The paper mill feeds a downstream box mill. The box mill's profit from each additional unit of boxes declines from $30 to $3. It costs the paper mill $9.50 to produce enough paper for one box. If the paper mill sets the paper price, it will maximize total profits by setting the price equal to the box mill's marginal profit from each additional box. At this price, company profits will be maximized. If the paper mill must transfer paper at its marginal cost of $9.50, the box mill will demand 10 units of paper, leading to total company profits of $24.

1. Suppose that a paper mill "feeds" a downstream box mill. For the downstream mill, the marginal
profitability of producing boxes declinies with volume. For example, the first unit of boxes
increases earnings by $30, the second by $27, the third by $24, and 50 on, until the tenth unit
increases profit by just $3 The cost the upstream mill incurs for producing enough paper (one
"unit" of paper) to make one unit of boxes is $9.50. Assume the two milis operate as separate
profit centers, and the paper mill sets the price of paper, It follows that the marginal profitabllity
of boxes represents the highest price that the box division would be willing to pay the paper
division for boxes.. Furthermore, assume that fixed costs are $0. for the paper mill. The
following table summarizes the quantity, total revenue, and marginal costs from the perspective
of the paper mill for selling paper to the box mill at various prices. In the foilowing tabie, fill in
the marginal reveaue, total cost, and total arofit for the paper mulil when seiling oaper to the
bour mill at each given price.
If the paper mill sets the price of paper to sell to the box mill, it will set a price of and sell for the
paper mill, Companywide profits will be units of qper to the box mill. Profits will be the
marginal profitability of each unit of paper; or box, to the box mill.) (Hint: Recall that the prices
in the table represent Suppose the paper mill is forced to transter paper to the box mill at
marginal cost ($9,50). In this case, the box mili. will demand units of paper. This leads to
companywide prorits of