$4.(20$ points$)$ Imagine now that the patent that granted our seller monopoly power expires, so new sellers offering their own version of widgets enter the market. The new sellers attract $5$ in $24$ of the total customer base of the original seller. Thus, the demand for our seller's original widgets is $\backslash (\backslash$frac$\{19\}\{24\}\backslash$cdot D$($p$)\backslash ),$ where $\backslash ($ D$($p$)\backslash )$ is the demand function you found in $1($c$).$

$($a$)(10$ points$)$ In this new context of monopolistic competition, how much output would the monopolist sell, and what price would the monopolist charge for their widgets?

$($b$)(5$ points$)$ In a $($hand$-$drawn$)$ graph, draw the demand curve, the MR curve, the MC curve, and the AC curve, and identify the optimal output and the monopoly price.

$($c$)(5$ points$)$ Compute the new Lerner Index for the seller.