Check Your Understanding
Chapter 7 & 8
Chapter 7: Problems 1, 6, 8, and 9
1. In the Deep Creek Mining Company example described in this chapter (Table 7.1), suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating.
a. Complete the following table:
Labor Input I
(No. of Workers) Total Product
Marginal Product
Average Product
1 3 0 + 3 = +3 3/1 = 3
2 6 6 – 3 = +3 6/2 = 3
3 16 16 – 6 = +10 16/3 = 5.33
4 29 29 – 16 = +13 29/4 = 7.25
5 43 43 – 29 = +14 43/5 = 8.6
6 55 55 – 43 = +12 55/6 = 9.17
7 58 58 – 55 = +3 58/7 = 8.29
8 60 60 – 58 = +2 60/8 = 7.5
9 59 59 – 60 = -1 59/9 = 6.56
10 56 56 – 59 = -3 56/10 = 5.6
b. Plot the (i) total product, (ii) marginal product, and (iii) average product functions.
c. Determine the boundaries of the three stages of production.
Based on the information total product would range anywhere from 3 to 60; marginal product would range from -3 to 14, and average product would range from 3 to 9.17.
6. Consider the following short-run production function (where L = variable input, Q = output):
a. Determine the marginal revenue product function.
Total = P x Q = 10(10L - 0.5L^2)
Marginal Revenue = 20(10L – 0.5L^2)
= 200 –10L
b. Determine the marginal factor cost function.
Q = 200/10
Marginal Factor L = 20
c. Determine the optimal value of L, given that the objective is to maximize profits.
20 = 100 – 10L
-100 -100
-80 = -10L
/-10 /-10
8 = L
8. Based on the production function parameter estimates reported in Table 7.4:
a. Which industry (or industries) appears to exhibit decreasing returns to scale?
(Ignore the issue of statistical significance.)
In my opinion I would say that Furniture exhibit decreasing returns to scale for it had the largest standard error.
b. Which industry comes closest to the exhibiting constant returns to scale?
Based on the information, Food and Beverages came
Chapter 7: Problems 1, 6, 8, and 9
1. In the Deep Creek Mining Company example described in this chapter (Table 7.1), suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating.
a. Complete the following table:
Labor Input I
(No. of Workers) Total Product
Marginal Product
Average Product
1 3 0 + 3 = +3 3/1 = 3
2 6 6 – 3 = +3 6/2 = 3
3 16 16 – 6 = +10 16/3 = 5.33
4 29 29 – 16 = +13 29/4 = 7.25
5 43 43 – 29 = +14 43/5 = 8.6
6 55 55 – 43 = +12 55/6 = 9.17
7 58 58 – 55 = +3 58/7 = 8.29
8 60 60 – 58 = +2 60/8 = 7.5
9 59 59 – 60 = -1 59/9 = 6.56
10 56 56 – 59 = -3 56/10 = 5.6
b. Plot the (i) total product, (ii) marginal product, and (iii) average product functions.
c. Determine the boundaries of the three stages of production.
Based on the information total product would range anywhere from 3 to 60; marginal product would range from -3 to 14, and average product would range from 3 to 9.17.
6. Consider the following short-run production function (where L = variable input, Q = output):
a. Determine the marginal revenue product function.
Total = P x Q = 10(10L - 0.5L^2)
Marginal Revenue = 20(10L – 0.5L^2)
= 200 –10L
b. Determine the marginal factor cost function.
Q = 200/10
Marginal Factor L = 20
c. Determine the optimal value of L, given that the objective is to maximize profits.
20 = 100 – 10L
-100 -100
-80 = -10L
/-10 /-10
8 = L
8. Based on the production function parameter estimates reported in Table 7.4:
a. Which industry (or industries) appears to exhibit decreasing returns to scale?
(Ignore the issue of statistical significance.)
In my opinion I would say that Furniture exhibit decreasing returns to scale for it had the largest standard error.
b. Which industry comes closest to the exhibiting constant returns to scale?
Based on the information, Food and Beverages came