Final. 1. (2 pts) What is the expected effect on the real demand for money of an increase in the nominal interest rate? How to explain this effect?

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1 Name: Number: Nova School of Business and Economics Macroeconomics, st Semester Prof. André C. Silva TAs: João Vaz, Paulo Fagandini, and Pedro Freitas Final Maximum points: 20. Time: 2h. Pages: 10. The exam is closed books, closed notes. No calculators are allowed. You may write on the back of the pages if you need space. 1. (2 pts) What is the expected effect on the real demand for money of an increase in the nominal interest rate? How to explain this effect? 1

2 2. (4 pts) Select the best answer. By consumption smoothing, savings are expected to (decrease / stay approximately constant / increase) during a recession. A steady state is understood as (a temporary equilibrium / the best situation / a long-run equilibrium / an economy with ongoing fluctuations). According to the Ricardian equivalence, (government debt policy must be handled correctly for the economy to grow / the period in which taxes are collected is neutral / government spending is neutral / an increase in government spending is neutral if taxesincreasebythesameamount). According to the real business cycles model, a likely cause for a decrease in real output falls is a (negative shock to total factor productivity/ positive shock to total factor productivity / a positive shock to the interest rate target). In this situation, the government should (do nothing / increase expenditures / increase investment / increase R&D expenditures). Fluctuations in the target interest rate in the New Keynesian model lead to all of the following except (procyclical real wages / procyclical employment / countercyclical prices / procyclical consumption). In the New Keynesian model, the central bank pursues a policy of (fixed money supply / inflation around 2%/ zero inflation / targeting the market interest rate). According to long-run data, the correlation between the money growth rate and the inflation rate is (negative and strong / approximately zero / positive but weak / strong and positive). Under the commitment problem of central banks: The inflation rate is (lower than / the same as / higher than) with commitment. Aggregate output is (lower than / thesameas/higherthan)withcommitment. 2

3 3. (4 pts) We have seen that taxes on labor income decrease hours of work, production, and welfare. Therefore, subsidies to labor income can only be good as they would (1) increase hours of work, (2) increase production, and (3) increase welfare. Do you agree? Justify. 3

4 4. (4 pts) The consumers in a country have preferences given by P =0 log.they also have a production function = 1 to produce goods out of capital and labor,where denotes productivity. The consumers start a period with capital and have to choose capital in the next period, +1. Their maximization problem can be stated as follows: max +1 P =0 log s.t = =0 1 2, (1) given 0 0. The problem uses the fact that each person works =1in every period. Wages in each period are given by =(1 ). Using the fact that = +1, the Lagrangian of this problem can be written as = P =0 log ( +1 ).Thatis, = + log ( +1 )+ +1 log (2) a. (2 pts) The solution to this problem is such that +1 = (3) (and so +2 = +1 andsoon). GiventheLagrangianin(2),obtainthefirst order condition of this problem with respect to +1 and show that (3) is indeed a solution to the problem. 4

5 (Extra Space) 5

6 b. (2 pts) Suppose that productivity is such that =1for a long time. Then, at time = 0, increases permanently to =2. How will consumption and wages change over time after the increase in productivity? Use graphs of consumption and wages over time to illustrate your answer. Justify. 6

7 5. (6 pts) The international interest rate is such that net exports are equal to zero for a certain country. a. (4 pts) Obtain the effects of a decrease in expectations about future total factor productivity. Use graphs in your answer. Especially, state your predictions about investment and consumption. 7

8 (Extra Space) 8

9 b. (2 pts) Consider the data for Portugal in the figures below for investment and for net exports. Does the evidence in the data agree with your findings in item a? Explain. 24 Investment as a Fraction of GDP (%) 2 Net Exports (X-M) as a Fraction of GDP (%)

10 (Extra Space) 10

11 SOLUTION SKETCH Question 1 1. (2 pts) What is the expected effect on the real demand for money of an increase in the nominal interest rate? How to explain this effect? Answer The expected effect of an increase in the nominal interest rate is a decrease in the real demand for money. This effect can be explained in the following way: (1) An increase in the nominal interest rate implies an increase in the opportunity cost of money. Money is useful for transactions but it does not receive interest. So, any resources left as money do not receive interest rates. These money holdings could be transformed into bonds and, as a result, receive interest. Bonds, especially government bonds, are highly liquid and can be easily exchanged to cash. The opportunity cost of money, therefore, is equal to the nominal interest rate that is paid to bonds. (2) As the cost of holding money increases, people will make efforttodecreasethe quantity of money. For example, firmswillhiremorepeopletomanagetheirassetsin a way that the real resources allocated to money decrease. These efforts disseminated in the economy will make the real demand for money decrease. Question 2 2. (4 pts) Select the best answer. 1. By consumption smoothing, savings are expected to (decrease / stay approximately constant / increase) during a recession. 2. A steady state is understood as (a temporary equilibrium / the best situation / a long-run equilibrium / an economy with ongoing fluctuations). 3. According to the Ricardian equivalence, (government debt policy must be handled correctly for the economy to grow / the period in which taxes are collected is neutral /governmentspendingisneutral/anincreaseingovernmentspending is neutral if taxes increase by the same amount). 4. According to the real business cycles model, a likely cause for a decrease in real output falls is a (negative shock to total factor productivity/ positive shock to total factor productivity / a positive shock to the interest rate target). In this situation, the government should (do nothing / increase expenditures / increase investment / increase R&D expenditures). 5.FluctuationsinthetargetinterestrateintheNewKeynesianmodelleadtoall of the following except (procyclical real wages / procyclical employment / countercyclical prices / procyclical consumption). 6. In the New Keynesian model, the central bank pursues a policy of (fixed money 11

12 supply / inflation around 2% / zero inflation / targeting the market interest rate). 7. According to long-run data, the correlation between the money growth rate and the inflation rate is (negative and strong / approximately zero / positive but weak / strong and positive). 8. Under the commitment problem of central banks: (1) The inflationrateis(lower than / the same as / higher than) with commitment. (2) Aggregate output is (lower than / thesameas/ higher than) with commitment. Question 3 3. (4 pts) We have seen that taxes on labor income decrease hours of work, production, and welfare. Therefore, subsidies to labor income can only be good as they would (1) increase hours of work, (2) increase production, and (3) increase welfare. Do you agree? Justify. Answer The expected effects of a subsidy on labor income are an increase in hours of work, an increase in production, and a decrease in welfare. So, points (1) and (2) are correct, but point (3), the main point as it considers the final effect on welfare, is incorrect. The reason is that the subsidy has to be financed by a tax. Even though workers see directly the subsidy paid for them for each hour of labor, they take the tax that they will have to pay as a constant, not under their influence. The tax is part of the payments made for the government, which is out of the direct influence of an individual worker. So, there is a difference between what the worker takes into account(thewagesafterthe subsidy) and what the firm pays (the wages before the subsidy). A labor income subsidy will generate inefficiencies, as the economy will generate welfare below its potential. Therefore, although the results on hours of work and of production will be the opposite, a labor income subsidy will be as negative for welfare as a labor income tax. Question 4 The consumers in a country have preferences given by P =0 log. They also have a production function = 1 to produce goods out of capital and labor,where denotes productivity. The consumers start a period with capital and have to choose capital in the next period, +1. Their maximization problem can be stated as follows: P =0 log max +1 s.t = =0 1 2, (1) 12

13 given a certain value for 0, 0 0. The problem uses the fact that each person works =1in every period. Wages in each period are given by =(1 ) Using the fact that = +1, the Lagrangian of this problem can be written as = P =0 log ( +1 ),thatis = + log ( +1 )+ +1 log (2) a. (2 pts) The solution to this problem is such that +1 = (3) (and so +2 = +1 andsoon). GiventheLagrangianin(2),obtainthefirst order condition of this problem with respect to +1 and show that (3) is indeed a solution to the problem. Answer The Lagragian implies that the first order condition with respect to +1 is given by = This equation holds for =0 1 2 The first order condition implies = Substitute +1 = and +2 = Weobtain = = = The two sides of this equation are equal as +1 =. So, the solution +1 = satisfies the first order condition, which means that it is indeed a solution to the maximization problem in (1). b. Suppose that productivity is such that =1for a long time. Then, at time = 0, increases permanently to =2. How will consumption and wages change over time after the increase in productivity? Justify. Use graphs of consumption and 13

14 wagesovertimetoillustrateyouranswer. Answer As has been constant for a long time, it can be understood that the economy is initially in the steady state. In this case, capital is constant. As +1 =. Setting +1 = =,where is the steady state level of capital, we have that = 1 =( 1 ) 1 1, where 1 =1. Consumption over time is given by = +1 =(1 ). As capital and productivity are constant in the steady state, consumption is also constant, = (1 ) 1. So, before the shock, capital at is given by and capital at +1 is given by +1 = 1, which is also equal to. To confirm, set = to obtain +1 = 1 ( 1 ) 1 =( 1 ) 1 1 =,asexpected. When increases, we have that capital at +1increases, as +1 = 2, with 2 =2. Higher productivity allows consumers to produce more and to leave more capital for the future. Although is the same as under 1 =1,thevalueof +1 is higher because productivity is higher. At +2,wehave +2 = So, capital increases from = 0 to +1because increases to =2.Moreover,capital increases from +1to +2because is still high and because capital is higher at +1. As a result, capital increases at = 0,because increases, and keeps increasing afterwards because more capital allows consumers to produce more and to leave more capital to the future. Capital will continue to increase toward the new steady state. The new steady state will be such that =( 2 ) 1 1. The evolution of consumption and wages will be similar. As =(1 ),the increase in will make consumption increase at = 0 and the subsequent increase in capital will make consumption increase gradually to its new steady state. The same description applies to wages, as =(1 ). Wages will increase at = 0 and will continue to increase toward its new steady state. So consumption and wages increase over time by the increase in productivity and by the gradual increase in capital over time. Question 5 a. (4 pts) Obtain the effects of a decrease in expectations about future total factor productivity. Use graphs in your answer. Especially, state your predictions about investment and consumption. Answer 14

15 Following the notation covered in class, this question studies a decrease in 0. As as stated in the question, = and are initially equal with =0. A decrease in expectations about future total factor productivity will decrease current investment and current consumption. Absorption = + + decreases. We suppose that the economy is small in a way that the changes in the economy does not affect the international interest rate. For a constant interest rate, and will be equal in the new equilibrium if 0. Therefore, net exports increase, investment decreases, and consumption decreases. See pages in Williamson 5th Ed. for more details. Notice that the book covers the case of an increase in 0. As here there was a decrease in 0,theeffects are the opposite. b. (2 pts) Consider the data for Portugal in the figures below for investment and for net exports. Does the evidence in the data agree with your findings in item a? Explain. Answer The curves show a decrease in investment and an increase in. So, yes, the evidence in the data agrees with the predictions in item a. 15

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