2. Consider the following Cobb Douglas utility function u(x1, x2) = xix,, with a, B > 0. Argue that this utility function represents the same preferences as v(x1,X2) = alnx1 + 8Inx2. Derive the demand functions, calculate the bud- get shares, by and b2, the income elasticity Em,) and both price elasticities. 61,1 and 621. Verify Engel and Cournot aggregation. Derive the indirect utility function v(p, m) and verify that it is increasing in m, decreasing in p1 and p2. Verify that it is homogenous of degree 0 in (p, m)