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One Plant -Two Markets—Price Discrimination (SHOW WORKING)

BOMBAY-CORP manufactures a proprietary pesticide that can be sold directly to retail outlets or to a wholesale firm for further processing and eventual sale as a completely different product. The demand function for each of these markets is:


Retail Outlets: P1 = 40-3Q1
Wholesale Company: P2= 40-Q2

What are the prices charged and what are the quantities sold in the respective markets. A total cost function for the manufacture of this product is TC=10+4(Q1+Q2)

A. Determine BOMBAY-CORP’S 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?


D. What are BOMBAY-CORP’S total profits if the firm is effectively able to charge different prices in the two markets?


E. Calculate the profit-maximizing level of price and output if BOMBAY-CORP is required to charge the same price per unit in each market and act like a competitive firm. What are BOMBAY-CORP’S profits under this condition?

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Divya Singh
Divya SinghLv10
28 Sep 2019

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Related questions

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.


The Hawaiian Sea Salt Company sells salt to retail grocery chains in Hawaii and on the mainland. The demand function in each of these markets is: Hawaii grocery chains: P1 = 180 – 8Q1 Mainland grocery chains: P2 = 100 – 4Q2 Where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Hawaiian Sea Salt Company’s total cost function for salt is: TC = 50 + 20 (Q1 + Q2) Assuming that the Hawaiian Sea Salt Company is able to charge different prices in the two markets, what are the profit maximizing prices and output levels for sea salt in the two markets? Please explain your answer a. Q1 = 8.75 & P1 = $110 and Q2 = 7.5 & P2 = $70 b. Q1 = 20 & P1 = $100 and Q2 = 20 & P2 = $60 c. Q1 = 10 & P1 = $100 and Q2 = 10 & P2 = $60 d. Q1 = 20 & P1 = $20 and Q2 = 20 & P2 = $20

1. Suppose that two identical firms produce widgets and they are the only firms in the market. The cost functions of the two firms are given by C1(Q1) = 60Q1 and C2(Q2) = 60Q2. The demand function of the market is given by the function P = 300 - Q where Q=Q1+Q2.

a. Find the Cournot equilibrium output levels and profit for each firm.

b. Suppose the two firms form a Cartel and to maximize joint profit. Calculate how many widgets each firm will produce and their output levels.

c. Suppose firm 1 is the only firm in the market. Determine the output and price that firm 1 will produce and charge. Also, determine the profit level.

d. Suppose firm 2 takes its output decision after firm1 has announced its output decision. Calculate the output levels and profit levels of the two firms. Comparing the output and profit of part (a), which firm is better off and which firm is worse off ? Explain your answer.

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