Analysts at the Fleetfeet Corporation estimate a demand function for its athleti

Question

Analysts at the Fleetfeet Corporation estimate a demand function for its athletic shoe line to be:



Qf = 5 – 2.4*Pf + 0.7*A + 0.002*I + 0.8*Ps



Where Qf = the quantity of shoes sold, Pf = the own price of shoes produced by Fleetfeet ($/pair)

A = the advertising expenditures for Fleetfeet shoes ($/ad unit in a year), I = income in Fleetfeet’s market ($/year), Ps = the price of shoes produced by the Swiftshoes corporation ($/pair)



(a) Interpret the coefficients of each explanatory variable.



(b) If Pf is $60, A is $200, I is $20,000 and Ps is 100, what is the quantity of Fleetfeet shoes sold?



(c) Calculate the own price elasticity of demand for Fleetfeet shoes. Interpret this measure.



(d) Calculate the income elasticity of demand. Interpret this measure.



(e) Calculate the cross price elasticity of demand. Interpret this measure.



(f) Given the answers of (c) through (e), what is the most important factor in determining the demand for shoes?



(g) If the Fleetfeet corporation seeks to reduce its advertising expenditures to $190, and seeks to offset the lost revenues in part by changing its price, should the price be increased or decreased? Explain.

Explanation / Answer

Qf = 5 – 2.4*Pf + 0.7*A + 0.002*I + 0.8*Ps a) - for each %age increase in Pf, Qf falls by 2,4% - for each 5age increase in A, Qf increases by 0.7% - for 1%age increase in I, Qf increases by 0.002% - for 1%age increase in Ps, Qf increases by 0.8% - the constant 5 indicates min. Qf when all other variables are 0. (ANSWER) b) Qf = 5 - 2.4*60 + 0.7*200 + 0.002*20000 + 0.8*100 = 121 (ANSWER) c) Own price (Pf) elasticity of demand = %age change in demand/% change of Pf = -2.4/1 = -2.4 (ANSWER) d) Income (I) elasticity of demand = %age change in demand/% change of I = 0.002/1 = 0.002 (ANSWER) e) Cross price (Ps) elasticity of demand = %age change in demand/% change of Ps = 0.8/1 = 0.8 (ANSWER) f) Own price is most important since it affects the demand most as is evident from (c) above. (ANSWER) g) If A is decreased by 190 $, demand will fall by 190*0.7 = 133 ($) To compensate, Pf is to be decreased to increase demand by $133 Change in Pf required = 133/(-2.4) = - 5.54 ($) i.e. decrease of $5.54 in Pf.

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