Question

Exercise 14.3

A U.S. export-import shipping company operates a general cargo carrier service between New York and several western European ports. It hauls two major categories of freight: manufactured items (Q1Q1) and semimanufactured raw materials (Q2Q2). The demand functions for these two classes of goods are:

P1=200−Q1P1=200−Q1

P2=80−Q2P2=80−Q2

where QiQi = tons of freight moved. The total cost function for the United States is

TC=20+4(Q1+Q2)TC=20+4(Q1+Q2)

What is the firm’s total profit function?

200Q1−Q12+80Q2−Q22−20200Q1−Q12+80Q2−Q22−20

199Q1−Q12+60Q2−Q22−20199Q1−Q12+60Q2−Q22−20

196Q1−Q12+76Q2−Q22196Q1−Q12+76Q2−Q22

196Q1−Q12+76Q2−Q22−20196Q1−Q12+76Q2−Q22−20

The profit-maximizing levels of price and output for manufactured items are

per ton and

tons, respectively.The profit-maximizing levels of price and output for semimanufactured raw materials are

per ton and

tons, respectively.At these levels of output the marginal revenue in the manufactured items market is

and the marginal revenue in the semimanufactured raw materials market is

.

At these prices, the price elasticity of demand in the manufactured items market is   and the the price elasticity of demand in the semimanufactured raw materials market is   . (Hint: ED=PMR−PED=PMR−P)

What are the total profits if the company is effectively able to charge different prices in the two markets?

.If the company is required by law to charge the same per-ton rate to all users, the new profit-maximizing level of price and output are

per ton and

tons respectively. The total profits in this situation is

.

Answer 1