A firms product sells for 4 per unit in a highly competitive

A firm’s product sells for $4 per unit in a highly competitive market. The firm produces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a contract for 20 hours of labor services). Complete the following table and use that information to answer the questions that follow.

Instruction: Round your answers for Average Product of Capital and Average Product of Labor to 2 decimal places.

What are the firm\'s fixed costs?

What is the variable cost of producing 475 units of output?

How many units of the variable input should be used to maximize profits?

What are the maximum profits this firm can earn?

Over what range of the variable input usage do increasing marginal returns exist?

Over what range of the variable input usage do decreasing marginal returns exist?

Over what range of input usage do negative marignal returns exist?

(3 7) alue Marginal 1) 4) 6) arginal verage Product of erage Product of apital Labor utput Product of Product of Capital apital MPK Capital APK Labor APL VMPK 20 20 20 20 20 20 20 20 20 20 20 20 50 150 300 400 450 475 475 450 400 300 150

Solution

Working notes:

(1) MPK = Change in output (Q) / Change in K

(2) APK = Q / K and APL = Q / L

(3) VMPK = MPK x Price = 4 x MPK

(4) Total cost = wL + rK

When Q = 0, TC = Fixed cost (FC)

So, FC = 20 x $30 = $600

(5) Profit = (P x Q) - TC = 4Q - (wL + rK) = 4Q - 600 - 25K

So:

(b) Variable cost = wL

When Q = 475, wL = $30 x 7 = $210

(c) Profit is maximum at $1150, when K (Variable input) is 6 units.

(d) Maximum profit = $1150

(e) MPK is increasing when K ranges from 0 to 3.

(f) MPK decreases from K = 4 to K = 11

(g) MPK is negative when K ranges from 8 to 11.

K	L	Q	MPK	APK	APL	VMPK	Profit = 4Q - (600+25K)
0	20	0				0	-600
1	20	50	50	50.00	0.00	200	-425
2	20	150	100	75.00	2.50	400	-50
3	20	300	150	100.00	7.50	600	525
4	20	400	100	100.00	15.00	400	900
5	20	450	50	90.00	20.00	200	1075
6	20	475	25	79.17	22.50	100	1150
7	20	475	0	67.86	23.75	0	1125
8	20	450	-25	56.25	23.75	-100	1000
9	20	400	-50	44.44	22.50	-200	775
10	20	300	-100	30.00	20.00	-400	350
11	20	150	-150	13.64	15.00	-600	-275