You are about to sign a contract with a book publisher. Under the terms of the contract the publisher has sole authority to set the price. The only issue is what percentage of the gross receipts you get. Is it always the case that you would want as high a percentage as possible? To make things concrete suppose the demand for the book as a function of its price p is 100-p. The unit cost of production and distribution of the book is $10. Suppose the author gets fraction α of the revenue generated.
1. Compute the publisher's pro?t maximizing price as a function of α.
2. Vary α between 0 and 1 and plot the author's gain.