Consider the problem of picking a price for an economics textbook. The marginal cost of production is constant at $20 per book. The publisher knows from experience that the slope of the demand curve is $.20: starting with a price of $48, a price cut of $.20 will increase the quantity of books demanded by 1 book. For example, here are some combinations of price and quantity:
Price 44 40 36 32 30
Quantity 80 100 120 140 150
a. Find the marginal revenue at each quantity?
b. What price will the publisher pick?
c. Suppose that the author receives a royalty payment equal to 10% of the total sales revenue from the book. If the author could pick a price, what would it be?
d. Why do the publisher and the author disagree about the price for the book?
e. Design an alternative author-compensation scheme under which the author and the publisher would pick the same price.