-determination theory (Deci & Ryan)A — autonomy, competence, relatedness.

Overjustification effectA — external rewards can kill intrinsic motivation.

Mentalism & stagecraft

Barnum / Forer effectA — vague statements feel personally accurate.

Cold reading — inferring from cues plus high-probability guesses.

Hot reading — using secretly-obtained information.

Corinda, 13 Steps — the field's foundational manual.

Annemann — practical mental effects; the performer's craft.

Banachek — psychological subtleties and PK routines.

Hofzinser, dual reality — two audiences believe different truths.

Equivoque / magician's choice — a "free" choice that forces the outcome.

Derren Brown, Tricks of the Mind — misdirection, suggestion, disclosure ethics.

Ray Hyman's rules — the classic exposé of how cold reading works.

Kuhn — misdirection researchA — the science of attention and misdirection.

Zeigarnik effectB — unfinished tasks stay lodged in mind.

Muscle reading (Hellstromism) — ideomotor cues guide the performer.

Forcing / one-ahead / pre-show — the standard mentalist infrastructure.

Choice blindness (Johansson & Hall)A — people defend choices they never actually made.

Propaganda & mass communication

Le Bon, The Crowd — crowds as suggestible, emotional, de-individuated.

Tarde — imitation as the engine of social life.

Bernays — "engineering of consent"; PR from Freud's nephew.

Lippmann — stereotypes, the "pictures in our heads", the pseudo-environment.

Lasswell — who says what, to whom, in what channel, with what effect.

Ellul — sociological propaganda: the whole environment persuades.

Herman & Chomsky — the propaganda model; five filters.

Agenda-setting (McCombs & Shaw)A — media set what we think about.

Framing & priming (media effects)A — packaging shapes response.

Spiral of silence (Noelle-Neumann)B — fear of isolation silences minority views.

Cultivation theory (Gerbner)B — heavy TV shapes worldview over time.

Two-step flow (Katz & Lazarsfeld) — opinion leaders mediate the media.

McLuhan — "the medium is the message".

Memetics (Dawkins) — ideas spreading like genes.

Thought reform (Lifton) — eight criteria of coercive persuasion.

BITE model (Hassan) — behaviour, information, thought, emotional control.

Agitprop / Goebbels — repetition, scapegoat, the big lie historical, cautionary

Firehose of falsehood — high-volume, multichannel, contradictory disinfo.

Political & economic ideologies

Liberalism — rights, liberty, justice as fairness (Locke, Mill, Rawls).

Conservatism — tradition, gradualism, scepticism of grand plans (Burke, Oakeshott, Scruton).

Socialism / Marxism — dialectical materialism, alienation, false consciousness; Gramsci's hegemony.

Leninism / Maoism / Trotskyism — vanguard, peasant revolution, permanent revolution.

Social democracy — markets plus a welfare state.

Anarchism — abolish the state; mutual aid (Proudhon, Bakunin, Kropotkin, Goldman).

Fascism / corporatism — ultranationalism, the organic state, the leader.

Nationalism / imagined communities (Anderson) — nations as constructed solidarities.

Populism (Laclau, Müller) — "the pure people vs the corrupt elite".

Libertarianism (Nozick, Rothbard) — minimal/no state; self-ownership.

Feminism (the waves) — suffrage → equality → intersectionality.

Postcolonialism (Fanon, Said) — power, orientalism, decolonising the mind.

Environmentalism / degrowth — ecological limits over growth.

Technocracy / accelerationism — rule by experts / speed the system to its end.

Keynesianism — demand management; the state spends in slumps.

Austrians (Mises, Hayek) — markets as information; the knowledge problem.

Chicago monetarism (Friedman) — money supply drives inflation.

New classical / rational expectations — agents anticipate policy.

MMT — a currency-issuer isn't budget-constrained like a household.

Institutionalism (North; Acemoglu & Robinson) — institutions decide prosperity.

Dependency / developmental state — core-periphery; state-led catch-up.

Mercantilism / physiocracy — trade surpluses / land as wealth's source.

Georgism — tax land value.

Neoliberalism — market primacy — both a practice and an epithet.

Philosophy

Stoicism — control what's yours, accept the rest (Epictetus, Aurelius, Seneca).

Epicureanism — pleasure as tranquillity, not excess.

Cynicism — virtue by rejecting convention.

Skepticism (Pyrrho, Sextus) — suspend judgment for peace of mind.

Confucianism — li (ritual), ren (humaneness), rectification of names.

Daoism — wu wei: effortless action with the grain.

Mohism — impartial care; consequentialist ethics.

Buddhism — Four Noble Truths; anatta (no-self).

Vedanta / the Gita — dharma; duty without attachment.

Plato — the Forms behind appearances.

Aristotle — virtue ethics (the mean); the four causes.

Aquinas / scholasticism — faith and reason reconciled.

Ibn Sina / Ibn Rushd — Islamic Aristotelianism preserving Greek thought.

Descartes — mind-body dualism; "I think, therefore I am".

Spinoza — God-or-Nature; determinism.

Leibniz — monads; the best of all possible worlds.

Locke / Berkeley — empiricism, the blank slate / idealism (to be is to be perceived).

Hume — the problem of induction; the is-ought gap.

Kant — the categorical imperative; transcendental idealism.

Hegel — the dialectic (thesis–antithesis–synthesis).

Schopenhauer — the world as blind will.

Kierkegaard — the leap of faith; subjectivity.

Nietzsche — will to power, master-slave morality, eternal recurrence.

Utilitarianism (Bentham, Mill) — the greatest good for the greatest number.

Marx — historical materialism; base and superstructure.

Pragmatism (James, Dewey) — truth as what works.

Husserl — phenomenology; back to the things themselves.

Heidegger — Being, thrownness, authenticity.

Sartre / Camus — existentialism and the absurd; radical freedom.

Wittgenstein — meaning as use; language games.

Popper — falsifiability demarcates science.

Kuhn — paradigm shifts; normal vs revolutionary science.

Frankfurt School — critical theory; the culture industry.

Foucault — power/knowledge, discipline, discourse. the most useful continental thinker here

Derrida — deconstruction; nothing outside the text.

Lyotard — incredulity toward metanarratives.

Baudrillard — simulacra and hyperreality.

Girard — mimetic desire; the scapegoat mechanism.

Rawls vs Nozick — justice as fairness vs entitlement.

MacIntyre — the virtue-ethics revival ("After Virtue").

Historical trend-frames

Ibn Khaldun, asabiyyah — group solidarity rises and decays in cycles.

Vico, corsi e ricorsi — history recurs in ages.

Spengler — civilisations as organisms that age and die.

Toynbee — challenge-and-response drives civilisations.

Sorokin — cultural supersystems alternate (sensate / ideational).

Strauss–Howe — generational cycles (the "fourth turning").

Turchin, cliodynamics — elite overproduction and unrest, quantified.

Marx, modes of production — history by economic stages.

Braudel / Annales — the longue durée; deep structures over events.

Great-man theory (Carlyle) vs structuralism — individuals vs forces.

Whig history — the past as progress toward the present.

Fukuyama, end of history — liberal democracy as the endpoint.

Huntington, clash of civilizations — culture blocs as the new fault lines.

Diamond — geography and biogeography shape fates.

Malthus / demographic transition — population vs resources; the fertility slide.

World-systems (Wallerstein) — core, periphery, semi-periphery.

Tilly — "war made the state and the state made war".

Scott, Seeing Like a State — legibility and high-modernist failure.

Polanyi, double movement — markets expand; society pushes back.

Kondratiev / Schumpeter — long waves; creative destruction.

How to use this shelfName the move when you spot it — "that's reciprocity", "that's a door-in-the-face", "that's agenda-setting". Naming is the first step to both using a technique cleanly and resisting it. Use the search bar to find any entry instantly. Want any of these promoted to a full L1→L4 module? Say which — door-in-the-face, scarcity, and motivational interviewing are the strongest candidates.

★

The Persuasion Stack — how they chain

In practice these rarely appear alone. A polished corporate sequence layers them.

The through-line is commitment & consistency: small self-consistent steps that end in a choice you experience as yours.

The ethics spectrum

Same techniques, either side of the line. What moves you rightward is concealment and whose interest it serves.

🛡

Recognise & Resist — field guide

Fast checklist

Spot the small favour / small yes. Ask why it came just before a bigger request.
Decouple. "I helped / I agreed earlier" ≠ "I endorse this ask." Judge each on its merits.
Un-hide the third option. Any "A or B?" that omits "neither" is a possible double bind.
Name presuppositions. "When you upgrade…" assumes you will — say it out loud.
Discount your own effort. Sunk labour ≠ market value (IKEA/sunk cost).
Slow the tempo. "I'll decide by tomorrow." Manipulation runs on momentum and urgency.
Apply the disclosure test. Would I feel used if I saw the technique? If yes, walk.

Use it ethicallyTo persuade without manipulating: be willing to show your reasoning, make the "no" genuinely available, and make sure the other side also benefits. Influence you'd be comfortable explaining afterwards is influence you can be proud of.

❓

Quiz Yourself — Influence

Mechanisms, evidence and defenses. Tap an option to check.

Score: 0 / 0

1. The Ben Franklin effect predicts that after doing you a small favour, a person will…

We infer attitudes from our behaviour: "I helped them, so I must like them." That's self-perception / dissonance reduction.

2. Which principle most directly powers the funnel technique's chain of small "yeses"?

Once we've agreed, refusing next feels like contradicting ourselves — Cialdini's consistency principle (foot-in-the-door).

3. The IKEA effect boost disappears when…

Successful completion is the boundary condition — an unfinished build produces no valuation bump (Norton, Mochon & Ariely, 2012).

4. "Would you like to begin now, or after a coffee?" is an example of a…

Both branches presuppose you'll begin; the hidden third option ("not at all") is removed. Defense: name the missing option.

5. The single best test for whether influence has crossed into manipulation is…

If the person would feel used the moment they saw the technique, it was covert and exploitative — i.e. manipulation.

6. Which claim is overstated / unsupported by evidence?

Clinical hypnosis is real; "mind control without consent" and strong NLP claims are not supported by controlled research.

Score: 0 / 0

No topics match your search in this subject. Try a shorter word.

Jean's Palace — jump to any section

Principles of Macroeconomics — your complete study companion

Introduction to Macroeconomics

Economics = the science of scarcity and choice

The three basic questions every society answers

Micro vs. Macro

Positive vs. Normative

The four goals — and the two big policy levers

Stock vs. Flow, and Nominal vs. Real

Stock vs. Flow

Nominal vs. Real

The dashboard of the economy

① Output & the business cycle

② Prices & inflation

③ Unemployment

④ Interest rates

⑤ Income distribution — Lorenz curve & Gini

From Classical to Keynesian — the big argument that runs through this course

National Income & Product Accounts (GDP)

Five sectors, one loop of money

Gross Domestic Product — read the definition word-by-word

Where vs. Whose

Same number, three doors — they must all agree

(a) Production (value-added) approach

(b) Expenditure approach — the one you'll use most

(c) Income approach

Separating "more stuff" from "higher prices"

GDP is not the same as well-being

National Income & Equilibrium Determination

Desired vs. Actual — the engine of Keynesian economics

The consumption function C = Ca + bYd

Saving is just the mirror image

Investment, Government & Net exports

Investment I

Government G & Net exports (X−M)

Add it all up

Y = DAE (the "Keynesian cross")

Injection = Leakage (must give the same YE)

Why a small push moves income a lot

If everyone saves more, everyone earns less

Inflationary vs. Deflationary gap

Fiscal Policy

Fiscal policy = the government's spending & taxing choices

Progressive · Proportional · Regressive

① Progressive — rate rises with income

② Proportional (constant)

③ Regressive — rate falls with income

Borrowing and the budget balance

Automatic vs. discretionary — and expansion vs. contraction

Six real-world problems

Worked Examples (Assignments, fully solved)

Nominal & Real GDP, deflator, inflation — base year = Year 3

Nominal GDP = Σ (current P × current Q)

Real GDP = Σ (Year-3 P × current Q) — prices fixed at 130 / 35 / 7

GDP deflator = (Nominal ÷ Real) × 100

Growth rates

Inflation (from the deflator)

Open economy with government — every step

Step 1 — substitute to get C in terms of Y

Step 2 — build DAE

Step 3 — set Y = DAE (Question 1)

Question 3 — multipliers (the important, subtle part)

Question 4 — ΔGa = +4 and ΔTa = +20

Question 5 — if current income is 700 (below YE)

Same economy, second method — should give YE = 880 again

Step 1 — saving function

Step 2 — set Injection = Leakage (Question 1)

Question 4 — autonomous saving rises 7 units (Paradox of Thrift)

Question 5 — if current income is 950 (above YE)

Quiz Yourself — Macro

Formula Cheat-Sheet

National accounts

Consumption & saving

Equilibrium (open, with gov)

Multipliers

Rates

Calculus I — limits, derivatives & their applications

Limits & Continuity

A limit is where a function is heading — not where it lands

Step 1: just plug in. Step 2: if you get 0/0, fix it.

The consumption function C = C_a + bY_d

Injection = Leakage (must give the same Y_E)

Question 4 — ΔG_a = +4 and ΔT_a = +20

Question 5 — if current income is 700 (below Y_E)

Same economy, second method — should give Y_E = 880 again

Question 5 — if current income is 950 (above Y_E)

Exam-style: find the constants that make `f` continuous

When you can't (or don't want to) solve for `y`

The trick for "variable to a variable power", like `xˣ`

1^∞, 0⁰, ∞⁰ → take ln, solve, then exponentiate

Near `x=a`, a curve looks like its tangent line