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

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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.