Junior Economist Qualification cheat sheet

Price elasticity of demand: E_d = (%ΔQ_d)/(%ΔP); |E_d|>1 elastic, <1 inelastic, =1 unit elastic; revenue rises with a price cut only when demand is elastic.

Point elasticity on a linear demand curve Q = a − bP: E_d = −b·(P/Q); it varies along the curve, equal to −1 at the revenue-maximizing midpoint.

Income elasticity E_I = (%ΔQ)/(%ΔI): positive for normal goods, negative for inferior goods, greater than 1 for luxuries.

Cross-price elasticity E_xy = (%ΔQ_x)/(%ΔP_y): positive for substitutes, negative for complements.

Consumer optimum: MRS_xy = MU_x/MU_y = P_x/P_y; equimarginal principle for inputs: MP_L/w = MP_K/r.

Profit maximization: MR = MC. Under perfect competition P = MR, so P = MC; a monopolist sets MR = MC and prices above MC, with Lerner index (P − MC)/P = 1/|E_d|.

Short-run shutdown rule: shut down if P < minimum AVC; exit the market if P < minimum ATC in the long run.

Externality correction: Pigouvian tax equals marginal external cost at the social optimum; a subsidy equals marginal external benefit. A public good is non-rival and non-excludable, so the efficient quantity satisfies ΣMB = MC (vertical summation).

Expenditure approach: GDP = C + I + G + (X − M); GDP counts domestic production, GNP counts income of residents.

Real vs nominal: GDP deflator = (nominal GDP / real GDP) × 100; real GDP uses base-year prices.

Expenditure multiplier = 1/(1 − MPC) = 1/MPS in a closed economy without income taxes; with proportional tax rate t, the multiplier is 1/(1 − MPC(1 − t)).

Tax multiplier = −MPC/(1 − MPC); the balanced-budget multiplier equals 1 when government spending and lump-sum taxes rise equally.

Cobb-Douglas production Y = A·K^α·L^(1−α): α is capital's income share; growth accounting gives g_Y = g_A + α·g_K + (1−α)·g_L.

Okun's law: each 1 percentage point of unemployment above the natural rate is associated with roughly 2 percentage points of negative output gap (coefficient varies by country and period).

Phillips curve: π = π^e − β(u − u_n) + shock; in the long run the curve is vertical at the natural rate, so there is no permanent inflation–unemployment trade-off.

Solow steady state: sf(k) = (n + g + δ)k; steady-state growth of output per worker equals the rate of technical progress g.

Mean, variance, standard deviation: s² = Σ(x_i − x̄)²/(n − 1) for a sample; the standard error of the mean is s/√n.

Expected value and variance of a linear combination: E(aX + bY) = aE(X) + bE(Y); Var(aX + bY) = a²Var(X) + b²Var(Y) + 2ab·Cov(X,Y), with the covariance term zero if X and Y are independent.

Bayes' theorem: P(A|B) = P(B|A)·P(A)/P(B); base rates matter - a rare condition keeps the posterior low even with a sensitive test.

Normal approximation: about 68% of observations lie within 1 SD of the mean, 95% within 1.96 SD, 99.7% within 3 SD.

Central limit theorem: the sampling distribution of the sample mean approaches normality with mean μ and variance σ²/n as n grows, regardless of the population distribution.

95% confidence interval for a mean with unknown σ: x̄ ± t_{0.025, n−1}·(s/√n); the interval narrows with larger n and widens with higher confidence.

Hypothesis testing: reject H0 when |t| exceeds the critical value; a p-value is the probability of a result at least as extreme as observed, given H0 is true - it is not the probability that H0 is true.

Type I error = rejecting a true H0 (probability α); Type II error = failing to reject a false H0 (probability β); power = 1 − β.

OLS slope: β̂ = Cov(X,Y)/Var(X) = Σ(x_i − x̄)(y_i − ȳ)/Σ(x_i − x̄)²; the fitted line passes through (x̄, ȳ).

Gauss-Markov assumptions: linearity in parameters, random sampling, no perfect collinearity, zero conditional mean E(u|X) = 0, homoskedasticity. Under these, OLS is BLUE.

R² = 1 − SSR/SST; adjusted R² penalizes added regressors and can fall when a variable with little explanatory power is added.

Omitted variable bias: bias in β̂ equals the effect of the omitted variable times its coefficient in a regression of the included regressor on the omitted one; sign = sign(γ)·sign(correlation).

Heteroskedasticity leaves OLS unbiased but invalidates standard errors; use robust (White) standard errors.

Autocorrelation (serial correlation) in time series inflates t-statistics; detect with the Durbin-Watson statistic (near 2 = no first-order autocorrelation) or Breusch-Godfrey test.

Multicollinearity inflates variances and standard errors but does not bias coefficients; detect with variance inflation factors (VIF above about 10 is severe).

Instrumental variables require relevance (the instrument correlates with the endogenous regressor) and exogeneity (the instrument is uncorrelated with the error); weak instruments cause biased, imprecise estimates.

Budget balance = T − G − transfers; the structural (cyclically adjusted) balance removes automatic-stabilizer effects and better measures the fiscal stance.

Automatic stabilizers (progressive taxes, unemployment benefits) dampen fluctuations without discretionary legislation; discretionary policy requires new legislation and acts with lags.

Tax incidence: the burden falls more on the less elastic side of the market; with perfectly inelastic demand the consumer bears the whole tax.

Deadweight loss of a tax rises with the square of the tax rate and is larger when supply and demand are more elastic.

Laffer curve: revenue is zero at 0% and at 100% tax rates and peaks somewhere between; the peak location is empirical, not a fixed number.

Ricardian equivalence: if households fully anticipate future taxes to finance current debt, deficit-financed spending does not raise aggregate demand.

Crowding out: government borrowing raises interest rates and can reduce private investment; the effect is larger when the economy is near full employment.

Fiscal sustainability: with debt ratio d, primary balance p, nominal growth g and interest rate r, the debt ratio stabilizes when p = d·(r − g).

Money multipliers: simple deposit multiplier = 1/reserve requirement ratio; the money multiplier m = (1 + c)/(r + c) where c is the currency–deposit ratio and r the reserve ratio.

Quantity theory: MV = PY; in growth terms g_M + g_V = π + g_Y, so long-run inflation ≈ money growth minus real growth if velocity is stable.

Fisher equation: i ≈ r + π^e; the real interest rate r = i − π (exact form (1+i)/(1+π) − 1).

Central bank tools: open market operations, reserve requirements, standing lending facilities and the policy rate; buying securities expands reserves and the money supply.

Bond price and yield move inversely; for a fixed-coupon bond, price = Σ C/(1+y)^t + F/(1+y)^n.

Duration measures price sensitivity: %ΔP ≈ −D·Δy/(1+y); longer maturity and lower coupons mean higher duration.

Term structure: expectations theory says long rates are averages of expected future short rates; an inverted yield curve has historically preceded recessions.

Bank balance sheet: assets = reserves + loans + securities; liabilities = deposits + borrowings; capital ratio = equity/assets; leverage magnifies both gains and losses.

Comparative advantage: a country gains from trade by specializing where its opportunity cost is lower, even if it has an absolute disadvantage in both goods.

Terms of trade = export price index / import price index × 100; a rise means each unit of exports buys more imports.

Balance of payments identity: current account + capital account + financial account + errors and omissions = 0.

Purchasing power parity: absolute PPP sets the exchange rate at the ratio of price levels; relative PPP says the exchange-rate change ≈ inflation differential.

Interest rate parity: covered parity ties the forward premium to the interest differential; uncovered parity links expected depreciation to the interest differential.

Marshall-Lerner condition: a devaluation improves the trade balance only if the sum of export and import demand elasticities exceeds 1.

J-curve: the trade balance often worsens before improving after a depreciation because of short-run quantity rigidities.

Tariff welfare effects for a small country: consumer surplus falls, producer surplus rises, government collects revenue, and the net effect is a deadweight loss.

Tinbergen rule: to hit n independent targets, a policymaker needs at least n independent instruments.

Policy lags: recognition, decision and implementation lags make discretionary stabilization prone to mistiming; rules can reduce time-inconsistency problems.

Market failure categories - market power, externalities, public goods, asymmetric information - justify regulation only where benefits exceed costs.

Cost-benefit analysis: discount future flows at an appropriate social discount rate; choose projects with positive net present value.

Natural monopoly regulation: marginal-cost pricing achieves allocative efficiency but requires a subsidy; average-cost pricing is self-financing but below the efficient output.

Regulatory capture occurs when an agency serves the interests of the industry it regulates; transparency and independent review are standard countermeasures.

Conflicts of interest must be disclosed and managed; an economist must not use confidential data for personal trading or present conflicted analysis as independent.

Professional ethics: state data sources and assumptions, distinguish positive from normative claims, avoid plagiarism, and correct errors promptly.