Use the information in the table to answer the questions below. L =1 L =2 L = 3
ID: 1153813 • Letter: U
Question
Use the information in the table to answer the questions below.
L =1
L =2
L = 3
L = 4
K = 1
100.00
131.95
155.18
174.11
K = 2
141.42
186.61
219.46
246.23
K = 3
173.21
228.55
268.79
301.57
K = 4
200.00
263.90
310.37
348.22
a. Does this production function exhibit a constant return to scale? Explain your answer.
b. How many units of output are produced with 4 units of labor and 2 units of capital?
c. Suppose the firm is using 3 units of capital and 2 units of labor and then decides to employ a third worker. What is the marginal product of the third worker?
L =1
L =2
L = 3
L = 4
K = 1
100.00
131.95
155.18
174.11
K = 2
141.42
186.61
219.46
246.23
K = 3
173.21
228.55
268.79
301.57
K = 4
200.00
263.90
310.37
348.22
Explanation / Answer
a) Constant return to scale means output will be doubled when inputs become double. Here the output is 100 when L=1 and K=1. But when L and K doubled that is L=2, K=2 then the output is 186.61 which is less than double of 100. So the production function exhibits decreasing return to scale.
b) when L=4 and K=2, 246.23 units of output is produced.
c) When the L=2 and K=3 output is 228.55 units.
When the L=3 and K=3 output is 268.79 units. So the marginal product of the third worker is (268.79-228.55)=40.24.
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