Suppose that a monopolist's market demand and total cost equations are

Q = 8 - 0.5P,

TC = Q + 0.5Q2 .

2.1 (2 points) Derive inverse demand, total revenue, marginal revenue and marginal cost equations.

Inverse demand equation: P = f(Q) = _______________________________

Total revenue equation: TR = f(Q) = _______________________________

Marginal revenue equation: MR = f(Q) = ___________________________

Marginal cost equation: MC = f(Q) = ______________________________

2.2 (3 points) Determine the monopolist's profit-maximizing output (Q*) and price (P*).

Q* = ______________ units.

P* = $_____________

2.3 (7 points) Draw a figure showing demand curve, marginal revenue curve, and marginal cost curve. In your figure, also show the profit-maximizing quantity (Q*) and price (P*).

2.4 (18 points) Now suppose that the firm's total cost is TC = 2Q. The market demand equation remains the same.

a) (3 points) Determine the new profit-maximizing quantity (Q*) and price (P*).

Q* = ______________ units.

P* = $_____________

b) (5 points) Draw a figure showing the demand curve, marginal revenue curve, and new marginal cost curve. In your figure, also show the profit-maximizing quantity (Q*) and price (P*).

c) (10 points) From your figure in Question 2.4b, determine the consumer surplus, the producer surplus and the deadweight loss.

The consumer surplus = $_____________

The producer surplus = $ _____________

The deadweight loss = $ ______________