Jim Whitney Economics 250

Monday, January 28, 2013

Elasticity formulas

%DQ
General formula for market elasticities (e):   e = ---------
%DX
where X=something which influences Q, such as price (P)
Common elasticities:
%DQd
Own-price elasticity of demand: e = ---------
%DP
e is negative, but we'll usually drop the minus sign.
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%DQd
Income elasticity of demand: eI = ---------
%DI
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%DQdx
Cross-price elasticity of demand: exPy = ---------
%DPy
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%DQs
Elasticity of supply: eS = ---------
%DP
Calculating elasticity:
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a. Arc elasticity:
    Arc elasticity (eARC): elasticity for a distinct pair of points (X1,Q1) and (X2,Q2):
DQ/avgQ     DQ=(Q2-Q1)
eARC = ---------

where:

    avgQ=(Q1+Q2)/2
DX/avgX     DX=(X2-X1)
    avgX=(X1+X2/2
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b. Point elasticity (example: own-price elasticity of demand):
%DQd DQd/Qd DQd P P whitespace.gif (816 bytes)whitespace.gif (816 bytes)
e = ---------- = ----------- = ------ x ---- = dQd/dP x ----
%DP DP/P DP Qd Qd
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where, at the point (Qd,P):
dQd/dP = the derivative of D, and
P/Qd = the ratio of P to Qd.
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point e = (dQd/dP) x (P/Qd)