3. A consumer has the utility function u= (x.31) + Bu(x2.32), 0

3. A consumer has the utility function where x, , y, are amount of goods consumed in period r = 1,2. The prices of goods are pl and p2, and are the same in each period. The consumer's income in period is m, and not neccessarily equal in both periods. (i) Assumes first that the consumer has separate budget constraints in each period. Derive the indirect utility function and comment on its form. Interpret the Lagrange multipliers in this problem. Under what conditions are they equal? (ii) NOW assume it is possible to borrow or lend income between the two periods at a fixed interest rate r. Show that consumer can not be worse Off as result Of this. Give conditions under Which she is strictly better off. Obtain the indirect utility function in this case.