American 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 and semimanufactured raw materials. The demand functions for these two classes of goods are:
P1 = 100 - 2Q1
P2 = 80 - Q2
where Q1 = tons of freight moved. The total cost function for American is:
TC = 20 + 4(Q1+Q2)
a. Determine the firm's total profit function.
b. What are the profit maximizing levels of price and output for the two freight categories?
c. At these levels of output, calculate the marginal revenue in each market.
d. What are American's total profits if it is effectively able to charge different prices in the two markets?
e. If American is required by law to charge the same per-ton rate to all users, calculate the new profit-maximizing level of price and output. What are the profits in this situation?
f. Explain the difference in profit levels between the differential pricing and uniform pricing cases. Hint: First calculate the point price elasticity of demand under the uniform price-output solution.