# Check Your Understanding

Pages: 5 (1348 words) Published: August 18, 2013
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 the closet to exhibiting constant returns to scale with .021 standard error. c. In which industry will a given percentage increase in capital result in the largest percentage increase in output? d. In what industry will a given percentage increase in production workers result in the largest percentage increase in output? 9. Consider the following Cobb-Douglas production for the bus transportation system in a particular city: Where L = labor input in workers hours

F = fuel input in gallons
K = capital input in number of buses
Q = output measured in millions of bus miles
Suppose that the parameters of this model were estimated using annual data for the past 25 years. The following results were obtained: A = 0.0012
Q =
a. Determine the (i) labor, (ii) fuel, and (iii) capital input production elasticities. Based on the information labor (L) would be 0.45, fuel (f) would be 0.20 and capital input (k) is 0.30. b. Suppose the labor input (worker hours) is increased by 2 percent next year (with the other inputs held constant). Determine the approximate percentage change in output. Based on the information if all other inputs are unchanged then the labor hours would increase by 2 percent (45 x 0.02) = 0.9 and 0.9 times the input of .30 equals (0.9 x .3) equals .27 which is rounded to 30 percent. Which means that with the increase output approximate percentage would increase by 30%. c. Suppose that capital input (number of buses) is decreased by 3 percent next year (when certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. Based on the information, capital input is currently .30 and if there is a 3 percent decrease, then the approximate percentage in output would be .9 percent (3 x .30) = 0.009, which is 0.9%. So with this change there would be a percentage change of 0.9%. d. What type of returns to scale appears to characterize this bus transportation system?...

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