I The following table shows the cost structure for a firm producing in a perfect
ID: 1248003 • Letter: I
Question
I The following table shows the cost structure for a firm producing in a
perfectly competitive market. Use this table to answer the questions below.
q C F ATC AVC MC
17 $189.25 $100.00 $11.13 $5.25 $9.50
18 $199.00 $100.00 $11.06 $5.50 $10.00
19 $209.25 $100.00 $11.01 $5.75 $10.50
20 $220.00 $100.00 $11.00 $6.00 $11.00
21 $231.25 $100.00 $11.01 $6.25 $11.50
22 $243.00 $100.00 $11.05 $6.50 $12.00
23 $255.25 $100.00 $11.10 $6.75 $12.50
24 $268.00 $100.00 $11.17 $7.00 $13.00
25 $281.25 $100.00 $11.25 $7.25 $13.50
26 $295.00 $100.00 $11.35 $7.50 $14.00
a. Suppose that market price is $12.00. Find the profit-maximizing
quantity, q*, for the firm. Show work. Calculate profits at q*. Show
work.
b. At the quantity you found in part a, is the firm producing on the
increasing, constant, or decreasing returns-to-scale part of its ATC
curve? Explain.
c. If the firm’s production function is q = 5.5 L0.5, and using the quantity
you found in part a, what is the profit-maximizing amount of labor for
the firm to hire? Show work.
d. At the quantity you found in part a, do you expect entry or exit of
firms in the long run? Explain.
e. What price should the firm expect to receive for its product in the long
run (after entry or exit has occurred)? Explain.
f. What quantity should the firm expect to produce in the long run (after
entry or exit has occurred)? Explain.
Explanation / Answer
a) For a competitive firm market price is equal to Marginal Revenue. So, P= MR= 12 Profit maximization of a perfect competitive firm occurs when MR= MC That implies, MC must be equal to 12 So, for Profit maximizing, MR= MC=P So at MC= 12 profit maximization occurs. At MC= 12, there are two quantities 22 and 23. At Q= 22, ATC is 11.05 And at Q= 23, ATC is 11.10. Hwere the average cost of production per unit increased from22 to 23 quantities, for max profit, we will take the minimum ATC from the above two, i.e, 11.05. So Proft Maximizing quantity = 22 units. B) At the quantity you found in part a, is the firm producing on the increasing, constant, or decreasing returns-to-scale part of its ATC curve? Explain. At point or out put at 22 units ATC is 11.05. The firm is producing at constant returns to scal. ATC curve first decreases gradually ie from 11.13 to 11.06. Here the firm prodtion will be increasing returns to scale, From 11.03 to 11.05 it is constant returns to scale. From 11.05 the cost increases will give a diminishing returns to scale. c. If the firm’s production function is q = 5.5 L0.5, and using the quantity you found in part a, what is the profit-maximizing amount of labor for the firm to hire? Show work. Q= 5.5 L to 0.5 L units. So profit max there should be min labor or optimum utilization of labor units Profit Max labour units Is Q= 0.5L 22 = 0.5L L= 22/0.5 = 44 units. d. At the quantity you found in part a, do you expect entry or exit of firms in the long run? Explain. The point 11.05 on the ATC curve gives constant returns to scale. But from that point further ATC starts climbing, poised to diminishing returns or diseconomies of scale. So in the long run, only competitive firms can stay in the market at that point, so the firms start exit from the market. e. What price should the firm expect to receive for its product in the long run (after entry or exit has occurred)? Explain. $12 is the competitive equilibrium price, because the MC curve cuts the ATC curve at that point and beyond that point on the ATC there is diminishing returns to scale. So a firm which can produce output and sell at price 12 can sustain in the market, below that price the firms face loss, so they will exit from the market. f. What quantity should the firm expect to produce in the long run (after entry or exit has occurred)? Explain. Competitive equilibrium quantity corresponding to the price ($12) is 22 units, because the MC curve cuts the ATC curve at that point and beyond that point on the ATC there are diminishing returns to scale. So a firm which can produce output of 22 units and sell at price 12 can sustain in the market, if the firm produces above 22 units the ATC rises beyond 11.05 and that position give diseconomies to the firm, pushing into losses.
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