Question

Suppose the demand function for ice cream (good X) is given by Qx^d= 1200-5Px-0.08Pz+0.04M+3A where Px =$40, Px=$100, M=3000, A= 700, Z is a related good, M is income and A is the level of advertising. •determine the own price elasticity, and whether the demand is elastic, inelastic, or unitary elastic? What should managers do to increase their profits? • determine the cross price elasticity between good X and good Z and state whether they are substitutes, or complements and why? • determine the income elasticity of demand and state whether the good is a normal or an inferior good and why? • Determind the advertising elasticity of demand

Answer 1

Replacing the values in the equation (Pz = $ 100):

Qd = 1200 - 5 x 40 - 0.08 x 100 + 0.04 x 3000 + 3 x 700

Qd = 3212

Own price elasticity = dQ/dP_x x P_x/Q = -5 x 40/3212 = - 0.062

Demand is inelastic as abs (PE) < 1, managers would increase prices to increase total revenue and profits.

cross price elasticity = dQ/dP_z x P_z/Q = -0.08 x 100/3212 = - 0.0025 (since CPE is negative, good Z is a complementary good)

income elasticity = dQ/dM x M/Q = 0.04 x 3000/3212 = 0.037 (a positive value would mean that this good is a normal good as quantity demanded increases with increase in income)

Advertising elasticity of demand = dQ/dA x A/Q = 3 x 700/3212 = 0.654