Problems: Chapters 21 and 22 4 . Individual Problems 22-]. Suppose that a paper mill "Feeds\" a downstream box mill. For the downstream mill.r the marginal protability of producing boa-05 declines with volume. For ample, the rst unit of boo-E increas earnings by $11]. the seoond by $3.. the third by $3.. and so on. until the tenth unit increass prot by just $1. The roost the upstream mill incurs for producing enough pap-er {one"unit" of paper] to [raise one unit otboaoE is $3.50. Assume the two n'l'lls operate as separate prot centers. and the paper mill sets the price of paper. It follows that the marginal protability of bounces reprers the highst price that the boon: division would be willing to pin.r the paper division For bows" Furthermore. assume that xed costs are 51] for the paper mill. The Following lable summaries the quantity, total revenue. and n'arginal oosls From the perspective of the paper mill for selling paper to the bout mill at various pricE. In the following table, ll in the marginal revenue, total cost. and total prot lbr the paper mill when selling paper to the box mill at each given once. Total Marginal Price Quantitvr Revenue Marginal revenue Total Cost Cost Prot [Marginal Pl'll'lahili'tv til m oFPaper the B\" "'1" Equivalent to IT} One Band {5) l5} (5') l5} {5'} $10 1 $111 5.3.5:] 5 5 22-22 :5 2 2 22 : $2 2 $22 E 53'5\" :2 * * l:l 2-22 22 2 222 :2 22-22 22 2 222 :2 22-22 22 2 222 :2 5 22-22 5 ? 23 :l *4 * l:l 5 22-22 5 2 2 22 : * * l:l 2-22 22 2 222 :2 22-22 22 22 222 :2 Ifthe paper mill sets the price at paperto sell to the bot: millr it will set a price of V and sell T unils otpaper to the ho}: mill. Pruls will be for the paper mill. Cormanfwide prols will tie . (Hint: Recall that the pl'iDE 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 tlanster paperbo the box mill at marginal DDEl: [$1.51) In this case. the boon: mill will derrand '7 units of paper. This leads to oomparrywide prots _ . N Save 8. Continue Continue without saving 3