Please help me on this one!

Question

You are planning to estimate a short-run production function for your firm, and you have the following data on labor usage and output:

Labor Output
3 1
7 2
9 3
11 5
17 8
17 10
20 15
24 18
26 22
28 21
30 23

A- Does a cubic equation appear to be a suitable specification, given these data? You may wish to construct a scatter diagram to help you answer this question.

B- Using a computer and software for regression analysis, estimate your firm short term production function using the data given here. Do the parameter estimates have appropriate algebraic signs? Are they statiscally significant at the 5 percent level?

C- At what point do you estimate marginal product begins to fall?

D- Calculate estimates of total, average, and marginal products when the firm employs 23 workers?

E- When the firm employs 23 workers, is short run marginal cost (SMC) rising or falling? How can you tell??

Answer 1

You still have two values of 17 labor with different outputs. That said, here goes.

A) I wish there was more data, but a skatterplot kinda looks like an S-curve, which can be generated with a Cubic. So, yes.
B) for y= ax + bx^2 + cx^3 + d
I get (parameter and t-statistic):
a=-.81426 (-1.30)
b=0.10442 (2.46)
c=.00183 (-2.17)
d=2.9235 (1.14)

Such parameters generate the shape shown in the skatter plot. With A cubic, its hard, a-priori to predict what the sign ought to be.
Only b is significant at the 5% level
C) the cubic is the total production function. Take the first dirivitive - this becomes the MP function. It has a maxima about 19. (check my math)
D) Plug 23 into the estimated cubic function and the derived MP function
E) since MP is falling at 23, SMC must be rising.

I hope this helps

Answer 2

my bad, the parameter for c in my response should be -.00183

Answer 3

Hi,economyst. Can you please show me the step by step solution for D)

thanks