Mictel Corporation has a world monopoly on the production of personal computers. It can make two kinds of computers: low end and high end. One-fifth of the potential buyers are casual users, and the rest are intensive users. The costs of production of the two kinds of machines as well as the benefits gained from the two, by the two types of prospective buyers, are given in the following table (all figures are in thousands of dollars): Benefit for User Type Cost Casual Intensive PC TYPE Low-end 5 High-end 3 Each type of buyer calculates the net payoff (benefit minus price) that he would get from each type of machine and buys the type that would give the higher net payoff, provided that this payoff is nonnegative. If both types give equal, nonnegative net payoffs for a buyer, he goes for the high end. Mictel wants to maximize its expected profit. However, Mictel does not know the type of any particular buyer. It just makes its catalog available for all buyers to choose from. Suppose the firm produces both types of machines, selling the low-end ones for price x and the high-end ones for price y. (a) If the firm wants the casual users to buy the low-end machines, it must satisfy the following incentive-compatibility constraint on x and y: (b) If the firm wants the intensive users to buy the high-end machines, it must satisfy the following incentive-compatibility constraint on x and y