Question

In: Economics

Consider this table containing long run production data: Units of Capital, K Units of Labor, L...

Consider this table containing long run production data:

Units of Capital, K

Units of Labor, L

1

2

3

4

1

100.00

131.95

155.18

174.11

2

141.42

186.61

219.46

246.23

3

173.21

228.55

268.79

301.57

4

200.00

263.90

310.37

348.22

  1.             Does this production function exhibit a constant return to scale? Explain your answer.

  1.             How many units of output are produced with 4 units of labor and 2 units of capital?

  1.              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?

  1.             Suppose the firm is using 1 unit of labor and 1 unit of capital. What is the marginal product of capital for K = 2, K = 3, and K = 4? Does return on capital diminish?

Solutions

Expert Solution

a. No, this production function does not exhibit constant return to scale. Constant returns to scale means when K and L are increased by a factor 't' then output must also increase by 't'. But this does not happen here. For example, when K = L = 1 then output = 100. If we multiply both K and L by 2 then K = 2*1 = 2 and L = 2*1 = 2 then output should also be multiplied by 2, that is, 2*100 = 200 but output when K = L = 2 is 186.61, so, this function does not exhibit constant returns to scale.

b. 246.23 units of output are produced with 4 units of labor and 2 units of capital.

c. With 3 units of capital, marginal product of 3rd worker = (Output with 3 workers - output with 2 workers)/Change in number of workers
= (268.79-228.55)/(3-2) = 40.24/1 = 40.24

d. With 1 unit of labor, marginal product of capital for K = 2 is (Output with K = 2 - output with K = 1)/Change in units of capital
= (141.42-100)/(2-1) = 41.42
With 1 unit of labor, marginal product of capital for K = 3 is (Output with K = 3 - output with K = 2)/Change in units of capital
= (173.21-141.42)/(3-2) = 31.79
With 1 unit of labor, marginal product of capital for K = 4 is (Output with K = 4 - output with K = 3)/Change in units of capital
​​​​​​​= (200-173.21)/(4-3) = 26.79

Yes, return on capital diminish as when K increases, addition to output is diminishing.

Rahul Sunny answered 1 year ago
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