1. Individual Problems 22-1 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 $30, the second by $27, the third by $24, and so 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 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 $0 for the paper mill. The following table summarizes the quantity, total revenue, and marginal costs from the perspective of the paper mill for selling paper to the box mill at various prices. In the following table, fill in the marginal revenue, total cost, and total profit for the paper mill when selling paper to the box mill at each given price. Total Marginal Price Quantity Revenue Marginal revenue Total Cost Cost Profit ( Marginal Profitability to (Units of Paper the Box Mill) equivalent to ($ One Box) ($) ($) ($) ($) ($) $30 $30 $9.50 $ $9.50 $27 $54 $ W N $9.50 $24 $72 $ $9.50 $21 $84 $ $9.50 $18 $90 $9.50 $15 6 $90 $9.50 $12 $84 CO $9.50 $9 $72 $9.50 $6 LD $54 $9.50 $3 10 $30In the following table, fill in the marginal revenue, total cost, and total profit for the paper mill when selling paper to the box mill at each given price. Total Marginal Price Quantity Revenue Marginal revenue Total Cost Cost Profit (Marginal Profitability to $3 (Units of Paper the Box Mill) equivalent to ($) One Box) ($) ($) $6 $ ($) ($) $30 $30 $9 $9.50 $ $27 $ $54 $9.50 N $ $ $12 $24 $9.50 W $72 $ $ $21 4 $9.50 $84 $15 $ $ $18 5 $9.50 $90 $ $18 $ $15 6 $9.50 $90 $12 $84 $21 $9.50 $9 $9.50 CO $72 $ $24 $ $6 9 $9.50 $54 $ $3 $9.50 10 $30 $27 $ $30 If the paper mill sets the price of paper to sell to the box mill, it will set a price of * and sell * units of paper to the box mill. Profits will be $ for the paper mill. Companywide profits will be $ . (Hint: Recall that the prices in the table represent the marginal profitability 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 ($9.50). In this case, the box mill will demand units of paper. This leads to companywide profits of $In the following table, fill in the marginal revenue, total cost, and total profit for the paper mill when selling paper to the box mill at each given price. Total Marginal Price Quantity Revenue Marginal revenue Total Cost Cost Profit (Marginal 1 Profitability to (Units of Paper the Box Mill) equivalent to 2 ($) One Box) ($) ($) ($) ($) ($) $30 $30 $9.5 3 $9.50 $27 N $54 4 $9.50 $24 W $72 69 $9.50 $21 $84 5 $9.50 $18 un $90 6 $9.50 $15 $90 $9.50 $12 $84 $9.50 $9 CO $72 8 $9.50 $6 9 $54 V $ $9.50 10 $30 $ 10 If the paper mill sets the price of paper to sell to the box mill, it will set a price of and sell units of paper to the box mill. Profits will be for the paper mill. Companywide profits will be | $ . (Hint: Recall that the prices in the table represent the marginal profitability 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 ($9.50). In this case, the box mill will demand * units of paper. This leads to companywide profits of $In the following table, mi in the marginal revenue, total cost, and tote.i profit for the paper mill when selling paper to the box mill at each given price. Total Marginal Price Quantity Revenue Marginal revenue Total Cost Cost Profit (Marginal Profitability to (Unis of Paper the Box "'ll) equivalent to (5) 059 Box} 1' 5) ($) (5) (S) {5) $30 1 $30 $9.50 5 2222 : $22 2 $22 :2 22-22 $22 2 $22 :2 2222 $22 2 $22 :2 22-22 $22 2 $22 :2 22-22 $22 2 $22 :2 22-22 $22 2 $22 :2 22-22 $2 2 $22 :2 22-22 $2 2 $22 A :2 22-22 $2 22 $22 :2 If the paper mill sets the price of pap. for the paper mill. marginal protability of each unit of p Suppose the paper mill is forced tot ,_. D to the box mill, it will set a price of V and sell V units of paper to the box mill. Profits will be nvwide prots will be 5 box, to the box mill.) .per to the box mill at marginal cost {$9.50). In this caser the box mill will demand V units of paper. This leads to companywide profits of . . (Hint: Recall that the prices in the table represent the