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Consolidated Salt Company sells table salt to both retail grocery chains and com

ID: 1195764 • Letter: C

Question

Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g., bakeries, snack food makers, etc.). The demand function for each of these markets is:

Retail grocery chains:

P1 = 180 - 8Q1

Commercial users:

P2 = 100 - 4Q2

where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Consolidated's total cost function (which includes a "normal" return to the owners) for salt is:

TC = 50 + 20(Q1 + Q2)

Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing output levels for the product in the two markets?

Q1 = 10, Q2 = 10

Q1 = 20, Q2 = 20

Q1 = 10, Q2 = 20

Q1 = 20, Q2 = 10

Assuming that Consolidated is effectively able to charge different prices in the two markets, what is Consolidated's total profit under this condition?

$1050

$1150

$1250

$1350

Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing price for the product in the two markets?

P1 = $60/unit, P2 = $100/unit

P1 = $100/unit, P2 = $60/unit

P1 = $60/unit, P2 = $60/unit

P1 = $100/unit, P2 = $100/unit

Retail grocery chains:

P1 = 180 - 8Q1

Commercial users:

P2 = 100 - 4Q2

Explanation / Answer

As shown by the TC function, the marginal cost of producing each unit of output is $20.

            MC      =          20

Calculate Marginal revenue of salt sold to Retain grocery chains.

P = 180 – 8Q

            TR = PQ = (180 – 8Q)Q

            TR = 180Q – 8Q2

            MR = dTR/dQ
            MR = 180 – 16Q

Find the profit maximizing quantity as follows.

            MC = MR

            20 = 180 – 16Q

            Q1 = 10

which is the profit maximizing quantity of salt sold to the retail grocery stores.

The price charged to the retail grocery stores is

            P = 180 – 8(10)

            P1 = 100

Calculate Marginal revenue of salt sold to COMMERCIAL USERS.

P = 100 – 4Q

            TR = PQ = (100 – 4Q)Q

            TR = 100Q – 4Q2

            MR = dTR/dQ
            MR = 100 – 8Q

Find the profit maximizing quantity as follows.

            MC = MR

            20 = 100 – 8Q

            Q2 = 10

which is the profit maximizing quantity of salt sold to commercial users.

The price charged to commerical users is

            P = 100 – 4(10)

            P2 = 60

Profit = P1Q1 + P2Q2 – [50 + 20(Q1 + Q2)]

            = 100(10) + 60(10) – [50 + 20(10 + 10)]

            = $1150

The correct answers are made bold hereunder.

Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing output levels for the product in the two markets?

A.

Q1 = 10, Q2 = 10

B.

Q1 = 20, Q2 = 20

C.

Q1 = 10, Q2 = 20

D.

Q1 = 20, Q2 = 10

Assuming that Consolidated is effectively able to charge different prices in the two markets, what is Consolidated's total profit under this condition?

A.

$1050

B.

$1150

C.

$1250

D.

$1350

Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing price for the product in the two markets?

A.

P1 = $60/unit, P2 = $100/unit

B.

P1 = $100/unit, P2 = $60/unit

C.

P1 = $60/unit, P2 = $60/unit

D.

P1 = $100/unit, P2 = $100/unit

A.

Q1 = 10, Q2 = 10

B.

Q1 = 20, Q2 = 20

C.

Q1 = 10, Q2 = 20

D.

Q1 = 20, Q2 = 10