The market demand curve is = + 13, and each firm's total cost function is = + !. a) (5 points) Suppose there is only one firm in the market. Find the market price, quantity, and the firm's profit. b) (6 points) Show the equilibrium on a diagram, depicting the demand function (with the vertical and horizontal intercepts), the marginal revenue function , and the marginal cost function , the optimal price, and the optimal quantity. Illustrate the firm's profit. c) (6 points) Using the demand function, find the elasticity of demand at the monopoly price and quantity. Using this elasticity value (and nothing else), calculate the monopolist's factor markup of price over marginal cost. How does the monopolist's factor markup of price over marginal cost compared to that of a perfectly competitive firm? d) (3 points) Verify that the monopoly price and quantity satisfy the monopolist's rule of thumb for pricing.