Part I - Key assumptions and conclusions of Oligopoly models:

1. The Cournot Model:

a. List the main assumptions and the main conclusions of the Cournot model.

b. Do you agree with the conclusions of the model?

2. Cartel Model:

a. List the main assumptions and the main conclusions of the Cartel model.

b. Outline the steps used to determine the price and output of the Cartel.

c. Would you expect the equilibrium output and price under the Cournot model to be higher or lower than the output and price under the Cartel model? Explain why your group thinks so.

3. The Stackelberg Model:

a. Discuss the main assumptions and the main conclusions of the Stackelberg model

b. Outline the steps used to determine the price and output under a Price Leadership environment.

4. The Kinked Demand Curve

a. Describe the main assumptions and conclusions of the Kinked Demand Curve model. Do they make sense to you? Why or why not?

b. Outline the steps used to determine the price and output given the assumptions of the model. 

c. Provide some examples of firms whose decisions may be constrained by a kinked demand curve.

2. Application of Theory: Comparting Perfect Competition, Monopoly, Cournot, Stakelberg

Two rival companies sell health care software packages that are perfect substitutes. The software is used by medical doctors to digitize patient records. Both companies' fixed costs are completely amortized and variable costs $15 per package. The demand for the software is Q = 1800 - 5P. Determine the quantity that each firm would sell and the price they would charge if these two firms made decisions as:

a. Perfect competitors

b. Cournot duopolists

c. Stakelberg duopolists

d. Monopoly

3 Application of Theory: Two firms with different marginal cost

Gray Computer, Inc., located in Colorado Springs is a producer of high-speed electronic supercomputers with immense storage capacity and computing capability. The company has profitably exploited its market niche by renting out storage space to industrial users and a few large government agencies (e.g., Department of Health, NASA, National Weather Service, etc.). Suppose a potential entrant into the market for supercomputers has asked you to evaluate the potential for this market. The following market demand and cost information has been developed for Gray Computer, Inc.:

P =  $54 - $1.5Q,

TC_A =  $200 + $6Q_A + $0.5Q_A²      (MC_A=6+Q_A)

where P is the market price (millions of dollars), Q is units measured by the number of supercomputers, per year, TC is total costs including a normal rate of return (assume that it is possible to rent out a fraction of a computer).

If your company entered the market for supercomputer it would have the following total cost function

TC_B = 100 + 14Q_B +1.5Q_B².      (MC_B=14+3Q_B)

Also, it would have to compete based on a Cournot duopolist model. Assuming that the market demand would not change and that no other near-term entrants are anticipated, would you recommend your company to enter the market for supercomputers? Support your recommendation with information about the level of output and profits that would be generated by this venture.