Problem 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) What is the range of workers where there are increasing returns to scale? Constant returns to scale? Decreasing returns to scale? Negative returns?
b) If the company wants 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?
Problem 2. Your engineering department estimated the following production function.
Q = 15L2 – 0.5L3
a. What is the marginal product of labor function, MPL?
b. What is the average product of labor function, APL?
c. What is the value of L that maximizes Q?
d. What is the value of L at which average product is maximized?
Problem 3. 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
a. What are the production elasticities of demand for labor, capital (trucks) and energy?
b. If worker hours (labor) are increased by 10% next year, how much will output (Q) increase?
c. If the number of trucks (K) decreases by 10% next year, how much will output (Q) decrease?
d. What type of returns to scale is consistent with the above production function?
Question 4: In a production process, if an excessive amount of the variable input is used relative to the amount of fixed input available to support the production of the desired output, production is occurring in which of the following stages?
- Stage II
- Stages I and II
- Stage I
- Stage III
Question 5: The marginal product of a variable input is defined as
a. the ratio of total output to the amount of the variable input used in producing the output.
b. the incremental change in total output that can be produced by the use of one more unit of the variable input in the production process.
c. the percentage change in output resulting from a given percentage change in the amount of the variable input X employed in the production process with Y.
d. a and b.
Question 6: A short-run production function assumes that
a. the level of output is fixed.
b. at least one input is a fixed input.
c. all inputs are fixed inputs.
d. all inputs can be varied.
Question 7: If a firm is producing a given level of output in a technically efficient manner, it must be the case that
a. The firm is using the cost minimizing combination of inputs to produce the level of output.
b. Each input is producing its maximum marginal product.
c. The level of output is the most that can be produced with the given combination of inputs.
d. All of the above
Question 8: The main difference between the short-run and the long-run production functions is that
a. in the short run all inputs are fixed and in the long run all inputs are variable.
b. in the short run the firm varies all of its inputs to find the least-cost combination of inputs.
c. in the short run, at least one of the firm’s input levels is fixed.
d. in the long run, the firm is making a constrained decision related to use existing plant and equipment efficiently, but there are no constraints determining short run production.
Question 9: The marginal rate of technical substitution is
a. the rate at which the firm can substitute labor for capital while holding output constant.
b. the rate at which the firm can substitute labor for capital while holding total cost constant.
c. the slope of the isocost curve.
d. all of the above.
Question 10: The rate at which one input X can be substituted for another input Y in a production process while keeping total output constant is
a. the slope of the isoquant curve.
b. the marginal rate of technical substitution (MRTS).
c. equal to MPx/MPy.
d. all of the above.
Question 11: The law of diminishing marginal returns
a. says that each and every increase in the amount of the variable input used in the production process will yield diminishing marginal returns.
b. is a mathematical theorem that can be logically proved or disproved.
c. says that after some point, the marginal product of an input will start to decline if the amount of other inputs is held constant.
d. none of the above.
Question 12: Marginal factor cost is defined as the amount that an additional unit of the variable input adds to
a. marginal cost.
b. variable cost.
c. marginal rate of technical substitution.
d. total cost.
Question 13: Every point along an isoquant is one associated with
a. economic efficiency.
b. technical efficiency.
c. competitive advantage.
d. cost minimization.
Question 14: A production function measures the relation between
a. input prices and output price.
b. the quantity of inputs and the quantity of output.
c. input prices and the quantity of output.
d. the quantity of inputs and input prices.
Question 15: If average product is increasing, marginal product
a. must be greater than average product.
b. must be less than average product.
c. must be decreasing.
d. must be increasing.
Question 16: At the point where total product is maximized
a. AP is maximized.
b. AP is equal to zero.
c. MP is maximized.
d. MP is equal to zero.
Question 17: Marginal revenue product is defined as the amount that an additional unit of the variable input adds to
a. marginal revenue.
b. total output.
c. total revenue.
d. marginal product.
Question 18: The marginal product of labor
a. measures how output changes as the wage rate changes.
b. is less than the average product of labor when the average product of labor is decreasing.
c. is negative when adding another unit of labor decreases output.
d. both b and c.