The Madison Corporation, a monopolist, receives a report from a consulting firm concluding that the

demand function for its product is

Q $=72-2$P $+2\mathrm{.}8$Y $+0\mathrm{.}82$A

where Q is the number of units sold, P is the price of its product $($in dollars$),$ Y is per capita income

$($in dollars$),$ and A is the firm$$s advertising expenditure $($in dollars$).$

The firm$$s average variable cost function is

AVC $=654$Q$+2$Q$^2$

where AVC is average variable cost $($in dollars$).$

a$)$ Can you calculate the firm$$s total variable cost curve? If yes, show your calculations. $[2$ marks$]$

b$)$ Can you calculate the firm$$s marginal cost curve from the total variable cost curve you found

above? If yes, show your calculations. $[2$ marks$]$

c$)$ Can you calculate the firm$$s marginal revenue curve? Show your calculations. $($Hint: MR will be a

function of A$,$ Y and Q$)[5$ marks$]$

d$)$ If per capita income is $$7,500$ and advertising expenditure is $$185,000,$ can you calculate the

output where marginal revenue equals marginal cost? Show your calculations. Round final answer to

the nearest whole number. $($Hint: Use the quadratic formula$)$