Chapter 14: Problems 3(b, c, d), 5(a, b, c), and 8(a, b, c)
3. American Export-Import Shipping Company operates a general cargo carrier service between New York and several Western European ports. It hauls tow 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 Q1 = 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 Americans total profits if it is effectively able to charge different prices in the two markets?
5. 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
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.
8. The Pear Computer Company just developed a totally revolutionary new personal computer. It estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be
P= 2,500 – 0.0005Q
The marginal (and average variable) cost of producing the computer is $900.
A. Compute the profit maximizing price and output levels assuming Pear acts as a monopolist for its products
B. Determine the total contribution to profits and fixed cost from the solution generated in Part A.
Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years:
Time Period Price Quantity Sold
1 $2,400 200,000
2 2,200 200,000
3 2,000 200,000
4 1,800 200,000
5 1,700 200,000
6 1,600 200,000
7 1,500 200,000
8 1,400 200,000
9 1,300 200,000
10 1,200 200,000
C. Calculate the contribution to profit and overhead for each of the 10 time periods and prices.
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