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 which it wishes to sell to performance artists, and a similar line of pianos that it markets under the Dundee name which it wants to sell to budget consumers. Although 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 instead that Rockway & Daughters tries to achieve incentive compatibility by raising the price of its Dundee line (but keeping the original price on Rockeways). Can it do this? And if so, what is the lowest price that achieves incentive compatibility? Explain your answer!

B)Consider the setting in the preceding subsection, but assume now that the company does not necessarily want to sell to all consumers. Suppose that there are 600 budget consumers and 400 performance artists in total. To which types of consumers (budget, performance, or both) will the company sell if it wants to maximize profits, and what is its resulting profit? Explain your answer!

d)Suppose now that the cost of producing Rockways and Dundee pianos were equal, and given at $6,000. Suppose that Rockway & Daughters still wants to sell one piano to each consumer but does no longer care which type of piano is sold to which type of consumer. Derive the price the (profit-maximizing) company would charge for Rockways!