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:

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

b. Using a computer for regression analysis, estimate your firm's short run production function using the data given here. Do the parameter estimates have the appropriate algebra signs? Are they statistically significant at the 5% 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?