5. _ (6%) To maximize profit, what value of the penalty d should Firm C choose? And what is its optimal profit?

Lastly, games played by consumers may also affect the competitive effect of exclusive dealing. Suppose now that there are three identical consumers, E, F, and G. Each consumer purchases at most one unit of product, and enjoys the consumption value ($4). For the next two questions, suppose that Firm D faces a higher entry cost, 3 < f < 9/2. But the marginal cost of the two firms remains the same as before. Consider the following exclusive dealing contract. Firm C simultaneously offers the same conditions to all three consumers: The price (p^C) is $4, the sign-up bonus (x) is $0.01, and the penalty (d) is $10. Consumers simultaneously decide whether to accept the contract. Then, Firm D observes the content of the contract and how many consumers have signed, and makes entry decision accordingly. Other aspects of the game remain the same. 6. _ (6%) Describe the best response of consumer E as a function of the acceptance or rejection decision of other two consumers.

7. _ (3%) Find out all the pure strategy Nash equilibrium of the game played by consumers.

IV. Consider a series of two-person two-commodity exchange economy. In each case, the two agents have the same endowments: each has one unit of good 1, and one unit of good 2. We normalize the price of good 2 to p2 = 1, and look for the competitive equilibrium, that is, both agents are price takers. Find out all, if any, of the equilibrium price of good 1, p1^+, according to the utility function specified in each case (where x_j^i denote Agent i's consumption of good j). 1. _ (4%) Agent H has a utility function u^H = min{x1^H, x2^H}; Agent I has a utility function u^I = min{x1^I, x2^I}.

2. _ (3%) Agent J has a utility function u^J = min{x1^J, x2^J}; Agent K has a utility function u^K = max{x1^K, x2^K}.

3. _ (3%) Agent L has a utility function u^L = max{x1^L, x2^L}; Agent M has a utility function u^M = max{x1^M, x2^M}.

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