Question

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.

Answer 1

(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.