First Welfare Theorem: Suppose we have an endowment economy with two consumers i=1,2. Let e = (1, 1) be the endowment for both consumers. Let preferences be given by U¹(x¹, y¹; x²) := (x¹y¹)¹/² + 7x² and U²(x², y²; y¹) := (x²y²)¹/2 + 7y¹. When maximimizing utilty each consumer takes the others choices as given. Show that p = (1,1) is a competitive equilibrium where each consumer demands her own endowment. Find a feasible allocation that is a Pareto improvement. Why does the first welfare theorem not apply? А

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