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
Does a cubic equation appear to be suitable specification, given these data? You may wish to construct a scatter diagram to help you answer the question.
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?
At what point do you estimate marginal product begins to fall?
Calculate estimates total, average, and marginal products when the firm employs 23 workers.
When the firm employs 23 workers, is short-run marginal cost (SMC) rising or falling? How can you tell?

Thank you for using the Jiskha Homework Help Forum BUT if you are trying to "cut and paste" it doesn't work here. You wil need to type out all the data.

Sra

To determine if a cubic equation is a suitable specification for the short-run production function, you can construct a scatter diagram using the labor usage and output data.

To create a scatter diagram:
1. Plot the labor usage data on the x-axis and the corresponding output data on the y-axis.
2. Connect the plotted points to observe the pattern of the data.

If the scatter diagram shows a curved pattern, a cubic equation may be a suitable specification. If the scatter diagram shows a linear or a different pattern, a cubic equation might not be appropriate.

To estimate the firm's short-run production function using regression analysis software, you can follow these steps:

1. Input the data into the regression analysis software, with labor usage as the independent variable and output as the dependent variable.
2. Conduct a regression analysis to estimate the parameters of the short-run production function.
3. Note the parameter estimates and their algebraic signs.

To determine if the parameter estimates are statistically significant at the 5 percent level, you can look at the p-values associated with each parameter estimate. If the p-value is less than 0.05, then the parameter estimate is considered statistically significant at the 5 percent level.

To estimate the point at which marginal product begins to fall, you can examine the labor usage-output data and observe where the rate of output increase starts to decline. This point indicates where marginal product begins to fall.

To calculate the estimates of total, average, and marginal products when the firm employs 23 workers, you can use the estimated short-run production function.

1. Plug in 23 for the labor usage variable in the estimated production function to estimate the total product at 23 workers.
2. Divide the total product by 23 to calculate the average product at 23 workers.
3. Calculate the marginal product by taking the difference in total product between 23 and 22 workers.

To determine if short-run marginal cost (SMC) is rising or falling when the firm employs 23 workers, you need to analyze the relationship between marginal cost and output.

1. Calculate the marginal cost by taking the difference in total cost between 23 and 22 workers.
2. If the marginal cost is increasing, then short-run marginal cost is rising. If the marginal cost is decreasing, then short-run marginal cost is falling.

By examining the change in marginal cost, you can determine whether it is rising or falling.