$4.$ a$)$ Using the following table, find this monopolist$$s MR$,$ MC and ATC by using midpoint approach.

$$

P $($$$)$

Q

TR $($$$)$

MR $($$$)$

TC $($$$)$

MC $($$$)$

ATC $($$$)$

$12$

$0$

$$

$$

$10$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$11$

$1$

$$

$$

$17$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$10$

$2$

$$

$$

$18$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$9$

$3$

$$

$$

$21$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$8$

$4$

$$

$$

$30$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$7$

$5$

$$

$$

$48$

$$

$$

$$

$$ b$)$ Plot the demand curve $($D$),$ marginal revenue curve $($MR$),$ marginal cost curve $($MC$),$ and average total cost curve $($ATC$)$ in one diagram.

$$ c$)$ What is the profit$-$maximizing level of output. How much profit per unit and in total does the monopolist make?

$$ d$)$ What is the markup? Please show the deadweight loss on the same diagram of $($b$).$