Question

In: Economics

Suppose that output market is in a perfect competition with the price of $10 per unit...

Suppose that output market is in a perfect competition with the price of $10 per unit and input market is a monopsony with the following information assuming that labor is the only input.

L: 1,2,3,4,5,6,7,8,9,10

MP: 20,18,16,14,12,10,8,6,4,2

W: 20,40,60,80,100,120,140,160,180,200

a. Fill in the missing values.

b. What are the optimal level of employment and the corresponding profit for this firm?

c. Graphically explain the profit maximization behavior for this firm.

Solutions

Expert Solution

(a)

  • MP = Change in Q / Change in L
  • MRP = Output price x MP = $10 x MP
  • TR = Product price x Q = $10 x Q
  • TC = Labor Cost = Wage rate x L = $110 x L
  • MFC = Wage rate = $110
  • Profit = TR - TC

Filled-in table as follows.

L

MP

MRP ($)

Q

TR ($)

TC ($)

MFC ($)

Profit ($)

1

20

200

20

200

110

110

90

2

18

180

38

380

220

110

160

3

16

160

54

540

330

110

210

4

14

140

68

680

440

110

240

5

12

120

80

800

550

110

250

6

10

100

90

900

660

110

240

7

8

80

98

980

770

110

210

8

6

60

104

1040

880

110

160

9

4

40

108

1080

990

110

90

10

2

20

110

1100

1100

110

0

(b)

Profit-maximizing hiring occurs with L = 5 units, since maximum profit occurs at this level (Maximum profit = $250).

(c)

Profit is maximized when MRP = MFC.

From above table, MRP = MFC condition does not hold, so profit-maximizing employment is computed as explained below.

For L = 5, MRP = $120 > Wage rate ($110), hence there is a marginal profit (= MRP - MFC = $120 - $110 = $10).

For L = 6, MRP = $100 < Wage rate ($110), hence there is a marginal loss (= MFC - MRP = $110 - $100 = $10).

So profit is maximized by hiring 5 workers.

In following graph, profit is maximized at point A where MRP curve intersects MFC curve.


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