Consider a small isolated town in which a brewery faces the following inverse demand: P Q $=150\mathrm{.}33.$ The brewery can produce beer at a constant marginal and average total cost of $$1$ per bottle. a$.$ Calculate the profit$-$maximizing price and quantity, as well as producer and consumer surplus and the deadweight loss from market power. b$.$ If it were possible to organize the townsfolk, how much would they be willing to pay the brewery to sell beer at a price equal to its marginal cost? c$.$ What is the minimum payment the brewery would be willing to accept to sell beer at a price equal to marginal cost? d$.$ Is it possible for consumers and the brewery to strike a bargain that results in gains for both?