Problem $2$: Monopoly Price Discrimination $[10$ Points$]$Suppose that a Monopolist has no fixed costs and a fixed Marginal Cost equal to $$4$ per unit. This monopolist also faces the demand: $=285.[3$ points$]$ If this monopolist is a single$-$price monopolist, then what price would it charge and what Quantity would it produce? What would be the Consumer Surplus $($CS$),$ Producer Surplus $($PS$),$ and Total Surplus $($TS$)$ in the single$-$price case?Now suppose that this firm can first$-$degree price discriminate$\mathrm{.}6.[2$ points$]$ What would be the Consumer Surplus $($CS$),$ Producer Surplus $($PS$),$ and Total Surplus $($TS$)$ in the case where this monopolist can first$-$degree price discriminate?Now suppose that this firm cannot first$-$degree price discriminate, but can instead second$-$degree price discriminate. Now suppose that this monopolist offers the menu of: $12$ units for p $=$ $$1618$ units for p $=$ $$107.[2$ points$]$ Will the above make consumers better off? Will it make firms better off?Now suppose that this monopolist continues to second$-$degree price discriminate, but offers the a different menu of: $9$ units for p $=$ $$1914$ units for p $=$ $$148.[3$ points$]$ What is the new Consumer Surplus $($CS$),$ Producer Surplus $($PS$),$ and Total Surplus $($TS$)$ in this second$-$degree price discrimination case?