In a market where Q$($p$)=20002$p describes the demand curve, a monopoly firm operates

with a constant marginal cost of $100.$ The fixed cost of production is $1000.$

$($a$)$ Calculate the total revenue function and the marginal revenue function as a function

of Q$.$

$($b$)$ What is the optimal output and price of the profit$-$maximizing monopoly?

$($c$)$ Calculate the consumer surplus of the monopoly.

$($d$)$ How much producer surplus is generated by the monopoly? What about its profit?

$($e$)$ What would be the competitive equilibrium given the cost and demand structure of

the market?

$($f$)$ Calculate how much deadweight loss is caused by the monopoly.

$($g$)$ The government wishes to combat the undesirable allocational effects of a monopoly

through the use of a subsidy. Analyze the effect of the following subsidy $($Do they

achieve the government$$s goal?$)$:

$$ A lump$-$sum subsidy of $2000$

$$ A per$-$unit$-$of$-$output subsidy of $500$