A monopolist is operating in two separate markets where the corresponding demands are

described by p$1=450\mathrm{.}5$y$1$ and p$2=30-$ y$2.$ The monopolist's cost of production is described by

c $($y$)=(1/6)$ y$2,$ where y $=$ y$1+$ y$2.$

$($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.