answers

) [10 points] Suppose that the central bank strictly followed a rule of keeping the real interest rate at 3% per year. That rate happens to be the real interest rate consistent with the economy's initial equilibrium (a) [5 points] Assume that the economy is hit by a money demand shock only. Under the central bank's rule, how will the money supply respond to a money demand shock? Will the rule make aggregate demand more stable or less stable than it would be if the money supply were constant? (b) [5 points] Assume that the economy is hit by IS shocks only. Under the central bank's rule, how will the money supply behave? Will the interest-rate rule make aggregate demand more stable or less stable than it would be if the money supply were constant?

1 (20 points) Answer true, false, or uncertain. Justify your answer. In an open economy with an overlapping generations demographic structure, an increase in the size of its pay-as-you-go social security system will not affect its current account. 2 (20 points) Answer true, false, or uncertain. Justify your answer. Money can lead to the first best allocation when households are infinitely lived, have heterogeneous endowment streams, and face borrowing constraints. 3 (20 points) Answer true, false, or uncertain. Justify your answer. When countries can be excluded from international capital markets if they default on their obligations, temptations to default in some states of nature prevent these countries from getting full consumption insurance. 4 (60 points) Consider a Ramsey economy with a continuum of households and firms operating under perfect competition. There is no population growth (with population normalized to one, such that aggregates and averages are identical), and the representative household is infinitely lived, has a unitary endowment of time each period which it supplies inelastically, and maximizes the following objective function under perfect foresight: max ct,kt+1 X t=0 t log ct , subject to a given initial level of capital, k0, and to the budget constraint: ct + kt+1 = wt + Rtkt , where ct is household consumption, wt is the wage rate, kt+1 is saving assumed to be in capital, and Rt = 1 + rt is the gross return on saving, and 0 < < 1 is the time discount factor. Production technology is Cobb-Douglas such that the representative firm i takes factor prices and aggregate capital as given and maximizes i t = Ki t htL i t 1 rtKi t wtL i t where Ki t is the demand for capital and L i t the demand for labor, and 0 < < 1, and ht Kt , with 0 < 1, Kt representing aggregate (or average) capital in the economy and 1/1+ 1 is a convenient normalization. This assumption implies that labor productivity, h increases with aggregate capital. a) Assume = 0. Write the Lagrangian for households' problem and derive its first order conditions with respect to ct , and kt+1. Derive the Euler equation and interpret it.

(6) [10 points] Consumption Theories (a) [3 points] What were Keynes's three conjectures about the consumption function? (b) [2 points] What is the consumption puzzle? (c) [3 points] How does the Permanent Income Hypothesis (PIH) resolve the puzzle? (d) [2 points] Demographers predict that the fraction of the population that is elderly will increase over the next 20 years. What does the Life-Cycle Hypothesis (LCH) predicts for the influence of this demographic change on the national saving rate? That is, will the national saving rate increase or decrease? Why? (7) [10 points] Money Supply and Inflation To increase tax revenue, the US government in 1932 imposed a two-cent tax on checks written on deposits in bank accounts (In today's dollars, this tax was about 25 cents per checks) (a) [2 points] How do you think the check tax affected the currency-deposit ratio? Briefly explain (b) [2 points] Briefly discuss how this tax affected the money supply using the model of the money supply under a fractional-reserve banking system (c) [3 points] Now use the IS LM model to discuss the impact of this tax on the economy in the short run. Was the check tax a good policy to implement in the middle of the Great Depression? (d) [3 points] Explain how this tax influenced nominal interest rates and inflation rates in the long run using the Quantity Theory of Money (QTM) and the Fisher effect 4 Part D (10 points) If you are a Graduate student, you should answer the following questions. This is a bonus question for Undergraduate Students (8) [10 points] Suppose that the central bank strictly followed a rule of keeping the real interest rate at 3% per year. That rate happens to be the real interest rate consistent with the economy's initial equilibrium (a) [5 points] Assume that the economy is hit by a money demand shock only. Under the central bank's rule, how will the money supply respond to a money demand shock? Will the rule make aggregate demand more stable or less stable than it would be if the money supply were constant? (b) [5 points] Assume that the economy is hit by IS shocks only. Under the central bank's rule, how will the money supply behave? Will the interest-rate rule make aggregate demand more stable or less stable than it would be if the money supply were constant?

1 (20 points) Answer true, false, or uncertain. Justify your answer. In an open economy with an overlapping generations demographic structure, an increase in the size of its pay-as-you-go social security system will not affect its current account. 2 (20 points) Answer true, false, or uncertain. Justify your answer. Money can lead to the first best allocation when households are infinitely lived, have heterogeneous endowment streams, and face borrowing constraints. 3 (20 points) Answer true, false, or uncertain. Justify your answer. When countries can be excluded from international capital markets if they default on their obligations, temptations to default in some states of nature prevent these countries from getting full consumption insurance. 4 (60 points) Consider a Ramsey economy with a continuum of households and firms operating under perfect competition. There is no population growth (with population normalized to one, such that aggregates and averages are identical), and the representative household is infinitely lived, has a unitary endowment of time each period which it supplies inelastically, and maximizes the following objective function under perfect foresight: max ct,kt+1 X t=0 t log ct , subject to a given initial level of capital, k0, and to the budget constraint: ct + kt+1 = wt + Rtkt , where ct is household consumption, wt is the wage rate, kt+1 is saving assumed to be in capital, and Rt = 1 + rt is the gross return on saving, and 0 < < 1 is the time discount factor. Production technology is Cobb-Douglas such that the representative firm i takes factor prices and aggregate capital as given and maximizes i t = Ki t htL i t 1 rtKi t wtL i t where Ki t is the demand for capital and L i t the demand for labor, and 0 < < 1, and ht Kt , with 0 < 1, Kt representing aggregate (or average) capital in the economy and 1/1+ 1 is a convenient normalization. This assumption implies that labor productivity, h increases with aggregate capital. a) Assume = 0. Write the Lagrangian for households' problem and derive its first order conditions with respect to ct , and kt+1. Derive the Euler equation and interpret it.