Consider a monopolist whose product is unknown to consumers. All consumers are identical with demand Q $=20$ P$.$ The monopolist cost of production is zero. For a consumer to learn about the product they must receive an ad from the monopolist. Sending ads are costly to the monopolist. Specifically, to reach n consumers it would cost the monopolist n$2($cost of advertising$).$ Solve for the profit maximizing level of advertising $($remember: think ahead and solve back$).$ Solve for the welfare maximizing level of advertising. Explain the difference. $($Not covered in class: what is the first best outcome? To do this, find the first best output, and then from that the level of advertising that is first best.$)$