1
. You are given the following information about the amount your company can produce per day given the number of workers it hires.
|
Numbers of Workers |
Quantity Produced |
|
|
0 |
||
| 1 | ||
|
2 |
3 |
|
|
6 |
||
|
4 |
11 |
|
|
5 |
1 9 |
|
|
24 |
||
|
7 |
2 8 |
|
| 8 |
31 |
|
| 9 |
33 |
|
|
10 |
34 |
|
|
12 |
1. What is the range of workers where there are increasing returns to scale? Constant returns to scale? Decreasing returns to scale? Negative returns?
1. If the company wants to maximize total output, what number of workers should be hired?
1. What is the number of workers that should be hired if the company wants to maximize output per worker?
1. Your engineering department estimated the following production function.
Q = 15L2 – 0.5L3
1. What is the marginal product of labor function, MPL?
1. What is the average product of labor function, APL?
1. What is the value of L that maximizes Q?
1. What is the value of L at which average product is maximized?
1. The following Cobb-Douglas production function is used to describe the output generated by a local government maintenance agency.
Q = αLβ1Kβ2Eβ3
Where L represents number of worker hours, K represents number of trucks used, and E represents energy used. Statistical estimated generated the following values for α, β1, β2, and β3.
Α = 0.01; β1 = 0.5, β2 = 0.4, and β3 = 0.2
1. What are the production elasticities of demand for labor, capital (trucks) and energy?
1. If worker hours (labor) are increased by 10% next year, how much will output (Q) increase?
1. If the number of trucks (K) decreases by 10% next year, how much will output (Q) decrease?
1. What type of returns to scale is consistent with the above production function?
