(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)
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