2 Double marginalization AlphaGas is a monopoly retail station that charges a per-gallon price of P r. Inverse demand for gasoline from retail customers is Pr = 20–2Qr. AlphaGas purchases gasoline from the local refiner, OmegaGas, at the per-gallon wholesale price of Pw. This is AlphaGas' only input, and and its cost function is therefore C(Qr) = PwQr. a. Find the level of production, Qr, that maximizes the profits of AlphaGas. This forms the demand curve for OmegaGas, a monopoly supplier. b. Suppose that Omega's cost of refining is $4 per gallon. Using your answer from (a) to find the level of production that maximizes Omega's profits. What price will it set? c. Combine your answers from (a) and (b) to find a value for Qr. What will be Pr? d. What are the combined profits of Alpha and Omega? What is consumer surplus? e. Suppose Omega acquired Alpha, forming a coming company called Omega Alpha. What is its profit maximizing quantity and price? What are profits, and what will consumer surplus be in this case? f. How do your answers to (d) and (e) compare and why?

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