13. Rockway & Daughters Piano Co. wishes to sell a piano to everyone. But some consumers are budget-conscious, and others are not, and unfortunately, Rockway cannot tell which is which.

So, Rockway produces a premium line of pianos that it markets under the Rockway name, and a similar line of pianos that it markets under the Dundee name. While the cost of producing these pianos is quite similar, all consumers agree that Rockway pianos are of higher quality than Dundee pianos, and would be willing to pay more for a Rockway. Budget-conscious consumers feel that Dundee pianos are worth $6,000, and Rockways are worth $8,000. Performance artists believe that Dundee pianos are worth

$7,000 and Rockways are worth $12,000.

a. Suppose Rockway & Daughters prices its Dundee pianos at $5,000 and its Rockway pianos at $10,500. Are these prices incentive compatible — that is, will more price-conscious consumers purchase the Dundee line, while more performance-oriented players choose the Rockway? Explain.

b. How much must Rockway & Daughters reduce the price of its Rockway line in order to achieve incentive compatibility?

c. Suppose instead that Rockway & Daughters tries to achieve incentive compatibility by raising the price of its Dundee line. Can it do so? And if so, how?