3. _ (2%) True or False: There is no contract, (p^c, x), such that the consumer will accept, and Firm C will make a strictly positive profit.

In fact, an exclusive dealing contract often contains a "penalty clause:" After signing the contract, if the consumer still wants to buy from other firms, he can do so by paying a penalty to the monopoly firm. In this case, of course, he also needs to pay the actual seller. Suppose that Firm C modifies the contract offer to the consumer: There is no sign-up bonus, and its price is p^c. If, after signing the contract, the consumer wants to buy from other firms, he needs to pay Firm C an amount of d. Other aspects of the game remain the same. 4. _ (3%) Suppose that the consumer has signed the contract, and Firm D has entered into the market. When Firm D sets its price at $p^D$, what condition should p^c, d, and p^D satisfy for the consumer to breach the contract and purchase from Firm D?

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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