Assume that there is an economy populated by a continuum [0,1] of households living in two periods, 0 and 1. Each Household is endowed with income in both periods. In terms of the income streams, there are two types of households. First, any household i in the interval [0, 0) is a type-A household. Type-A households are endowed with incomes y and yf in periods 0 and 1, respectively, where yo is substantially greater than yf (i.e., y y). Second, any household i in the interval [0, 1] is a type-B household. Type-B households are endowed with incomes y and y in periods 0 and 1, respectively, where yo is substantially smaller than y (i.e., y < < y). Both types of households have utility function u(co) + Bu(c), where co and c are household consumption in periods 0 and 1, respectively. Importantly, households can borrow or lend in period 0, and the repayment takes place in period 1. Let r denote the net interest rate with regard to the borrowing/lending. (i.e., the gross interest rate is 1 + r.) For questions (a)-(j), assume that the per-period utility is given by c-0 1 - o' u(c) o > 0, 01. (e) Derive the aggregate bond supply (Sbond) and the aggregate bond demand (Dbond) in this econ- omy. (f) Determine the equilibrium interest rate r*. (g) When goes down, how does the equilibrium interest rate change? Explain the economic reason why. (h) When goes down, how does the equilibrium interest rate change? Explain the economic reason why.