AlphaGas is a retail station which sells gasoline to consumers at the per-gallon price Pr. It is the only gasoline station in town. Inverse demand for gasoline from retail customers is Pr = 20-2Q¹. AlphaGas purchases gasoline from the local refiner, OmegaGas, at the per-gallon wholesale price of PW. Denote the quantity of wholesale gasoline sold to AlphaGas as QW. This is AlphaGas' only input, and its production function is given by Q=f(Q)=Qw. The cost function is therefore given by C(Q¹)=PW Q¹. (a) Find the level of production, Q', that maximizes the profits of AlphaGas. (b) Use your answer from (a) to form the demand curve for OmegaGas. (c) Sunnose that Omega's cost of refining is $4 per gallon Using your answer from (h) to find the

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Chapter1: Making Economics Decisions
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AlphaGas is a retail station which sells gasoline to consumers at the per-gallon price Pº. It is the only
gasoline station in town. Inverse demand for gasoline from retail customers is Pr = 20-2Q¹. AlphaGas
purchases gasoline from the local refiner, OmegaGas, at the per-gallon wholesale price of PW. Denote the
quantity of wholesale gasoline sold to AlphaGas as QW. This is AlphaGas' only input, and its production
function is given by Q¹=f(Qw)=Qw. The cost function is therefore given by C(Q¹)=PW Q™ .
(a) Find the level of production, Q¹, that maximizes the profits of AlphaGas.
(b) Use your answer from (a) to form the demand curve for OmegaGas.
(c) Suppose that Omega's cost of refining is $4 per gallon. Using your answer from (b) to find the
level of production that maximizes Omega's profits. What price will it set?
(d) Combine your answers from (a) and (c) to find a value for Q¹. What will be pr?
(e) What are the combined profits of Alpha and Omega? What is consumer surplus?
(f) Suppose Omega acquired Alpha, forming a coming company called OmegaAlpha. What is its
profit maximizing quantity and price? What are profits, and what will consumer surplus be in this
case?
(g) How do your answers to (e) and (f) compare and why?
Transcribed Image Text:AlphaGas is a retail station which sells gasoline to consumers at the per-gallon price Pº. It is the only gasoline station in town. Inverse demand for gasoline from retail customers is Pr = 20-2Q¹. AlphaGas purchases gasoline from the local refiner, OmegaGas, at the per-gallon wholesale price of PW. Denote the quantity of wholesale gasoline sold to AlphaGas as QW. This is AlphaGas' only input, and its production function is given by Q¹=f(Qw)=Qw. The cost function is therefore given by C(Q¹)=PW Q™ . (a) Find the level of production, Q¹, that maximizes the profits of AlphaGas. (b) Use your answer from (a) to form the demand curve for OmegaGas. (c) Suppose that Omega's cost of refining is $4 per gallon. Using your answer from (b) to find the level of production that maximizes Omega's profits. What price will it set? (d) Combine your answers from (a) and (c) to find a value for Q¹. What will be pr? (e) What are the combined profits of Alpha and Omega? What is consumer surplus? (f) Suppose Omega acquired Alpha, forming a coming company called OmegaAlpha. What is its profit maximizing quantity and price? What are profits, and what will consumer surplus be in this case? (g) How do your answers to (e) and (f) compare and why?
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