(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. (i) Assume that households' borrowing and saving in period 0 are intermediated by financial institutions. Assume further that without these financial institutions, the economy has to be in the state of financial autarky because a) it is very costly for individual borrowers and lenders to find each other, and b) even when they find each other, it is not possible for individual lenders to enforce individual borrowers to make repayments in period 1. Let 1 W= L Uleoli), ca ()i be the aggregate welfare of the economy. Prove that the financial intermediation implemented by the financial institutions improves the aggregate welfare of the economy. Then, discuss the evonomic reason why the financial intermedation improves the welfare of the economy. {j) By construction, cannot be 1 because the denominator of u(c) = :;: becomes zero when = 1. For a moment, forget about this issue and substitute with & = 1 into the answers you provided in parts (c), (d), (e), and (f) (ie., f, ', s, oF, f, 5, P DP and the equilibrium interest rate r*). Compare them with the corresponding objects in Lecture Mote 3, in which the per-period utility function is given by log (where log is the natural log). Are they identical? If so, explain the mathematical reason why they have to be equal with each other. For questions (k}-(m), assume that the per-period utility is given by u(c) = loge. (k) Using question (j), express the aggregate bond demand D" and the aggregate bond supply ghond ynder uic) = logc. Then, draw the aggregate demand curve and the aggregate supply curve on the p-( plot, where p is the bond price and (0 is the bond quantity. () A central bank of this economy wanted to conduct an expansionary monetary policy by lower- ing the equilibrium interest rate r. To achieve this goal, the central bank went to the bond market and purchased M amount of bonds. (This practice is called an Open Market Operation (OMO).) Using the p- plot, explain why this operation can lower the equilibrium interest rate. {m) Let y' = %, y': = &, yDB = 1\".%, and yf = 4,100. Moreover, assume that # = (0.5 and 8= i% Compute the equilibrium interest rate when there is no intervention of a central bank. Then, explain how the central bank can adjust the interest rate to 3% through an Open Market Operation. ECON 38000 - 001, 002 Seungki Hong Money and Banking Department of Economics Spring 2024 Purdue University Problem Set 2 (Due February 15, 2024) 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 yo and yf in periods 0 and 1, respectively, where yo is substantially greater than yf (ie., yo > > yf). Second, any household i in the interval [0, 1] is a type-B household. Type-B households are endowed with incomes yo and y, in periods 0 and 1, respectively, where yo is substantially smaller than y; (ie., y;