Question 1 The firm SpaceX Inc. is a monopolist in the market of space rockets. It faces an inverse demand curve of p(q) = 524 4q, and has a total cost function of C(q) = 500 + 12q + 4q 2 .

(a) Obtain the monopolist's total revenue function, average revenue function, and marginal revenue function.

(b) Obtain the monopolist's average total cost function, average variable cost function, and marginal cost function.

(c) Determine the monopolist's optimal level of production in the short run, and the price it will charge to the consumer in case it produces a positive quantity.

(d) Calculate the monopolist's profit.

(e) In a well labeled diagram, draw a sketch (i.e., not necessarily a figure to scale) of the average total cost function, the average variable cost function, and the marginal cost function. Indicate the optimal quantity you found in (c). Indicate the profit made by the monopolist as found in part (d).

(f) Compute the consumer and producer surplus for the quantity and price you found in part (c).

(g) Obtain the quantity and the price if the firm were operating in a competitive market instead of being a monopolist.

(h) Compute the consumer and producer surplus for the quantity and price you found in part (f).

(i) Determine the deadweight loss caused by the monopolist.

(j) Compute the elasticity of the demand at the point you found in part (c).

(k) Obtain the market power of the monopolist at the point you found in part (c). What would happen to the monopolist market power if the demand becomes more elastic?