ECON 311 Intermediate Microeconomics
Problem Set #5 Production
. This homework is due 4/3/2024 at 12:45PM.
. Please complete the following sections.
My-Lab Section (Total Points: 40 points)
This section of the homework should be submitted through blackboard. Please answer the multiple-choice questions and problems available in the tools tab in Blackboard. Please refer to Problem Set#5. Please note that there are 50 points available. I give 10 additional points in this section to compensate for potential issues with My-lab grading.
Extended written section (Total Points: 60 points).
To receive full credit, you must show all your work in obtaining numerical solutions, state the formulas used, and make clear your understanding of the concepts involved. Please use complete sentences and express your points clearly and fully. Use graphs whenever appropriate to help illustrate your points. Be sure to label your graphs.
Production in the Short-Run
1. Table 6.1 shows some values of labor inputs and output quantities from a short-run production
function. Complete the Table. We use a Cobb-Douglas production function and fix capital (k(̅) = 4) to 4 units do the numbers of the production function Q = f(k(̅), L) = k0 5(̅̅̅̅̅)L0.5 = 40.5L0.5 = 2L0.5
|
Capital, K |
Labor, L |
Output, Q |
Marginal Product of Labor, MPL = |
Average Product of Labor, APL = |
|
4 |
0 |
0 |
-- |
-- |
|
4 |
1 |
2.00 |
2.00 |
2.00 |
|
4 |
2 |
2.83 |
0.83 |
1.42 |
|
4 |
3 |
|
|
|
|
4 |
4 |
|
|
|
|
4 |
5 |
|
|
|
|
4 |
6 |
|
|
|
|
4 |
7 |
|
|
|
|
4 |
8 |
|
|
|
a. Explain what happens to the total output as we add more inputs.
b. Explain what happens to the rate at which output rises as we hire more and more labor.
c. Describe the MPL and APL curve. What is the relationship between MPL and APL? What are the uses for MPL?
d. When do diminishing returns of labor set in?
2. The short-run production function for a firm the produces pizzas is Q = f(k(̅), L) = 15k0 25(̅̅̅̅̅̅̅)L0.75,
where Q is the number of pizzas produced per hour, K is the number of ovens (which is fixed at 3 in the short-run), and L is the number of workers employed.
a. Write an equation for the short-run production function for the firm showing output as a function of labor.
b. Calculate the total output produced per hour for L=0, 1,2,3,4,and5.
c. Calculate the MPL for L=1 to L=5. Is MPL Diminishing? Explain
d. Calculate APL for L=1 to L=5.
3. Answer the following questions based on the following production process schedules. Suppose a
firm's short-run total product schedule is given in the table below.
|
Production Process (K=1) |
Production Process (K=2) |
Production Process (K=3) |
Production Process (K=4) |
||||
|
Labor |
Output Produced |
Labor |
Output Produced |
Labor |
Output Produced |
Labor |
Output Produced |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
1 |
25 |
1 |
50 |
1 |
90 |
1 |
120 |
|
2 |
50 |
2 |
100 |
2 |
150 |
2 |
180 |
|
3 |
70 |
3 |
130 |
3 |
180 |
3 |
220 |
|
4 |
88 |
4 |
150 |
4 |
200 |
4 |
240 |
|
5 |
103 |
5 |
160 |
5 |
210 |
5 |
250 |
|
6 |
115 |
6 |
165 |
6 |
210 |
6 |
255 |
|
7 |
125 |
7 |
168 |
7 |
200 |
7 |
230 |
|
8 |
132 |
8 |
170 |
8 |
190 |
8 |
200 |
|
9 |
136 |
9 |
170 |
9 |
180 |
9 |
170 |
|
10 |
138 |
10 |
168 |
10 |
175 |
10 |
140 |
a. What is the marginal product of hiring the 8th and 9th worker, when the firm rents 2 units of capital? If this company is only interested in maximizing output, should this company hire 8 or 9 units of labor? Explain.
b. In this case, should the firm hire one additional worker, that is the 10th unit of labor? Explain.
Production in the Long-Run
4. Suppose that Jack can hire workers for $12 per hour or rent capital for $7 per hour.
a. Write an expression for Jacks total cost as a function of how many workers he hires and how much capital he employs.
b. Assume Jack wishes to hold their total costs to exactly $100. Use the expression in (a) to find the equation for an isocost line corresponding to exactly $100 of costs. Rearrange your equation to isolate capital.
c. Graph the equation for the isocost line, putting labor on the horizontal axis and capital on the vertical axis.
d. What is the vertical intercept of the line you drew? The horizontal intercept? What does each represent?
e. What is the slope of the line you drew? What does it represent?
f. Suppose that bargaining with the local labor union raises wages. Jack must now pay $14 per hour. What happens to the isocost line corresponding to $100 of expenditure?
Explain. Show the new isocost line on your graph.
5. Baldor measures the marginal rate of technical substitution (MRTS) at −MP K(MP L) = −3. The prices of labor and capital faced by Baldor are such that − 
= −4.
a. Is Baldor minimizing costs? Explain.
b. What can Baldor do to improve its company situation?