Question

A publisher of adult coloring books is currently selling 800 pper week at a price of $25 each. A consultant tells them the own-price elasticity of demand at that price is -4.

a. if the consultant is correct, how will sales change if they drop te price by 1%?

b. Estimate a linear demand curve for the coloring books

c. At what price will the own-price elasticity of demand be -1

d. If P=$25 is profit-maximizing, what is the implied marginal cost?

Answer 1

A publisher of adult coloring books is currently selling 800 pper week at a price of $25 each. A consultant tells them the own-price elasticity of demand at that price is -4.

a. if the consultant is correct, how will sales change if they drop the price by 1%?

We know that own-price elasticity of demand = % change in Qd/% change in P = % change in sales / % change in P

-4 = % rise in sales/-1%

= 4%

This indicates that sales will up by 4%. to reach 800*(1 + 4%) =832

b. Estimate a linear demand curve for the coloring books

Elasticity is given by ed = price coefficient x Price / Quantity for a demand function Q = a - bP. We have P = 25, Q = 800 and ed = -4

-4 = -b x 25/800

This gives b = 128. When b is 128, we have 800 = a - 128*25 or a = 4000. Hence demand function is Q = 4000 - 128P.

c. At what price will the own-price elasticity of demand be -1

-1 = -128 x P/(4000 - 128P)

4000 - 128P = 128P

P* = 4000/256 = 15.625. At this price the own-price elasticity of demand will be -1

d. If P=$25 is profit-maximizing, what is the implied marginal cost?

P = MC (e / e + 1)

25 = MC (-4/-3)

MC = -75/-4 = 18.75