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 $70, the second by $63, the third by $56, and so on, until the tenth unit increases profit by just $7.

The cost the upstream mill incurs for producing enough paper (one "unit" of paper) to make one unit of boxes is $7.50.

Assume the two mills operate as separate profit centers, and the paper mill sets the price of paper. It follows that the marginal profitability 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 foowing table, in the marginal revenue, tetai cost, and total prot for the paper mill when selling paper to the box mi' at each given price. Total Marginal Price Quantity Revenue Marginal revenue Total Cost Cost Prot (Marginal Prota_ hilitv t0 the {UNITS Of paper Box MI") equivalent to One ($3! BOX) ($1 ($1 ($J' ($3! ($J' m 1 m we 3 $150 was 2 we s 3 $150 we a ma s 3 $150 $49 4 $196 3 95 $150 $42 5 $210 9 13 $150 $35 a m s 13 $150 w ? mm s 13 $150 $21 s we 9, w a we 9' s \"'5\" $ $150 is? 10 Wu 3' [f the paper mill sets the price of paper to sell to the hex mill, it will set a price of V and sell 7 units of paper to the hex mill. Prets will be for the paper mill. Companvwide prots will be . (Hint: Recall that the prices in the table represent the marginal protability of each unit of paper, or box, to the box mill.) Suppose the paper mill is forced to transfer paper to the box mill at marginal cost ($150). In this caser the hex mill will demand V units of paper. This leads to wmpanywide prots _