E601 Final Exam: Take –Home. Bring your completed exam to class on 2/ 26. Those of you who are doing this remotely, e-mail me your completed exam no later than the beginning of our next class session.

Answer all parts of any 8 out of the following 10 items below. Remember there is always partial credit for partial displays of brilliance.

It was a pleasure having you in my class. I hope you all have a wonderful experience in your MBA program. Perhaps someday our paths will again cross!

  1. Determine the profit maximizing output for a firm exhibiting the following:

Demand Schedule: P = 4000 – 33Q

TC = 2Q3 – 3Q2 + 400 + 5000

Be sure to check the second order conditions to assure your solution is valid.

  1. Suppose a firm exhibits the following cost function:

TC = Q3 – 5Q2 + 60Q

  1. Is this firm operating in the long run or short run? How do you know?
  2. Find the level of output at which this would operate at minimum efficient scale.
  1. Given the following production function;

Q = 10K 0.7 L 0.1, where PK = 28 and PL = 10 and C = 4000

  1. Does this production function exhibit diminishing returns in both capital and labor? How do you know?
  2. Does this production function exhibit increasing, decreasing, or constant returns to scale? How do you know?
  3. Find the optimal levels of capital and labor that will maximize output.
  1. Given the following short run production function:

Q = 7.5L2 – 0.5L3

Find:

  1. The level of labor at which diminishing returns begins.
  2. The levels of labor at which stage II production begins and ends.
  1. Given what you know about profits, total revenue, and total cost, derive the break even formula.
  1. Draw the demand, marginal revenue, average total cost and marginal cost curves for a monopolistically competitive firm with;
  1. Positive economic profit.
  2. Negative economic profit.
  3. Explain briefly what might happen, if anything, to alter the situation you have depicted in the graphs.

7.Sally spends all of her income of $3,000 on goods x & y. The price of good x is $30 and the price of good y is $60. She is currently spending half of her income of each good and is maximizing her utility. (Assume her utility function is: U = xy)

  1. How much of each good is she consuming?
  2. What is Sally’s level of utility at equilibrium?
  3. Show Sally’s budget line and indifference curve at her equilibrium.

8.Using the initial information given in #7 above, show how a price reduction for good x would result in more good x being consumed, even if good x was considered an inferior good. (Hint: show the income and substitute effects of the price change graphically.)

9.The Crusader Company sells in two distinct markets. Each of the demand functions for the markets are given:

Q1 = 20 - 0.1P1

Q2 = 20 - 0.2P2

We have determined that this firm also incurs a marginal cost function of:MC = 10Q where Q = Q1 + Q2.

a. Find the optimal prices and output in each market under the conditions of price discrimination.

b. Suppose this firm was not allowed to discriminate on price. What should the firm charge for its product in both markets?

10.Payless Shoe Stores, Inc. cut the prices of women’s dress shoes by 2% during the first quarter and enjoyed a 4% increase in unit sales over the period compared to with a year earlier.

  1. Calculate the point price elasticity of demand for Payless Shoes.
  2. Calculate the company’s optimal shoe price if the marginal cost is $10 per unit.