$19$th Assignment

Consider a monopolist with a total costs of $TC=16+\frac{1}{4}{Q}^2($and a marginal cost of $\frac{1}{2}Q,MC=\frac{1}{2}Q).$ The market demand curve is given by $P=32-\frac{1}{4}Q.$

Derive the marginal revenue curve

Find the monopoly price and quantity

Sketch the monopolist market and shade the region of profit on the graph.

Find the $($numerical$)$ value of the monopolist's profit.