A firm’s product sells for $4 per unit in a highly competitive market. The firm

Question

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

Explanation / Answer

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

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