Problem $7.$ A monopolist is operating in two separate markets where the corresponding

demands are

described by $p1=45-0\mathrm{.}5y1$ and $p2=30-y2.$ The monopolist's cost of production is

described by

c $(y)=(\frac{1}{6})y2,$ where $y=y1+y2.$

$($a$)$ Derive the monopolist's profit maximizing quantity, the resulting monopoly

price, and the monopolist's profits IF he cannot price discriminate.

$($b$)$ Derive the monopolist's profit maximizing quantities, the resulting monopoly

prices, and the monopolist's profits under price discrimination of third degree.

Compare the profits you find with those in part $($a$).$

$($c$)$ Can the monopolist do better than in $($a$),$ and$/$or $($b$)$ by just dropping one of the

two markets? Explain.