In: Economics
You are planning to estimate a short- run production function for your firm, and you have collected the following data on labor usage (L) and output (Q):
Labor usage | Output |
3 | 1 |
7 | 2 |
9 | 3 |
11 | 5 |
17 | 8 |
17 | 10 |
20 | 15 |
24 | 18 |
26 | 22 |
28 | 21 |
30 | 23 |
a. Please key in the data into MS Excel for regression analysis.
Estimate your firm’s
short-run production function. Do the parameter estimates have the
appropriate algebraic
signs? Are they statistically significant at the 5 percent
level?
b. At what point do you estimate marginal product (MP) begins to
fall?
c. Calculate estimates of average products (AP) and marginal
products (MP) when the
firm employs 20 workers.
d. When the firm employs 20 workers, is short-run marginal cost
(MC) rising or falling?
How can you tell?
a.
SUMMARY OUTPUT |
||||||
Regression Statistics |
||||||
Multiple R |
0.98048 |
|||||
R Square |
0.96135 |
|||||
Adjusted R Square |
0.95705 |
|||||
Standard Error |
1.75423 |
|||||
Observations |
11 |
|||||
ANOVA |
||||||
df |
SS |
MS |
F |
Significance F |
||
Regression |
1 |
688.85 |
688.85 |
223.85 |
1.15357E-07 |
|
Residual |
9 |
27.70 |
3.08 |
|||
Total |
10 |
716.55 |
||||
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
-4.3350 |
1.1914 |
-3.6388 |
0.0054 |
-7.0300 |
-1.6400 |
Labor usage |
0.9150 |
0.0612 |
14.9615 |
0.0000 |
0.7767 |
1.0534 |
Production function: Output = -4.33 + 0.915*Labor Usage
Yes, the labor usage and output are positively related and hence the sign positive for labor usage is justified
Yes, the coefficient of labor usage is significant at 5 percent level as the P-value is less than 0.05
b.
When the firm employs 17th labor, we can observe that the marginal product starts to decline
Labor usage |
Output |
MP=(change in output)/(change in labor) |
AP = Output/Labor |
3 |
1 |
||
7 |
2 |
0.250 |
0.286 |
9 |
3 |
0.500 |
0.333 |
11 |
5 |
1.000 |
0.455 |
17 |
8 |
0.500 |
0.471 |
17 |
10 |
0.588 |
|
20 |
15 |
1.667 |
0.750 |
24 |
18 |
0.750 |
0.750 |
26 |
22 |
2.000 |
0.846 |
28 |
21 |
-0.500 |
0.750 |
30 |
23 |
1.000 |
0.767 |
c.
MP at 20 the labor = (15-10).(20-17) = 1.67
AP at 20th labor = 15/20 = 0.75
d. The marginal cost is rising as we can observe that the marginal product decreases which indicates about increasing cost as the productivity falls.