Question

DP Gumby produces sleeveless sweaters. He can separate the demand function into a domestic component: QD = 32 – 0.4PD and a foreign component QF = 18 – 0.1PF His total cost function is: C = 50 + 40Q

(a) On three separate diagrams sketch the demand curve in the domestic market, the demand curve in the foreign market and the total demand curve.

(b)If Gumby must charge the same price both home and abroad, how many sweaters should he sell and what price should he charge to maximize profits? How much profit does he make?

(c) Calculate the price elasticity of demand when the market is in equilibrium.

(d)If fixed costs increase from 50 to 100 what is the effect on the profit maximizing output? How is profit affected?

(e) Suppose total costs were to change to C = 50 + 60Q. How would the equilibrium change?

(f) Imagine his costs are once again C = 50 + 40Q. If Gumby can charge a different price in each market, how many sweaters should he sell domestically? How many sweaters should he sell in the foreign market? What price does he charge in each market?

(g) What is Gumby’s total profit with price discrimination? Is price discrimination profitable for Gumby’s? Comment on your result.

(h) What is the price elasticity of demand in each market? Does these values appear sensible? Explain.

(i) Suppose Gumby can discriminate perfectly among the buyers of sleeveless sweaters. What is his profit maximizing output?

(j) What is the maximum price anyone will pay under perfect price discrimination? What is the minimum price anyone will pay? Explain your choice.

Answer 1