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 0
1 1
2 3
3 6
4 11
5 19
6 24
7 28
8 31
9 33
10 34
11 34
12 33
a. Find the range of workers where there are increasing returns to scale? Constant returns to scale? Decreasing returns to scale? Negative returns?
b. If company wishes to maximize total output, what number of workers should be hired?
c. What is the number of workers that should be hired if the company wants to maximize output per worker?
2. Your engineering department estimated the following production function.
Q = 15L2 – 0.5L3
a. Find the marginal product of labor function, MPL?
b. Find the average product of labor function, APL?
c. Find the value of L that maximizes Q?
d. Find the value of L at which average product is maximized?
3. The following Cobb-Douglas production function is used to describe the output generated by a local government maintenance agency.
Q = αL^{β1}K^{β2}E^{β3}
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
a. What are production elasticities of demand for labor, capital (trucks) and energy?
b. If worker hours (labor) are increased by 10% next year, how much would output (Q) increase?
c. If the number of trucks (K) decreases by 10% next year, how much would output (Q) decrease?
d. What kind of returns to scale is consistent with above production function?