A firm\'s product sells for $3 per unit in a highly competitive market. The firm
ID: 1217672 • Letter: A
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 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 9 20 400 10 20 300 11 20 150 Identify the fixed and variable inputs. What are the firm's fixed costs? What is the variable cost of producing 475 units of output? How many units of 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 marginal returns exist?Explanation / Answer
K
L
Q
MPK
APK
APL
VMPK
0
20
0
1
20
50
50
50
2.5
150
2
20
150
100
75
7.5
300
3
20
300
150
100
15
450
4
20
400
100
100
20
300
5
20
450
50
90
22.5
150
6
20
475
25
79.17
23.75
75
7
20
475
0
67.86
23.75
0
8
20
450
25
56.25
22.5
75
9
20
400
50
44.44
20
150
10
20
300
100
30
15
300
11
20
150
150
13.64
7.5
450
a. Labor is the fixed input while capital is the variable input.
b. Fixed costs are 20($20) = $400.
c. To produce 475 units in the least cost manner requires 6 units of capital, which cost $80 each. Thus, variable costs are ($80)(6) = $480.
d. Using the VMP K = r rule, K = 6 maximizes profits.
e. The maximum profits are $3(475)-$20(20)-$80(6) = $545.
f. There are increasing marginal returns when K is between 0 and 3.
g. There are decreasing marginal returns when K is between 3 and 11.
h. There are negative marginal returns when K is greater than 7.
K
L
Q
MPK
APK
APL
VMPK
0
20
0
1
20
50
50
50
2.5
150
2
20
150
100
75
7.5
300
3
20
300
150
100
15
450
4
20
400
100
100
20
300
5
20
450
50
90
22.5
150
6
20
475
25
79.17
23.75
75
7
20
475
0
67.86
23.75
0
8
20
450
25
56.25
22.5
75
9
20
400
50
44.44
20
150
10
20
300
100
30
15
300
11
20
150
150
13.64
7.5
450
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