Suppose that a paper mill "feuds" a downstream bas mill. For the downstream mill, the marginal profitability of producing buses dacdines with volume. just $\backslash$$$3.$ represints the highest price that the box division would be willing to pay the paper division for boxes.. Furthermore, assume that fixid cests are for the papir mill.

The following table summariaes the quantity, total reveinue, and marginal costs from the perspective of the paper mill for selling paper to the box mill at vilribus prices.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

Price $\backslash \backslash$

$($Marginal Profitabitity to the Bax Mill$)($s$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Quantity $\backslash \backslash$

$($Uninits of Papitr equivialevat to Obe Boxy

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Total $\backslash \backslash$

Revenue

$(\backslash$$$)$

$\backslash$end$\{$tabular$\}$ & Marginal revenue

$(\backslash$$$)$ & Total Cost

$(\backslash$$$)$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Marginal $\backslash \backslash$

Cost

$(\backslash$$$)$

$\backslash$end$\{$tabular$\}$ & Profit

$(5)\backslash \backslash$

$\backslash$hline $530$ & $1$ & $\backslash (\backslash$$ $30\backslash )$ & & $50\mathrm{.}50$ & & $5\backslash \backslash$

$\backslash$hline $327$ & $2$ & $\backslash (\backslash$$ $54\backslash )$ & & & & $5\backslash \backslash$

$\backslash$hline $324$ & $3$ & $\backslash (\backslash$$ $72\backslash )$ & & $5$ & & $\backslash \backslash$

$\backslash$hline $321$ & $4$ & $\backslash$$$84$ & & $5$ & & $5\backslash \backslash$

$\backslash$hline $518$ & $5$ & $\backslash (\backslash$$ $00\backslash )$ & & $5$ & & $5\backslash \backslash$

$\backslash$hline $515$ & $6$ & $\backslash (\backslash$$ $00\backslash )$ & & $5$ & & $\backslash \backslash$

$\backslash$hline $512$ & $7$ & $\backslash (\backslash$$ $84\backslash )$ & & & & $\backslash \backslash$

$\backslash$hline $59$ & $8$ & $\backslash (\backslash$$ $72\backslash )$ & & $5$ & & $\backslash \backslash$

$\backslash$hline $36$ & $9$ & $\backslash (\backslash$$ $54\backslash )$ & & & & $\backslash \backslash$

$\backslash$hline $53$ & $10$ & $\backslash (\backslash$$ $30\backslash )$ & & $[$ & & $5\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

If the paper mil sets the price of paper to sell to the box mill, it will set a price of $\backslash (\backslash$qquad $\backslash )$ and sell $\backslash (\backslash$qquad $\backslash )$ urits of paper to the box mill. Profits mill be

for the paper mill. Companywide profits will be $-($Hint: flocall that the prices in the table rejpriseint the mar$$inal profitability of each unit of papet, or box, to the box mill.$)$

In this carke, the ber mill will demand $\backslash (\backslash$qquad $\backslash )$ units of papec. This leads to companywide profits of