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Additional Topics in Demand Theory
Solution a. Substituting the given information into the demand function yields Q = 62 - 2 P + 0.2 I + 25 A = 62 - 2(4) + 0.2(150) + 25(4) = 62 - 8 + 30 + 100 = 184 b. The price elasticity of demand is given by the expression ep =
Ê ∂Q ˆ Ê P ˆ Ê 4 ˆ -8 = -2 = = -0.04 Ë ∂P ¯ Ë Q ¯ Ë 184 ¯ 184
This result indicates that a 1% reduction in the price of Sergeant Garcia’s Revenge results in a 0.04% increase in quantity demanded. Since |ep| < 1, the demand for this product is price inelastic. It suggests, perhaps, that Sergeant Garcia’s Revenge has no close substitutes. c. The income elasticity of demand is given as eI =
Ê ∂Q ˆ Ê I ˆ Ê 150 ˆ 30 = 0.2 = = 0.16 Ë ∂I ¯ Ë Q ¯ Ë 184 ¯ 184
This result suggests that a 1% increase in consumer income results in a 0.16% increase in the demand for this product. Since eI > 0, this good is characterized as a “normal” good. Moreover, since 0 < eI < 1, this product is also characterized as a “necessity.” This suggests that people just cannot get along without Sergeant Garcia’s Revenge hot sauce. d. The advertising elasticity of demand is given as Ê ∂Q ˆ Ê A ˆ = 25Ê 4 ˆ = 100 = 0.54 eA = Ë ∂ A¯ Ë Q ¯ Ë 184 ¯ 184 This result suggests that a 1% increase in Rubicon & Styx’s advertising budget would result in a 0.54% increase in sales.
CHAPTER REVIEW Elasticity is a general concept that relates the sensitivity of a dependent variable to changes in the value of some explanatory (independent) variable. Suppose, for example, that the value of variable y depends in some systematic way on the value of variable x. This relationship can be read “y is a function of x.” Elasticity measures the percentage change in the value of y given a percentage change in the value of x. There are several elasticity concepts associated with the demand curve including price elasticity of demand, income elasticity, cross (or cross-price) elasticity, advertising elasticity, and interest elasticity.
