Discussion:
1. 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 semi manufactured raw materials.
The demand functions for these two classes of goods are
P1 = 100 - 2Q1
P2 = 80 - Q2
where Qi = tons of freight moved. The total cost function for American is
TC = 20 + 4(Q1 + Q2)
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?
2. Phillips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is
Retail Outlets: P1 = 60 - 2Q1
Superior Company: P2 = 40 - Q2
where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillips' total cost function for the manufacture of this product is
TC = 10 + 8(Q1 + Q2)
a. Determine Phillips' total profit function.
b. What are the profit-maximizing price and output levels for the product in the two markets?
c. At these levels of output, calculate the marginal revenue in each market.