Quesiton: Suppose there are two individuals and two goods. The initial endowments are ?1 = (1, 0) and ?2 = (1, 1). Preferences are given by u1(x, y) = x + y and u2(x, y) = y
(a) Prove that in equilibrium-if it ever exists-individual 2 consumes (0, 1). Hint: Does individual 2 buy any of good 1? Is it possible that individual 2 prefers initial allocation more than equilibrium allocation?
(b) Using the fact you found in (a), prove that there is no equilibrium in this economy. Hint: Initial allocation is ?1 = (1, 0) and ?2 = (1, 1). From (a), equilibrium allocation-if it exists-is (2, 0) and (0, 1). What is the price for this?