Answer to Question #49491 in Microeconomics for shakeeti

Question

Suppose that when the price of a burger decreases from $2.00 to $1.75 and other things remain the same, the quantity demanded of burgers increases from 200 an hour to 400 an hour and the quantity demanded of pizza decreases from 400 an hour to 200 an hour. At the same time, the quantity demanded of soda increases from 150 an hour to 300 an hour.
a) Calculate the cross elasticity of demand for soda with respect to burgers.
b) Are soda and burgers substitutes or complements? Why?
c) Calculate the cross elasticity of demand for pizza with respect to burgers.
d) Are pizza and burgers substitutes or complements? Why?
e) Describe how the demand for soda and the demand for pizza have changed.

Answer 1

Pb1 = $2.00, Pb2 = $1.75, Qb1 = 200, Qb2 = 400, Qp1 = 400, Qp2 = 200, Qs1 = 150, Qs2 = 300 per hour.
a) The cross elasticity of demand for soda with respect to burgers is:
E s,b = (2 + 1.75)/(150 + 300)*(300 - 150)/(1.75 - 2) = 3.75/450*150/(-0.25) = -5.
b) Soda and burgers are complements, because E s,d < 0
c) The cross elasticity of demand for pizza with respect to burgers is:
E p,b = (2 + 1.75)/(400 + 200)*(200 - 400)/(1.75 - 2) = 3.75/600*(-200)/(-0.25) = 5.
d) Pizza and burgers are substitutes, because E p,b > 0.
e) The demand for soda increases, as soda and burgers are complements, and the demand for pizza decreases, as pizza and burgers are substitutes.