# Open Excel and answer the following questions. Save the workbook when you are done. 1. Starting…

Open Excel and answer the following questions. Save the workbook when you are done.

1. Starting from a blank workbook, with K = 100, draw total, marginal, and average product curves for L = 1 to 100 by 1 for the Cobb-Douglas production function, Y = LαKβ, where α = 3/4 and β = 1/2. Use the derivative to compute the marginal product of labor. Hint: Label cells in a row in columns A, B, C, and D as L, Q, MPL, and APL. For L, create a list of numbers from 1 to 100. For the other three columns, enter the appropriate formula and fill down. For MPL, do not use the change in Q divided by the change in L; instead use the derivative for the MPL at a point.

2. For what range of L does the Cobb-Douglas function in question 1 exhibit the Law of Diminishing Returns? Put your answer in a text box in your workbook.

3. Determine whether this function has increasing, decreasing, or constant returns to scale. Use the workbook for computations and include your answer in a text box.

4. From your work in question 3 and the comment in the text that you cannot have constant returns to scale “if the exponents in the Cobb-Douglas function do not sum to 1,” provide a rule to determine the returns to scale for a Cobb-Douglas functional form.

5. Is it possible for a production function to exhibit the Law of Diminishing Returns and increasing returns to scale at the same time? If so, give an example. Put your answer in a text box in your workbook.

6. Draw an isoquant for 50 units of output for the Cobb-Douglas function in question 1. Hint: Use algebra to find an equation that tells you the K needed to produce 50 units given L. Create a column for K that uses this equation based on L ranging from 20 to 40 by 1 and then create a chart of the L and K data.

7. Compute the TRS of the Cobb-Douglas function at L = 23, K = 312.5. Show your work on the spreadsheet.