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

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. 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’s short-run production function using the data given here. Do the parameter estimates have the appropriate algebraic signs? Are they statistically 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?