Chapter 14 Exercise 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 two major categories of freight: manufactured items and semi-manufactured raw material. The demand functions for these two classes of goods are
P1 = 100 %u2013 2Q1
P2 = 80 %u2013 Q2
where Qi = tons of freight moved. The total cost function for American is
TC = 20 + 4(Q1 +Q2)
b. What are the profits-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%u2019s 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 %u2013 2Q1
Superior Company: P2 = 40 %u2013 Q2
Where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillips%u2019 total cost function for the manufacture of this product is
TC = 10 + 8(Q1 + Q2)
a) Determine Phillips%u2019 total profit function.
b) What are the profit-maximizing price and outlet 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 %u2013 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 product.
b) Determine the total contribution to profits and fixed costs 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
a. Calculate the contribution to profit and overhead for each of the 10 time periods and prices.
Chapter 14 Exercise 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 two major categories of freight: manufactured items and semi-manufactured raw material. The demand functions for these two classes of goods are
P1 = 100 %u2013 2Q1
P2 = 80 %u2013 Q2
where Qi = tons of freight moved. The total cost function for American is
TC = 20 + 4(Q1 +Q2)
b. What are the profits-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%u2019s 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 %u2013 2Q1
Superior Company: P2 = 40 %u2013 Q2
Where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillips%u2019 total cost function for the manufacture of this product is
TC = 10 + 8(Q1 + Q2)
a) Determine Phillips%u2019 total profit function.
b) What are the profit-maximizing price and outlet 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 %u2013 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 product.
b) Determine the total contribution to profits and fixed costs 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 |
a. Calculate the contribution to profit and overhead for each of the 10 time periods and prices.
