Microeconomics Formulas

Elasticity of Demand

Own-price elasticity: $E_{P_x}^d=\frac{\%\Delta Q_x^d}{\%\Delta P_x}=(Q_d{)}_P^{\prime }\times \frac{P_x}{Q_x^d}$ where $(Q_d{)}_P^{\prime }$ = slope of demand function (not demand curve)

Income elasticity: $E_I^d=\frac{\%\Delta Q_x^d}{\%\Delta I}$

Cross-price elasticity: $E_{P_y}^d=\frac{\%\Delta Q_x^d}{\%\Delta P_y}$

Cost Functions

$TC=TFC+TVC$ $MC=\frac{\Delta TC}{\Delta Q}$ $AFC=\frac{TFC}{Q},AVC=\frac{TVC}{Q},ATC=\frac{TC}{Q}$

Revenue Functions

$TR=\sum (P_i\times Q_i)$ $AR=\frac{TR}{Q}$ $MR=\frac{\Delta TR}{\Delta Q}=P\left(1+\frac{1}{\text{elasticity}}\right)$

MR and Demand relationship (linear demand $Q_D=a-bP$):

• Demand: $P=\frac{a-Q_D}{b}$, slope = $-1/b$
• $MR=\frac{a-2Q_D}{b}$, slope = $-2/b$ (twice as steep)

Profit Maximization

$\text{Profit max at }MR=MC$

Breakeven: $TR=TC$ or $AR=ATC$

Shutdown (SR): $TR<TVC$ or $AR<AVC$

Concentration Measures

N-firm concentration ratio: $C{R}_N={\sum }_{i=1}^N{s}_i$

Herfindahl-Hirschman Index: $HHI={\sum }_{i=1}^N{s}_i^2$

where $s_i$ = market share of firm $i$