Exercise Set 11
MARGINAL PRODUCT OF LABOR

I. Objectives

• To understand the Law of Diminishing Marginal Returns
• To understand the concepts of Marginal Product (of an input) and Marginal Revenue Product (of an input)
• To determine the amount of labor a firm should hire (given MP_L, the wage rate, and the output price)

II. Data

• A firm's production function is: Q = aL - bL², where Q is output, L is labor, and a and b are positive constants.
• The corresponding Marginal Product of Labor is: MP_L = a - 2bL.
  [Technical note: The derivative of Q with respect to L yields MP_L.]
• Using the calculator below:
  1. Select values for a, b, the wage rate (W) and the price of the output (P).
  2. Obtain the firm's optimal number of workers (L*).
  3. Click on Gimme Love's Labors Lost! to confirm.

III. Questions

1. Select values for the parameters: a = ______,   b = ________.
2. Obtain the MP_L function.
3. Sketch the MP_L function with L on the horizontal axis.
4. Does the production function exhibit the Law of Diminishing Marginal Productivity? Explain.
5. Select values for the wage rate and the price of output: W = ______,   P = ________.
   1. Obtain, and sketch, the MRP_L function.
   2. Determine the optimal quantity of labor demanded by the firm (L^*).
6. What is the change, if any, in MP_L, MRP_L and L^* as a result of:
   1. An increase in the wage rate?
   2. A decrease in the price of output?
   3. An increase in a? [What does an increase in a mean? Look at the production function.]
7. If the wage rate decreases, ceteris paribus, the firm will find it optimal to hire [ more / fewer ] workers. Explain.
8. If the price of output rises, ceteris paribus, the firm will find it optimal to hire [ more / fewer ] workers. Explain.

IV. Additional Questions

1. Define the following terms:
   1. Marginal product
   2. Marginal revenue
   3. Marginal revenue product
   4. Average product
   5. Total product
2. The Bogey Company uses steel to produce golf clubs. The price of a pound of steel is $45. Bogey sells golf clubs in the market at a price of $25 each. The firm's production function is given in the table below:

   Steel (lb)	Number of golf clubs produced	MPL (no. of clubs per lb of steel)	MRPL ($ per lb of steel)
   3	28
   4	35
   5	41
   6	45
   7	47
   8	47

   1. Does the given data exhibit the law of diminishing marginal returns? Assume a value for the marginal product of the 3rd pound of steel.
   2. Complete the table above.
   3. In order to maximize profits, Bogey will use ______ pounds of steel and produce ________ golf clubs. At the optimal point, the marginal revenue product of steel is $_______/lb. Explain.
   4. Suppose Bogey is able to charge a higher price for its clubs. Ceteris paribus, will the firm use more steel, or less, as a result? Explain, using above table.
   5. Suppose Bogey has to pay a higher price for the input (steel). Will the firm increase its output of clubs, ceteris paribus? Explain.
3. Dell produces personal computers (PCs) using labor, capital stock and components (chips, hard drives, etc.) as inputs.
   1. What information does Dell's production function provide?
   2. Explain what the marginal revenue product of labor (MRP_L) means in this case.
   3. Dell is currently using 100 workers to produce 5000 PCs. Construct an example using 101, 102, 103, 104 and 105 workers, and corresponding output levels, to illustrate the law of diminishing marginal returns. Provide a sketch of MP_L, using your numbers.