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1. [20 marks] Consider an economy with two consumers (Consumer 1 and Consumer 2) and two goods (x and y). Preferences are given by the utility functions U, ( X ] , ) ) = XV and U2 (X2 , )/2 ) = X2V2 The initial endowments are x, =6, ), =4, x, = 2 and y, =2, and assume that the price of good y is given and it is p, = 1. (a) Illustrate and analyse this pure exchange economy. Find the set of Pareto optimal allocations. (b) Find and characterise the competitive equilibrium of this economy. (c) What does the Second Fundamental Theorem of Welfare Economics say? Without calculating any transfers, illustrate it in your Edgeworth Box