Question

The demand for pizza in a large town is written as: Qd = 26 - 10P + 5Pb - Ps + 10Y, where Qd is the quantity demanded, P is the price of pizza, Pb is the price of burittos, Ps is the price of soft drinks sold in the pizza restaurants, and Y is personal income per month (in thousand dollars). Suppose Pb = $4; Ps = $1 and Y = 3 (in thousand dollars) The supply of pizza is: QS = 30 + 5P - 15Pinput Where: P = price of pizza Pinput = price of the inputs = $2

Estimate the following elasticities and interpret the values. (a) Price elasticity of demand for pizza at the equilibrium. (b) Cross-price elasticity of demand between pizza and burrito at the equilibrium. (c) Cross-price elasticity of demand between pizza and soda at the equilibrium. (d) Income elasticity of demand for pizza at the equilibrium. (e) Price elasticity of supply of pizza at the equilibrium.

Answer 1

Plugging in given values,

Qd = 26 - 10P + (5 x 4) - 1 + (10 x 3) = 26 - 10P + 20 - 1 + 30 = 75 - 10P

Qs = 30 + 5P - (15 x 2) = 30 + 5P - 30 = 5P

In equilibrium, Qd = Qs

75 - 10P = 5P

15P = 75

P = $5

Q = 5 x 5 = 25

(a) Price elasticity = (dQd / dP) x (P / Q) = - 10 x (5 / 25) = - 2

(b) Cross price elasticity = (dQd / dPb) x (Pb / Qd) = 5 x (4 / 25) = 0.8

(c) Cross price elasticity = (dQd / dPs) x (Ps / Qd) = - 1 x (1 / 25) = - 0.04

(d) Income elasticity = (dQd / dY) x (Y / Qd) = 10 x (3 / 25) = 1.2

(e) Price elasticity of supply = (dQs / dP) x (P / Qs) = 5 x (5 / 25) = 1