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CDILMPRS

Cobb–Douglas Production Function

Y=A Kα LβY = A\,K^{\alpha}\,L^{\beta}

Prices & MarketsOutput produced from capital and labour, each raised to its own exponent, times a productivity factor A. Charles Cobb and Paul Douglas fitted it to US manufacturing from 1899 to 1922 and published it in 1928.

Consumer Surplus (Linear Demand)

CS=12 (Pmax⁡−P) Q\mathit{CS} = \tfrac{1}{2}\,(P_{\max} - P)\,Q

Prices & MarketsArea of the triangle between a straight-line demand curve and the price actually paid: what buyers would have been willing to pay, less what they did pay. P_max is the choke price, where the demand line meets the vertical axis and the quantity demanded reaches zero.

Deadweight Loss of a Per-Unit Tax

DWL=12 t ΔQ\mathit{DWL} = \tfrac{1}{2}\,t\,\Delta Q

Prices & MarketsValue destroyed by a per-unit tax beyond the revenue it collects: half the tax times the fall in quantity traded. Those are the trades that were worth making, and that the tax stopped.

Inflation Rate from a Price Index

π=I2−I1I1\pi = \frac{I_2 - I_1}{I_1}

Prices & MarketsPercentage change in a price index between two periods — the ordinary definition of an inflation rate. Divide by the EARLIER index, always, because the rate is measured against where prices started.

Lerner Index of Market Power

L=P−MCPL = \frac{P - \mathit{MC}}{P}

Prices & MarketsAbba Lerner's 1934 measure of market power: the gap between price and MARGINAL cost, as a fraction of price. Zero under perfect competition, and approaching one for a seller facing almost no competitive constraint.

Marginal Revenue from Elasticity (Amoroso–Robinson)

MR=P(1+1Ed)\mathit{MR} = P\left(1 + \frac{1}{E_d}\right)

Prices & MarketsRevenue brought in by the next unit sold, when selling it requires cutting the price on every unit. Below the price whenever demand slopes down, and NEGATIVE once demand turns inelastic — which is why no firm with any pricing power sells there.

Money Multiplier (Textbook Reserve Model)

m=1rrm = \frac{1}{r_r}

Prices & MarketsThe textbook relation between a reserve requirement and the deposits a banking system can support: the reciprocal of the required reserve ratio. Read the learning zone before using it — the Bank of England's own 2014 bulletin says plainly that this is not how money is created in a modern economy.

Price Elasticity of Demand (Midpoint Form)

Ed=Q2−Q1(Q1+Q2)/2P2−P1(P1+P2)/2E_d = \frac{\dfrac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\dfrac{P_2 - P_1}{(P_1 + P_2)/2}}

Prices & MarketsProportional change in quantity demanded divided by the proportional change in price, with both changes measured against the MIDPOINT of the two observations. Negative for a normal good: below −1 is elastic, between −1 and 0 is inelastic.

Price Elasticity of Supply (Midpoint Form)

Es=Q2−Q1(Q1+Q2)/2P2−P1(P1+P2)/2E_s = \frac{\dfrac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\dfrac{P_2 - P_1}{(P_1 + P_2)/2}}

Prices & MarketsProportional change in quantity supplied divided by the proportional change in price, both measured against the midpoint. POSITIVE for an ordinary supply curve: above 1 is elastic, below 1 inelastic, and near zero is a fixed stock.

Producer Surplus (Linear Supply)

PS=12 (P−Pmin⁡) Q\mathit{PS} = \tfrac{1}{2}\,(P - P_{\min})\,Q

Prices & MarketsArea of the triangle between the price received and a straight-line supply curve: what sellers were paid, less the least they would have accepted. P_min is the shutdown price, where the supply line meets the vertical axis and the first unit is offered.

Real Value from a Nominal Value (Deflating by an Index)

Vreal=Vnom IbaseItV_{\text{real}} = V_{\text{nom}}\,\frac{I_{\text{base}}}{I_t}

Prices & MarketsRestates an amount of money measured in one year's prices in another year's prices, by multiplying by the ratio of the two index values. The base year is whichever year you want the answer expressed in.

Revenue Response to a Price Change

%ΔR≈%ΔP (1+Ed)\%\Delta R \approx \%\Delta P\,(1 + E_d)

Prices & MarketsApproximate percentage change in total revenue caused by a small percentage change in price. The sign of the bracket decides everything: with E_d between −1 and 0 a price rise RAISES revenue, and below −1 it CUTS it.

Solow Steady-State Capital per Effective Worker

k∗=(s An+g+δ)11−αk^{*} = \left(\frac{s\,A}{n + g + \delta}\right)^{\frac{1}{1 - \alpha}}

Prices & MarketsCapital per effective worker at which investment exactly replaces what depreciation and growth dilute away, for a Cobb–Douglas economy. Robert Solow published the model in 1956; this is the level the capital stock converges toward and never quite reaches.