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Competitive Equilibrium, Public Economics

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Alice and Bob survive on hamburgers and salads. Aliceís utility function is

UA = hA(sA 1)

where hA and sA are her consumption of hamburgers and salads respectively. Bobís utility function is

UB = (hB 1)2 sB

where hB and sB are his consumption of hamburgers and salads respectively. Let p be the price of hamburgers measured in salads. Alice is endowed with one salad and two hamburgers. Bob is endowed with six salads and two hamburgers. Find the competitive equilibrium.

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