Suppose a monopolist faces a market demand curve given by Q = 300 - P. Marginal cost is constant at $30 per unit, and fixed cost is equal to $10,000.

What is the profit-maximizing allocation (price and quantity) for the monopolist? Draw the graph too.

What is the efficient or socially optimal allocation? [Hint: This would be the allocation that equates the marginal benefit (given by demand) to the marginal cost, so that price would equal marginal cost.]

Suppose the government institutes a price ceiling at the socially optimal price you determined in part b. Under this price ceiling, what quantity would the firm choose to produce (at least in the short run)?

What is average variable cost? [Hint: Given that MC is constant, you can easily determine AVC. If you are unsure, make a table.]

Give the equation for total cost as a function of Q. [Hint: Remember that total cost equals total variable cost plus total fixed cost. I'm looking for you to write equation of the form: TC = (some number) + (some other number).]

Give the equation for average total cost. One way to figure this out is by recalling that ATC = TC/.

Can the government achieve the socially optimal allocation (in the long run) using only a price control? Why or why not? [Hint: Will the firm be profitable in the long run? How do you know?]