$(2022$ Fall Final Q$59-64)$ A monopolist faces a demand curve of $\backslash ($ P$=200-0\mathrm{.}1$ Q $\backslash )$ and has a constant marginal cost of $\backslash (\backslash$$ $5\backslash )$ per unit.

$($a$)$ Assume zero fixed cost of production. To maximize profit, the monopolist produces units and charges $\backslash (\backslash$$ $\backslash )$ per unit.

$($b$)$ Assume zero fixed cost of production. If the government imposes a price ceiling at $\backslash (\backslash$$ $6\backslash )$ per unit, the monopolist will produce units.

$($c$)$ Assume zero fixed cost of production. If the government imposes a price ceiling at $\backslash (\backslash$$ $6\backslash )$ per unit, the deadweight lossa. increasesb. decreases

by $\backslash$$ compared to an unregulated market.

$($d$)$ Suppose fixed cost of production is non$-$zero. If the government imposes a price ceiling at $\backslash (\backslash$$ $6\backslash )$ per unit, the monopolist will not exit the market in the long run if the fixed cost isa. higherb. lower

than $\backslash$$

$($e$)$ Suppose the fixed cost of the monopolist is $\backslash (\backslash$$ $47531\backslash ).$ The lowest ceiling price that can be imposed by the government in the long run is $\backslash (\backslash$$ $\backslash )$ per unit.

$($f$)$ Assume zero fixed cost of production. If the government provides a per$-$unit subsidy of $\backslash (\backslash$$ $1\backslash )$ to the monopolist, the deadweight loss in this market is $\backslash (\backslash$$ $\backslash )$