A firm’s product sells for $3 per unit in a highly competitive market. The firm

Question

A firm’s product sells for $3 per unit in a highly competitive market. The firm produces output using capital (which it rents at $80 per hour) and labor (which is paid a wage of $20 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. K L Q MPK APK APL VMPK 0 20 0 1 20 50 2 20 150 3 20 300 4 20 400 5 20 450 6 20 475 7 20 475 8 20 450 9 20 400 10 20 300 11 20 150 a. Identify the fixed and variable inputs. b. What are the firm’s fixed costs? c. What is the variable cost of producing 475 units of output? d. How many units of variable input should be used to maximize profits? e. What are the maximum profits this firm can earn? f. Over what range of the variable input usage do increasing marginal returns exist? g. Over what range of the variable input usage do decreasing marginal returns exist? h. Over what range of input usage do negative marginal returns exist?

Explanation / Answer

a) From the data given in the table it is clear that it is incurring cost of labor when production is zero. Labor charges are in this case is fixed cost. Also it is not incurring capital cost so it must be variable cost.

b) Its labor is under the contract of 20$ for 20 hours of service so it is the ficed cost.

c) Quantity of 475 is produced when 6 and 7 units of capital employed. So at this production point 480 (80*6=480) and 560 (80*7=560) of variable cost is incurred.

d) From the data baove it is clear that at capital of 6 unit production is maximum and then it is showing 'Law of Diminishing Return'. So it to maximize profit, it should employ 6 units of capital which is variable.

e) revenue = 475 * 3 = 1425

Profit = Revenue - Cost

Cost = (6 * 80) + 20 = 500

Profit = 1425 -500 = 925

f) For capital input of 0 to 6, increasing marginal return exists. This could be verified by increasing output seen from 0 to 475.

g) At 6 units of capital output is 475 and it is same for 7 units of capital. Then we can see it is decreasing as for 8 units it is 450 and for 9 units it is 400. So we can say that it has decreasing marginal return from 7 to 11.

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