In C + 3 ln C2, where C denotes consumption in period 1, C denotes consumption in period 2, and 3 = 1/1.1 is the subjective discount factor. Potential output in each period is the same, denoted Y = 10 units in quantity. There is only one type of goods in the economy. Let P and P denote the price levels in periods 1 and 2, respectively. Assume that prices are fixed at P = P = 1 and that the economy is always in full employment in period 2 (the long run). The central bank uses the net nominal interest rate, denoted i, as its monetary instrument. The nominal interest rate is subject to the zero lower bound (ZLB). Suppose the endowment in each period is respectively Y and Y. Based on our assumption, Y = Y all the time. 3 Since we assume that the economy is an endowment economy, so in the equilibrium the investment is I = 0. And we also assume that the economy is a closed economy. At the beginning, let us start with an economy without government, i.e. G = 0. (a) Write down the budget constraint of the household with nominal income and nominal interest rate. Denote S as the nominal saving in the first period. . (b) What is the value of S in the equilibrium. . (c) Assume further that the central bank sets the nominal interest rate so as to maximize employment and minimize excess aggregate demand for goods. Denote this interest rate by i*. Find i*. Hint: The economy achieves full employment when the output is at the potential level. And The excess aggregate demand for goods is minimized when CYC2Y2=0. (d) Now suppose that a financial panic causes households to become more patient. Specifically, suppose that the subjective discount factor increases to 1/0.9. Suppose that the central bank is slow to react and keeps the interest rate at . Find the output gap, defined as (Y/Y - 1) 100. . (e) Now suppose that contrary to the assumption of the previous ques- tion (d), the central bank acts quickly and changes the interest rate to maximize employment. Denote this interest rate by i. Find i and the output gap. Now let us consider the scenario in which the government decides to intervene. So from now on, suppose G 0. Moreover, the government spending is not financed by public debt, but by balanced tax. (f) Does the private saving S changes in this new scenario? . (g) We are still in the case i=i**. Let G* denote the lowest level of government spending that eliminates unemployment and achieves the full employment. Find G*. Calculate private consumption in period 1. In C + 3 ln C2, where C denotes consumption in period 1, C denotes consumption in period 2, and 3 = 1/1.1 is the subjective discount factor. Potential output in each period is the same, denoted Y = 10 units in quantity. There is only one type of goods in the economy. Let P and P denote the price levels in periods 1 and 2, respectively. Assume that prices are fixed at P = P = 1 and that the economy is always in full employment in period 2 (the long run). The central bank uses the net nominal interest rate, denoted i, as its monetary instrument. The nominal interest rate is subject to the zero lower bound (ZLB). Suppose the endowment in each period is respectively Y and Y. Based on our assumption, Y = Y all the time. 3 Since we assume that the economy is an endowment economy, so in the equilibrium the investment is I = 0. And we also assume that the economy is a closed economy. At the beginning, let us start with an economy without government, i.e. G = 0. (a) Write down the budget constraint of the household with nominal income and nominal interest rate. Denote S as the nominal saving in the first period. . (b) What is the value of S in the equilibrium. . (c) Assume further that the central bank sets the nominal interest rate so as to maximize employment and minimize excess aggregate demand for goods. Denote this interest rate by i*. Find i*. Hint: The economy achieves full employment when the output is at the potential level. And The excess aggregate demand for goods is minimized when CYC2Y2=0. (d) Now suppose that a financial panic causes households to become more patient. Specifically, suppose that the subjective discount factor increases to 1/0.9. Suppose that the central bank is slow to react and keeps the interest rate at . Find the output gap, defined as (Y/Y - 1) 100. . (e) Now suppose that contrary to the assumption of the previous ques- tion (d), the central bank acts quickly and changes the interest rate to maximize employment. Denote this interest rate by i. Find i and the output gap. Now let us consider the scenario in which the government decides to intervene. So from now on, suppose G 0. Moreover, the government spending is not financed by public debt, but by balanced tax. (f) Does the private saving S changes in this new scenario? . (g) We are still in the case i=i**. Let G* denote the lowest level of government spending that eliminates unemployment and achieves the full employment. Find G*. Calculate private consumption in period 1
