The production technology of a firm is given in the table below.
|
Number of workers
|
Units of output
|
MPN
|
|
0
|
0
|
-
|
|
1
|
48
|
48
|
|
2
|
88
|
40
|
|
3
|
119
|
31
|
|
4
|
144
|
25
|
|
5
|
166
|
22
|
|
6
|
184
|
18
|
|
7
|
196
|
12
|
a.Define the marginal product of labor and explain how it relates to the production function (with N on horizontal axis and Y on vertical axis). What shape does a production function typically take and why?
The marginal product of labor is the change in output (Y) in relation to a change in labor (N). It can be numerically defined as ΔY/ΔN. The production function typically shows a positive relation (line with positive slope) between number of workers and units of output; an increase in the number of workers will result in an increase in output. The curve is upward sloping because the change in output in relation to the change in labor increases at a decreasing rate.
b. Fill in the MPN column. Does this production function have the typical shape that you identified above. Why or why not?
The production function does have the upward sloping shape that I identified above, as the number of workers increases, so does the units of output, but at a decreasing rate.
c. Assume that the price of a unit of output is $10 and the nominal wage that you pay is $210. Calculate the number of workers that you will hire and the associated profit in REAL terms (as we did in class, we 'assume away' all other costs of production).
|
Number of workers
|
Units of output
|
MPN
|
MRPN
|
Marginal Profit
|
Total Profit
|
|
0
|
0
|
-
|
-
|
-
|
-
|
|
1
|
48
|
48
|
480
|
270
|
270
|
|
2
|
88
|
40
|
400
|
190
|
460
|
|
3
|
119
|
31
|
310
|
100
|
560
|
|
4
|
144
|
25
|
250
|
40
|
600
|
|
5
|
166
|
22
|
220
|
10
|
610
|
|
6
|
184
|
18
|
180
|
-30
|
580
|
|
7
|
196
|
12
|
120
|
-90
|
490
|
You will hire 5 workers.
d. Suppose that you are producing a commodity that you sell to China and given the slowdown in China's economy, the price of your product falls to $7. Explain how and why you would change your behavior. Please provide the intuition beginning your answer with... at the same level of labor input I am no longer ......... (please be as specific as possible).
|
Number of workers
|
Units of output
|
MPN
|
MRPN
|
Marginal Profit
|
Total Profit
|
|
0
|
0
|
-
|
-
|
-
|
-
|
|
1
|
48
|
48
|
336
|
126
|
126
|
|
2
|
88
|
40
|
280
|
70
|
196
|
|
3
|
119
|
31
|
217
|
7
|
203
|
|
4
|
144
|
25
|
175
|
-35
|
168
|
|
5
|
166
|
22
|
154
|
-56
|
112
|
|
6
|
184
|
18
|
126
|
-84
|
28
|
|
7
|
196
|
12
|
84
|
-126
|
-98
|
At the same level of labor input I am no longer maximizing profit because the real wage is not equal to the MPN. MPN is equal to W/P, and with the price of the product falling from $10 to $7, the real wage is greater than the marginal revenue product of labor. Because the additional revenue that is generated by each additional worker is less than the real wage, the firm will hire less workers.
e. Calculate the new level of profits in REAL terms given the fall in price
f. Suppose that you have debt and that the payment is $200 per period. Calculate the percent of profits that $ 200 represents given the conditions in part c. and then calculate the percent of profits that $200 represents given the conditions in d.
Conditions in Part C with debt:
Total profit = $610
Percent of debt = (200/610) x 100 = 33%
Conditions in Part D with debt:
Total profit = $287
Percent of debt = (200/203) x 100 = 99%
g. Suppose that profits and stock prices together as they usually do and that you own stock in this company. If you had a crystal and predicted the slowdown in China, would you sell stock before China slows down or would you hold on and sell the stock after China slows down?
h. Let’s return the initial conditions where the nominal wage rate = $210 and the price of a unit of output = $10. Assume that a new technology increases the number of units of output that each worker can produce by 5 units of output (i.e., each worker's MPN rises by 5). Given this development. fill in table below.
|
Number of workers
|
Units of output
|
MPN
|
|
0
|
0
|
-
|
|
1
|
53
|
53
|
|
2
|
98
|
45
|
|
3
|
134
|
36
|
|
4
|
164
|
30
|
|
5
|
191
|
27
|
|
6
|
214
|
23
|
|
7
|
231
|
17
|
i. (10 points) Given that the workers are more productive, they demand a pay increase and you give it to them. The wage that is agreed upon is $220. Calculate the following: Assume P = 10 as in part c)
Employment: Before and after the changes in parts h. and i.
Output: Before and after the changes in parts h. and i.
Real Profits (in terms of output) : Before and after the changes in parts h. and i.
Real Wages: Before and after the changes in parts h. and i.
What are the implications of this change in conditions on the government budget?
*****Did I calculate real profits and wages and what are the implications?
Before the changes in h and i:
|
Number of workers
|
Units of output
|
MPN
|
MRPN
|
Marginal Profit
|
Total Profit
|
|
0
|
0
|
-
|
-
|
-
|
-
|
|
1
|
48
|
48
|
480
|
270
|
270
|
|
2
|
88
|
40
|
400
|
190
|
460
|
|
3
|
119
|
31
|
310
|
100
|
560
|
|
4
|
144
|
25
|
250
|
40
|
600
|
|
5
|
166
|
22
|
220
|
10
|
610
|
|
6
|
184
|
18
|
180
|
-30
|
580
|
|
7
|
196
|
12
|
120
|
-90
|
490
|
After the changes in h and i:
|
Number of workers
|
Units of output
|
MPN
|
MRPM
|
Marginal Profit
|
Total Profit
|
|
0
|
0
|
-
|
-
|
-
|
|
|
1
|
53
|
53
|
530
|
310
|
310
|
|
2
|
98
|
45
|
450
|
230
|
540
|
|
3
|
134
|
36
|
360
|
140
|
680
|
|
4
|
164
|
30
|
300
|
80
|
760
|
|
5
|
191
|
27
|
270
|
50
|
810
|
|
6
|
214
|
23
|
230
|
10
|
820
|
|
7
|
231
|
17
|
170
|
-50
|
770
|