$1.(2$ points each, $14$ points total$)$ A monopolist can produce at constant average and

marginal cost ATC $=$ MC $=5.$ The firm faces a market demand curve given by P

$=53-$ Q$.$

$(1)$ Calculate the profit$-$maximizing price$-$quantity combination for the monopolist.

Also calculate the monopolist's profits.

$(2)$ What output level would be produced by this industry under perfect

competition $($where price $=$ marginal cost$)?$

$(3)$ Calculate the consumer surplus obtained by consumers in case $(2).$ Show that

this exceeds the sum of the monopolist profit and the consumer surplus

received in case $(1).$ What is the value of the deadweight loss" from

monopolization?

$(4)$ Suppose that another firm identical to the monopolist entered the industry, the

market demand remains at P$=53-$Q$,$ where Q$=$Q $1+$Q$2.$ In the Cournot

equilibrium, what is the total output?