Consider an economy consisting of two individuals each with preferences over two goods, X and Y. The

Consider an economy consisting of two individuals each with preferences over two goods, X and Y. Their preferences can be described by the utility function Ui(Xi,Yi) = (Xi^1/2)(Yi^1/2), where Xi and Yi are the amounts of each good consumed by individual i. Suppose the individuals purchase these goods on a competitive market at prices Px and Py. Finally, suppose that the individuals endowments of good X and Y are given by W1=(1,1) and W2=(3,1).a) What is the individuals’ marginal rate of substitution and their budget lines? Derive each indivudals demand equations for each good.b) Graph this economy in an Edgeworth Box. Find the contract curve for the economy. What does this curve represent?c) Given the problem described above, find the competitive (Walrasian) equillibirum for the economy.d) Is the equillibium found above Pareto efficient? Explain.e) Suppose individual 2’s endowment increases from (3,1) to (29, 1). Calculate the new competitive equillibium. Both individuals are better off from this change, but who experiences the largest increase in well being? Explain your answer using the intuition of how prices are determined.

 

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