Question

For the purposes of this problem, the quantity produced (?) will be measured in units of hundreds of customers per month. Prices and costs will be measured in “dollars per drinker”. “Dollars per drinker” is a measure of the price (or cost) for the mixture of beer, cocktails, and hard alcohol consumed by an average patron on an average night. Note that the units do not affect your method of solving the profit-maximization problem as long as the units are consistent. However, you should convert the quantities and prices back to single drinkers and dollars at the end.

There is a single liquor license for a small town held by a bar.

The bar faces the demand curve:

? = 30 − 0.5?

and has the cost function:

? = ? 2 + 6? + 48

a) Solve the monopolists’ problem (finding optimal quantity, price, and profit) with output as the choice variable and setting marginal revenue equal to marginal cost.

b) Solve the monopolists’ problem (finding optimal quantity, price, and profit) with output as the choice variable and setting marginal profit equal to zero.

c) Solve the monopolists’ problem (finding optimal quantity, price, and profit) with price as the choice variable and setting marginal profit equal to zero.

d) Graph the monopolists’ problem indicating demand, marginal revenue, marginal cost, average total cost, optimal output, optimal price, and profit

Answer 1