1. Ace and Baumont Corporations make and sell electrical equipment. Both have to decide whether or not to discount. The payoff matrix of "Discount" and "Not to Discount" expressed in terms of profit (+) or loss (-) for each firm is given below for each combination of strategies.
Read my lecture note on game theory
Baumont Corporation
No Discount Discount
No Discount ($10mil, $10mil) (-$4mil, $16mil)
Ace Corporation
Discount ($16mil, -$4mil) (4mil, $4mil)
In the above matrix, the first number is for Ace and the second, for Baumont respectively.
a. What are the optimum strategy for each, the resulting profit/loss for each and why?
b. Is there any other strategy better than the one they took in (a), which makes each firm better off as opposed to the strategy taken? If there is, why did they not take it?
c. How would you compare this case to the so called "prisoner's dilemma" case? Explain it clearly.
d. How would you compare this case to the so called "Nash Equilibrium"? Explain the difference between this case and Nash Equilibrium clearly.
e. Does it matter whether this is one-shot deal or meant to be a situation in which each corporation faces continuously for some time? Why or why not?
f. Suppose that the profits for "discount strategy" for both Ace and Baumont are reduced to $8 millions from the current profit of $16 million respectively. The revised payoff matrix is shown below for your convenience.
Baumont Corporation
No Discount Discount
No Discount ($10mil, $10mil) (-$4mil, $8mil)
Ace Corporation
Discount ($8mil, - $4mil) ($4mil, $4mil)
What would be the optimum strategy for each and why?
g. What fundamental changes took place in the revised matrix above, which made the situation quite different from the original payoff matrix at the beginning? Please be succinct and to the point in your explanation.
h. How does such a corporation as General Electric use the concept involved in the revised payoff matrix above in its marketing strategy? Be specific in your explanation.
2. The Plymouth Software Company has the following demand curve with MC = $10 and P = 100 - Q with MR = 100 - 2Q. The company has option of charging monopolist price or perfect competitor price. Here it is assumed that monopoly demand curve is identical with market demand curve of perfectly competitive market (i.e., they share the same demand curve): Read my lecture note on Pure Competition and Monopoly
a. Compute profit maximizing price and output under perfectly competitive market and under monopoly. And compare the difference between them in terms of P and Q and discuss reason for the difference.
b. Compute consumer surplus under perfect competition and monopoly.
c. Is there any additional downside of monopolist vis-à-vis pure competition from a society's point of view in terms of Pareto's efficiency? Hint: reexamine consumer surplus discussed in (b).
d. Many amusement parks charge entrance fee and separate fees for each ride. In view of the above discussion, what do you think is the reason for it? Hint: consider consumer surplus.
e. What is the advantage for duopoly (two oligopoly firms) with equal size sharing the identical demand to behave as one monopolist and split the profit afterward rather than behave as two different firms under oligopoly? Under duopoly, each duopoly each firm would be able sell 30 units each. Present your arguments clearly with quantitative support for your answer.
f. Suppose that the two firms under the above duopoly have now two different demand curves, not one identical market demand curve; one is more elastic than the other. Would it be still advantageous for them to behave as one monopolist or not? Why or why not?