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(Short run profit maximization) A perfectly competitive firm has the following f

ID: 1177767 • Letter: #

Question

(Short run profit maximization) A perfectly competitive firm has the following fixed and variable costs in the short run. The market price for the firm's product is $150.

Output FC   VC   TC   TR PROFIT/LOSS


Output 0, FC $100, VC $0,    TC TR 0 Profit /Loss
output 1, FC $100, VC $100, TC TR Profit/loss
output 2, FC $100, VC $180, TC, TR Profit/loss
output 3, FC $100, VC $300, TC TR Profit/loss
output 4, FC $100, VC $440, TC TR, Profit/loss
output 5, FC $100, VC $600, TC TRprofit/loss
output 6, FC $100, VC $780, TC TR profit/loss

Complete the table above

b. At what output rate does the firm maximize profit or minimize loss?

c. What is the firm's marginal revenue at each positive level of output? Its average revenue?

d. What can you say about the relationship between marginal revenue and marginal cost for output rates below the profit maximizing(or loss minimizing) rate? For output rates above the profit maximizing(or loss minimizing) rate?

please show all work. Thank You

Explanation / Answer

Short run profit maximization) A perfectly competitive firm has the following fixed and variable costs in the short run. The market price for the firm's product is $150.

Output

FC

VC

TC [=FC+VC]

TR [=P*Q]

Profit/Loss [=TR-TC]

0

100

0

100

0

-100 (Loss)

1

100

100

200

150

-50 (loss)

2

100

180

280

300

20 (profit)

3

100

300

400

450

50 (profit)

4

100

440

540

600

60 (profit)

5

100

600

700

750

50 (profit)

6

100

780

880

900

20 (profit)

Complete the table above

b. At what output rate does the firm maximize profit or minimize loss?

Profits are maximized when Q=4.

c. What is the firm's marginal revenue at each positive level of output? Its average revenue?

Since each unit is sold at the same price, the addition to total revenue from each additional unit sold is the same. The addition to total revenue from each additional unit sold is nothing else but the price. Hence MR=Price = $150.

We have AR=TR/Q = (P*Q)/Q =P.

Hence AR=MR=P=$150.

d. What can you say about the relationship between marginal revenue and marginal cost for output rates below the profit maximizing(or loss minimizing) rate? For output rates above the profit maximizing(or loss minimizing) rate?

We have profits given by, Profit = TR %u2013 TC.

Profits are maximized when dProfits/dQ=0,

i.e. dProfits/dQ = dTR/dQ %u2013 dTC/dQ = MR-MC =0,

i.e. MR = MC.

At all quantities below the profit maximizing output, we can conclude that MR>MC. None of the quantity below the profit maximizing level is optimum because as you produce more the additional to total revenue from selling that additional unit exceeds the addition to total costs of producing that additional unit. That is, the marginal revenue exceeds the marginal cost. Hence by producing additional units you earn higher profits.

At all quantities above the profit maximizing output, we can conclude that MR<MC. None of the quantity above the profit maximizing level is optimum because as you produce more the additional to total revenue from selling that additional unit is less than the addition to total costs of producing that additional unit. That is, the marginal revenue is less than the marginal cost. Hence by producing additional units you earn less profits.

Output

FC

VC

TC [=FC+VC]

TR [=P*Q]

Profit/Loss [=TR-TC]

0

100

0

100

0

-100 (Loss)

1

100

100

200

150

-50 (loss)

2

100

180

280

300

20 (profit)

3

100

300

400

450

50 (profit)

4

100

440

540

600

60 (profit)

5

100

600

700

750

50 (profit)

6

100

780

880

900

20 (profit)