Econ 4140/5140 Managerial Economics

Econ 4140/5140 Managerial Economics Dr. Michael Nieswiadomy Homework #2 Due date: Feb. 8, 2010

Show your work. Answer 100 points worth of questions.

1. (20 pts.) The total cost function at the Tate company is TC = 200 + 3Q + .5Q2, where TC is total cost, and Q is output. a. What is marginal cost (the derivative of TC with respect to Q) when Q = 1? b. What is marginal cost when Q = 5? c. What is marginal cost when Q = 10? d. Graph the TC function in Excel for values of Q ranging from 0 to 20 in increments of one.

2. (20 pts.) Find the partial derivative of Y with respect to X in each of the following cases: a. Y = 8 + 3X + 7Z b. Y = 8 X + 3X2 + 9Z c. Y = 8 X + 2X2 + 5Z + 2Z2 d. Y = X + Z e. Y = 8 X + 5X2 + 6Z + 4Z2 + 3XZ

3. (20 pts.) At the Peoria Company, the relationship between profit () and output (Q) is as follows:

 = -40 + 20Q – 4Q2

a. At what value of Q does d/dQ = 0? b. Is  minimized or maximized at the value of Q? c. What is the second derivative of  with respect to Q at this value of Q?

4. (25 pts.) Ilona Stafford manages a small firm that produces wool rugs and cotton rugs. Her total cost per day (in dollars) equals

2 2 C = 5X1 + 6X2 – 1.25X1X2,

where X1 equals the number of cotton rugs produced per day, and X2 equals the number of wool rugs produced per day. Because of commitments to retail stores that sell her rugs to consumers, she must produce ten rugs per day, but any mix of wool and cotton rugs is acceptable.

a. If she wants to minimize her costs (without violating her commitment to the retail stores), how many cotton rugs and wool rugs should she produce per day? (Do not use the method of Lagrangian multipliers.) b. Now, use the method of Lagrangian multipliers to solve the problem. c. Do you get the same answer as you do without using this method? d. What does  (lambda) equal? What does this mean?

1 5. (15 pts.) This is your first test as an economist in which you are asked to find real world data. What is the “median household income” (according to the 2000 U.S. Census) for your hometown ZIP code? If you were born outside of the United States, you may use your current ZIP cope. Hint: look at the link to U.S. Census Bureau on my web site. Print the page and mark with a highlighter your answer.