Economics 5315Fall 1999

Managerial EconomicsProfessor Henderson

Final Exam

  1. The Zinger Company manufactures and sells a line of sewing machines. Monthly demand for one its most popular models is given by the following relationship:

Q = 400 – 0.5P

where P is price and Q is quantity demanded. Total costs of production (including a “normal” return on owners’ investment) per month are:

C = 20,000 + 50Q + 3Q2

  1. Express total profits () in terms of Q.
  2. At what level of output are total profits maximized? What price will be charged? What are total profits at this output level?
  3. What market structure did you assume? Why?
  4. Would your answers in b change if the market for sewing machines were competitive? How? (Specify price, quantity, and profit levels.)
  1. Zar Island Gas Company is the sole producer of natural gas in the remote island country of Zar. The State Energy Commission regulates the company’s operations. The demand function for gas in Zar has been estimated as:

P = 1,000 – 0.2Q

where Q is output (measured in gas units) and P is price (measured in dollars per gas unit). Zar Island’s cost function is:

C = 300,000 + 10Q

This cost function does not include a “normal” return on the firm’s invested capital of $4 million.

  1. In the absence of any government price regulations, determine Zar Island’s optimal (i) output level, (ii) selling price, (iii) total profits, and (iv) rate of return on its asset base.
  2. The State Energy Commission has ordered the firm to charge a price that will provide it with no more than a 12 percent return on its total assets. Determine Zar Island’s optimal (i) output level, (ii) selling price, and (iii) total profits under this constraint. You will need to use the quadratic equation on the next page to solve this problem.
  3. Is this a perfectly competitive solution? Why or why not?


  1. Two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following demand function:

P = 10,000 -Q

where Q = QA + QB are the quantities sold by the respective firms and P is the selling price.

Total cost functions for the two companies are:

CA = 500,000 + 200QA + 0.5QA2

CB = 200,000 + 400QB + QB2

  1. Assume that the two firms act independently as in the Cournot model. Determine the long run output and selling price for each firm. What are there respective profit levels?
  2. Assume the firms form a cartel. Determine the optimal output and selling price for each firm. How have profits changed?
  3. What problems will the cartel face? How can these problems be addressed successfully?
  1. The major oil producing countries (OPCs) face a classic prisoner’s dilemma. If they can maintain reduced output, oil prices will remain high. But the temptation to produce beyond established quotas is compelling, making it difficult to keep prices high. The payoff matrix below may be a good representation of the game faced by the OPCs.

OPC2

High PriceLow Price

OPC1

High Price 14

Low Price

  1. If viewed as a simultaneous game with no collusion, what is the dominant strategy? What will OPC1 and OPC2 decide to do in a one-play game? Why?
  2. How will your analysis change if the game is viewed as a repeated game? Why?
  3. What are some of the reasons that collusion is difficult to maintain?
  1. The demand functions for a firm producing products A and B jointly in fixed proportions are:

PA = 18 – 0.1QA

PB = 10 – 0.1 QB

  1. Determine the best level of output and price for products A and B if marginal cost (MC) = 8 + 0.1Q.
  2. How does your answer change if MC = 2Q/35? Explain.

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