Assume the demand function for beer is defined as: Q_b = 10P^b^-2. From this dem

Question

Assume the demand function for beer is defined as: Q_b = 10P^b^-2. From this demand equation is it easy to verify that the slope of this equation,defined as delta Q/delta P, is equal to - 20P_b^-3 What is the general form of the point elasticity formula for this given equation? The own-price elasticity of this equation is equal to -2, formally, epsilon_d = -2. This is a special class of demand functions that are called constant-elasticity demand functions. Using your answer from a, prove that epsilon_d = -2. Convert Q_b = 10P_b^-2 to a log-linear function (you can use log or In). Can your answer be estimated with a regression equation? Could your original demand equation be estimated with a regression equation?

Explanation / Answer

(a) General form of price elasticity, eP = (dQb / dPb) x (Pb / Qb)

(b) For given function,

dQb / dPb = - 20 x Pb-3

eP = (- 20 x Pb-3) x (Pb / 10Pb-2) = - 20 / 10 = - 2

(c) Qb = 10Pb-2

ln Qb = ln (10Pb-2)

ln Qb = ln 10 + (- 2 x ln Pb)

ln Qb = ln 10 - 2 ln Pb

This log-linear form cannot be directly estimated using regression, since a regression function is strictly linear in form. But the original function can be estimated using regression.

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