2. An economy consists of two consumers with labels i=1,2. They exchange two goods labelled j=1,2. Suppose there is a fixed total endowment e; of each good to be distributed between two consumers. Let c denote i's consumption of good j. Suppose that each consumer i has preference represented by the utility function U(c{,c) = lnc{ + alnc where the parameters a are positive and independent of i, with + = 1. Suppose the goods are to be distributed in order to maximize social welfare in the form of the weighted sum W = BU + BU where I are positive and B + B = 1 2-A) Formulate the welfare maximization problem with one equality constraint for each of the goods. 2-B) Write down the Lagrangian where ; denotes the Lagrange multiplier associated with the constraint for good j. Find the welfare maximizing distribution of the goods. aw* 2-C) Verify that where W* denotes the maximum value of W. 2 =