Dixit Exercise 4.3: Borrowing and Lending

Exercise 4.3: Borrowing and Lending Consider a consumer planning his consumption over two years. He will have income I1 during the rst year and I 2 during the second. In each year there are two goods to consume. In year 1, the prices are p1 and q1, and the corresponding quantities x1 and y1. In year 2, we similarly have pg, (12 and 3:2, yg. The utility function is 'u, = a11n($1) + 31 111(yi) + 062 111(932) + 32 111(92) This is to be maximized subject to two budget constraints, one for each year. Solve this problem, and nd the multipliers A1 and A2 for the two con straints. Examine how they depend on money income and other parameters of the problem. How much more of year2 income will the consumer require if he is to give up L111 of year1 income? In other words, what is the rate of return needed to induce him to save a little? You would expect borrowing and lending institutions arise in an economy p0pulated by such consumers. What governs who will borrow and who will lend