Suppose that a paper mill “feeds” a downstream box mill. For the downstream mill, the marginal profitability of producing boxes declines with volume. For example, the first unit of boxes increases earnings by $10, the second by $9, the third by $8, and so on, until the tenth unit increases profit by just $1. The cost the upstream mill incurs for producing enough paper to make one unit of boxes is $3.50.

a. If the two companies are separate profit centers, and the upstream paper mill sets a single transfer price (the price the box company pays the paper mill), what price will it set, and how much money will the company make?

b. If the paper mill were forced to transfer at marginal cost, how much money would the company make?