Question

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 $20, the second by $18, the third by $16, and so on, until the tenth unit increases profit by just $2. The cost the upstream mill incurs for producing enough paper (one "unit of paper) to make one unit of boxes is $10.50. Assume the two mills operate as separate profit centers, and the paper mill sets the price of paper. It follows that the marginal profitability of boxes represents the highest price that the box division would be willing to pay the paper division for boxes.. Furthermore, assume that fixed costs are so for the paper mill. The following table summarizes the quantity, total revenue, and marginal costs from the perspective of the paper mill for selling paper to the box mill at various prices. In the following table, fill in the marginal revenue, total cost, and total profit for the paper mill when selling paper to the box mill at each given price. Total Revenue Quantity Marginal revenue Marginal Cost Total Cost Profit Price (Marginal Profitability to the Box Mill) ($) (Units of Paper equivalent to One Box) ($) ($) $10.50 $20 ($) $20 $36 $48 S18 $16 $14 $56 $12 $60 $10 AAAAA $08 $36 $20 If the paper mill sets the price of paper to sell to the box mill, it will set a price of bes for the paper mill. Company wide profits will be marginal profitability of each unit of paper, or box, to the box mill.) and sell units of paper to the box mill. Profits will . (Hint: Recall that the prices in the table represent the Suppose the paper mill is forced to transfer paper to the box millat marginal cost ($10.50). In this case, the box mill will demand units of paper. This leads to companywide profits of

Answer 1

P	Q	TR=P*Q	MR	TC	MC	Profit=TR-TC
20	1	20	20	10.5	10.5	9.5
18	2	36	16	21	10.5	15
16	3	48	12	31.5	10.5	16.5
14	4	56	8	42	10.5	14
12	5	60	4	52.5	10.5	7.5
10	6	60	0	63	10.5	-3
8	7	56	-4	73.5	10.5	-17.5
6	8	48	-8	84	10.5	-36
4	9	36	-12	94.5	10.5	-58.5
2	10	20	-16	105	10.5	-85

The paper mill will set the price where MR > MC and the profits are maximum. As seen from the above table, at P = 16 and Q = 3, profits are maximum and MR > MC. So, the paper mill will set a price of $16 and sell 3 units of paper to the box mill. Profits will be $16.5 for the paper mill.

Company-wide profits are (20+18+16) - 3*10.5 = 54 - 31.5 = $22.5

If paper mill transfers paper to the box mill, then the box mill demand 4 units of paper. This leads to companywide profits of

(20+18+16+14) - 4*10.5 = 68 - 42 = $26