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 ofC(q) = 500 + 12q + 4q2.(a) Obtain the monopolist’s total revenue function, average revenue function, and mar-ginal 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 theprice it will charge to the consumer in case it produces a positive quantity.(d) Calculate the monopolist’s profit.(e) In a well labelled diagram, draw a sketch (i.e., not necessarily a figure to scale) ofthe average total cost function, the average variable cost function, and the marginalcost function. Indicate the optimal quantity you found in (c). Indicate the profitmade by the the monopolist as found in part (d).(f) Compute the consumer and producer surplus for the quantity and price you foundin part (c).(g) Obtain the quantity and the price if the firm were operating in a competitive marketinstead of being a monopolist.(h) Compute the consumer and producer surplus for the quantity and price you foundin 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).1(k) Obtain the market power of the monopolist at the point you found in part (c). Whatwould happen to the monopolist market power if the demand becomes more elastic?Question 2 Third-degree price discrimination often comes up in the context of discountsfor certain groups to some form of entertainment (e.g., a play, movie or a sporting event).Consider an event for which there are two audiences (e.g., students and non-students)and assume that the seller’s additional expenses (i.e., marginal cost) associated withhaving an additional seat occupied are essentially zero but the capacity of the venue islimited to K.(a) To make everything a bit more concrete, let the students’ and non-students’ inversedemands beP1 (x1) = 40 − x1 and P2 (x2) = 100 − x2.Solve for the single monopoly outcome (that is, no discrimination) without a capacityconstraint (i.e., K is a very large number).(b) Suppose now that the monopolist engages in third-degree price discrimination. Findthe optimal quantity sold to both groups of consumers, the price and the monopolist’sprofit. How does this compare to the answer you found in part (a) ?In the next two questions assume K = 50.(c) Suppose the monopolist does not engage in price discrimination. Find the profitmaximizing quantities, the price and the monopolist’s profit.(d) Suppose now that the monopolist engages in third-degree price discrimination. Findthe optimal quantity sold to both groups of consumers, the price and the monopolist’sprofit. How does this compare to the answer you found in part (c) ?2