Question

A firm’s product sells for $2 per unit in a highly competitive market. The firm produces output using capital (which it rents at $75 per hour) and labor (which is paid a wage of $15 per hour under a contract for 20 hours of labor services). Complete the following table and use the information to answer the questions that follow.

Table 1

K	L	Q	MP(K)	AP(K)	AP(L)	VMP(K)
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

1. What are the firm’s fixed costs?
   
2. What is the variable cost of producing 400 units of output?
   
3. How many units of the variable input should be used to maximize the profits this firm can earn?
   
4. What are the maximum profits this firm can earn?
   
5. Over what range of the variable input do decreasing (marginal) returns exist?
   
6. Over what range of the variable input do negative (marginal) returns exist?

Answer 1

K	L	Q	MP(K)=∆Q/∆K	AP(K)=Q/K	AP(L)=Q/L	VMP(K)=$2*MP(K)
0	20	0	-	-	-	-
1	20	50	50	50.00	2.50	100
2	20	150	100	75.00	7.50	200
3	20	300	150	100.00	15.00	300
4	20	400	100	100.00	20.00	200
5	20	450	50	90.00	22.50	100
6	20	475	25	79.17	23.75	50
7	20	475	0	67.86	23.75	0
8	20	450	-25	56.25	22.50	-50

a) Here, Labor is fixed factor.

Firm's fixed cost = $15 * 20 = $300

b) Here, Capital is variable factor. From the table it is clear that to produce 400 units of output, 4 units of capital is required. So, the variable cost of producing 400 units of output = $75 * 4 = $300.

c) To maximize profit, the firm can use the quantity of variable input upto the point where VMP is equal to or greater than the rent. From the table, it is clear that the VMP(i.e.$100) is greater than the rent (i.e., $75) when the firm uses 5 units of capital. Thus, 5 units of the variable input should be used to maximize the profits this firm can earn.

d) Total Revenue = P * Q = $2 * 450 = $900

     Total cost = TFC + TVC = $300 + ($75 * 5) = $675

     Total profit = TR - TC = $900 - $675 = $225

e) Over the range of 4 to 7 variable input decreasing (marginal) returns exist.

f) Over the range of 7 to 8 variable input negative (marginal) returns exist.