ECO 550 WEEK 4 CHAPTER 7 AND CHAPTER 8 PROBLEMS
ECO 550 WEEK 4 CHAPTER 7 AND CHAPTER 8 PROBLEMS
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Chapter 7
In the deep creek mining company 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 tableLabor input L(#of workers
Total production TPL (=Q)
Marginal Product (MPL)
Average Product APL
1
2
3
4
5
6
7
8
9
10
`
B. Plot the (i) total product, (ii) marginal product, (iii) average product functions.
C. Determine the boundaries of these three stages of production.
6. Consider the following short-Run production function (where input, ):
A. Determine the marginal product
B. Determine the average product function
C. Find the value of L that maximizes Q
D. Find the value of L at which the marginal product function takes on its maximum value
E. Find the value of L at which the average product function takes on its maximum value.
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.)
B. Which industry comes closest to exhibiting constant returns to scale?
C. In which 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 function for the bus transportation system in a particular city:
Q= ?L ^?1 F^?2 K^?3
Where L is the labor input in worker hours;
F is the fuel input in gallons;
K is the capital input in number of buses;
Q is the output measured in millions of bus miles
Suppose that the parameters (a,? 1, ?2, ?3) of this model were estimated using annual data for the past 25 years. The following results were obtained:
?= 0.0012;?;
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Chapter 7
In the deep creek mining company 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 tableLabor input L(#of workers
Total production TPL (=Q)
Marginal Product (MPL)
Average Product APL
1
2
3
4
5
6
7
8
9
10
`
B. Plot the (i) total product, (ii) marginal product, (iii) average product functions.
C. Determine the boundaries of these three stages of production.
6. Consider the following short-Run production function (where input, ):
A. Determine the marginal product
B. Determine the average product function
C. Find the value of L that maximizes Q
D. Find the value of L at which the marginal product function takes on its maximum value
E. Find the value of L at which the average product function takes on its maximum value.
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.)
B. Which industry comes closest to exhibiting constant returns to scale?
C. In which 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 function for the bus transportation system in a particular city:
Q= ?L ^?1 F^?2 K^?3
Where L is the labor input in worker hours;
F is the fuel input in gallons;
K is the capital input in number of buses;
Q is the output measured in millions of bus miles
Suppose that the parameters (a,? 1, ?2, ?3) of this model were estimated using annual data for the past 25 years. The following results were obtained:
?= 0.0012;?;