Question

In: Economics

You are planning to estimate a short- run production function for your firm, and you have...

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?

Solutions

Expert Solution

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.


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