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Log Functions and Elasticity of Variables

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The demand for haddock has been estimated as:

log Q = a + b log P + c log I = d log Pm

where Q = quantity of haddock sold in New England

P = price per pound of haddock

I = a measure of personal income in the New England region

Pm = an index of the price of meat and poultry

If b = -2.174, c = .461, and d = 1.909,

Calculate the elasticity of demand for each parameter.

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Solution Summary

The solution describes the steps to calculate elasticity of demand for each of the parameters.

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Calculating Own price elasticity of demand
log Q = a + b log P + c log I - d log Pm

Differentiating with respect to P, we get
(1/Q)*dQ/dP=b*(1/P)
dQ/dP=bQ/P
Own price elasticity of demand=(dQ/dP)*(P/Q)=(bQ/P)*(P/Q)=b
So, own price elasticity of ...

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  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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