Exam with suggested answers

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1 Paul Klein Office: Södra huset, A757 Phone: URL: Department of Economics Exam with suggested answers Course name: Intermediate Macroeconomics Course code: EC2201 Examiner: Paul Klein Number of credits: 7.5 Date of exam: October 25, 2016 Time of exam: 9:00-14:00 Instructions Please write you student identification number on each paper and cover sheet. Use only one cover sheet per question. If you introduce notation not used in the question, please provide definitions. If you find a question ambiguous, please specify your interpretation. Please write legibly. Scientific (but not programmable) calculators are allowed. All questions must be answered in English except the essay question, which may be answered in English, Swedish, Norwegian or Danish. The exam consists of four parts as follows. I. Multiple choice. II. Short answers. III. Mathematical problems. IV. Essay. Each part may offer a choice of which question or questions to answer. Each part accounts for a quarter of your total grade. The maximum total score is 100. For the grade E, 45 points are required; for D, 50; for C, 60; for B, 75; and for A, 90 points. If you have submitted acceptable answers to four out of five assignments, please solve one of the mathematical problems in part III. Otherwise, solve two. Your results will be available on November 7 at the latest. The exam review will be held on November 16, 13:00-15:00 in B4. Good luck!

2 Part I. Multiple choice questions. Instructions For each question, please indicate the best alternative. Each correct answer yields 3 points. Full marks yields a bonus point. The maximum total score for this part is A balanced growth path is, by definition, a situation where... (a) consumption, output and the capital stock all grow at the same rate. (b) output is constant over time. (c) the marginal product of labour is constant over time. (d) the capital stock is constant over time. 2. According to standard economic theory, higher taxes lead to lower labour supply if the increase in revenue is used to... (a) refurbish the royal palace. (b) send diplomats around the world to secure a spot on the UN Security Council. (c) increase the child benefit (barnbidrag). (d) increase subsidies on childcare (barnomsorg). 3. Which aphorism comes closest to capturing the truth about how a country best achieves prosperity? (a) With law shall the land be built. (Västgötalagen and many other sources) (b) An imbalance between rich and poor is the oldest and most fatal ailment of all republics. (Plato) (c) Republics have a longer life and enjoy better fortune than principalities. (Macchiavelli) (d) Learning, whether speculative or practical, is... the natural source of wealth and honour. (Franklin) 2

3 4. According to the Kydland-Prescott model of real business cycles, a greater than expected improvement in technology leads to a rise in labour supply because... (a) the substitution and income effects cancel out. (b) it is not expected to last forever. (c) leisure is an inferior good. (d) the endowment income effect dominates all the other effects because everyone is a net supplier of leisure. 5. If government consumption shocks were the only driving force behind the business cycle, the correlation between hours worked and output per hour would be... (a) close to +1. (b) close to 1. (c) close to 0. (d) about +1/2. 6. When you see a country running a large current account deficit you conclude that this country... (a) needs to introduce currency controls to stem the outflow of capital. (b) might recently have discovered that it is abundant in natural resources. (c) needs to increase its tariffs to reduce the trade deficit. (d) may have a lot of middle-aged people. 7. The credibility problem in monetary policy arises because of... (a) the desire to raise employment above its natural rate. (b) irresponsible, populist politicians. (c) irrational expectations. (d) policy makers who are mistaken about how the economy works. 8. Unemployment is likely to increase if unemployment benefits are raised because... (a) wages fall and hence the unemployed have weaker incentives to search for a job. (b) wages rise and hence fewer vacancies are posted. (c) the Beveridge curve shifts to the right. (d) the Beveridge curve shifts to the left. 3

4 Part II. Short answer questions. Instructions This part contains five questions. Please choose three of them and answer only those. Each answer should cover no more than half a page. Each answer carries a maximum score of 8, though a particularly good answer may score a bonus point. The maximum total score for this part is The Solow model is not a model of growth. Discuss. Answer: This is true in the following sense: the long-run growth rate of output is exogenous in the Solow model. However, the model does have something to say about growth in the short run. For instance, suppose half the capital stock is destroyed. Then the model has definite implications for the speed of recovery. 2. Minimum wages kill jobs. Discuss. Answer: They can if they are set too high. A supply-demand diagram can be used here to show that jobs are rationed if the wage is set above its competitive equilibrium level. However, if the employer is a monopsonist (perhaps a brukspatron) then an appropriately set minimum wage can actually raise employment. A diagram may be used to show this. It should feature a marginal cost of labour curve which should be steeper than the labour supply curve. Finally, students get credit for mentioning the empirical work of Card and Krueger which suggests that minimum wage legislation has had little or no effect on employment in the United States. 3. Labour supply curves slope up if leisure is a normal good. Discuss. Answer: Not necessarily. Because of the endowment income effect, the total income effect can dominate the substitution effect even if leisure is a normal good. What determines the slope of the labour supply curve is (1) the importance of unearned income and (2) the substitutability between consumption and leisure. If a person has enough unearned income, the income effect of a wage change is proportionally small (relative to total income) and so the 4

5 substitution effect dominates. If leisure and consumption are good enough substitutes, then the substitution effect is again strong enough to dominate. 4. Higher taxes on labour income and consumption leads to fewer hours worked. Discuss. Answer: Not necessarily. It depends on what the tax revenue is spent on. Suppose for instance that the elasticity of substitution between leisure and consumption is one and that there is no unearned income (apart perhaps from any transfer payment). Then if the tax revenue is spent on something that is a poor substitute for consumption and so has no effect on the MRS between consumption and leisure, then the tax has no effect on labour supply. The other extreme case is if the revenue is used to fund a lump-sum transfer payment, in which case the effect on labour supply is negative. 5. Higher unemployment benefits lead to higher unemployment because the unemployed search less eagerly for a new job. Discuss. Answer: That may be true, but that is not the main mechanism in the Mortensen- Pissarides model that we have studied. The main mechanism is that higher unemployment benefits strengthen the bargaining position of workers and hence raise wages, making it less profitable for firms to hire, thus reducing the number of vacancies posted, hence increasing unemployment. Hagedorn, Manovskii and Mitman argue that there is little evidence (in the United States) for the eagerness-of-search mechanism but strong evidence for the bidding-up-wages-leading-to-fewer-vacancies mechanism. 5

6 Part III. Mathematical problems. Instructions This part contains three questions. Please choose two of them (if you have not submitted acceptable assignment answers) or just one (if you have). This part carries a maximum score of 25 points. If you handed in acceptable answers to the assignments, you have automatically gained 13 points already. 1. Consider Solow s growth model in continuous time where output is produced according to Y (t) = K α (t)l 1 α (t) where labour input is equal to population so that L(t) = N(t). We assume that population N(t) grows at the rate 0.03 and that the depreciation rate is δ = Capital s share of income α is 1/3. The investment rate s is 0.3. (a) Suppose you are given the capital/labour ratio k. What is then the capital/output ratio (in terms of k and parameters)? Answer: Y = K α L 1 α ( ) 1 α K Y = K1 α K L = = k 1 α. 1 α L (b) What is the long-run capital/output ratio in this model (in terms of parameters only)? Answer: This is a standard formula and does not need to be derived, though of course it could be. ( ) K = s Y n + δ = = (c) Consider an instant t = s such that the capital/output ratio is 2.5. (i) Is the economy below or above its balanced growth path at t = t 0? (The notation s is unfortunate, and I apologize.) Answer: It s below, because 2.5<

7 (ii) Find the (instantaneous) growth rate of output at t = t 0. Answer: Notice (or recall) that Ẏ (t) Y (t) = α K(t) L(t) + (1 α) K(t) L(t). Meanwhile, so that and it follows that K(t) K(t) = s Y (t) K(t) δ K(t 0 ) K(t 0 ) = = Ẏ (t) Y (t) = = (iii) What is the growth rate of output as t? Answer: As t, the capital/output ratio tends to 10/3 and we have and hence K(t) K(t) = = Ẏ (t) Y (t) =

8 2. Consider a country that exists for two periods, t = 1 and t = 2. It production possibilities are described by y 1 0, y 2 0, and y1 2 + αy2 2 4 where y t is output in period t; t = 1, 2. The country can borrow and lend in international capital markets, where the rate of return is r. Its preferences are represented by u(c 1, c 2 ) = ln c 1 + β ln c 2. where c t is consumption in period t; t = 1, 2. (a) Draw (sketch) the production possibility frontier (PPF) for this economy. Indicate how the frontier would shift as you change α. Answer: The PPF is a quarter-circle if α = 1; otherwise it is a quarteroval. The important thing is that it slopes down in (y 1, y 2 )-space and that it is concave to the origin. As α increases, production opportunities in period 2 diminish, making the economy relatively more efficient at producing now as opposed to later. (b) Write down a single equation intertemporal budget constraint for this e- conomy. or c 1 + c r = y 1 + y r c 2 = (1 + r)y 1 + y 2 (1 + r)c 1. (c) Explain why, in equilibrium, the slope of the PPF and the slope of the budget line should be equal. Answer: By choosing y 1 and y 2, we determine the intercept of the budget line. We want to maximize that intercept. It is easy to see geometrically that the maximum is characterized by tangency between the PPF and the budget line. Incidentally, the slope of the PPF is dy 2 dy 1 = y 1 αy 2 (d) Draw (sketch) a typical consumer indifference curve. Derive an expression for its slope. Explain why, in equilibrium, the slope of an indifference 8

9 curve should equal the slope of the budget line. Answer: The indifference curve need not be quantitatively consistent with the preference specification, but it should be qualitatively consistent. In particular, it needs to slope down in c 1, c 2 -space and be convex to the origin. By choosing an indifference curve that is tangent to the budget line, we choose one that is furthest from the origin and hence associated with the highest level of utility, among those that intersect the budget line and is therefore attainable. To find an expression for the slope of an indifference curve, note that, along an indifference curve ln c 1 + β ln c 2 (c 1 ) k. Differentiating with respect to c 1, we get 1 c 1 + β c 2 dc 2 dc 1 = 0. Solving for dc 2 /dc 1, we get dc 2 dc 1 = c 2 βc 1. (e) Write down all four equations that must hold in equilibrium. Answer: Production is feasible and there is no waste. The budget constraint is satisfied y αy 2 2 = 4 c 1 + c r = y 1 + y r The slope of the PPF equals the slope of a budget line y 1 αy 2 = 1 + r The slope of an indifference curve equals the slope of a budget line c 2 = β(1 + r)c 1. 9

10 (f) Suppose α = 5/4, β = 4/5, r = 0. Show that the period 1 trade balance is zero. Answer: We begin by determining y 1 and y 2. Apparently, by the equality of the slope of the PPF and the budget line, y 1 = α(1 + r)y 2 = 5 4 y 2. Substituting this into the PPF, we have ( ) 2 5 y y2 2 = 4 so that and y 2 = y 1 = which is perhaps a bit unfortunate. Next, we solve for c 1 and c 2. The budget constraint now says that so that, at the optimum, and hence that and c 2 = c c 1 = 6 5 c 1 5 c 1 = c 2 = It follows that trade is balanced in both periods. (g) Suppose α = 1/3. β = 4/5, r = 0. Show that the period 1 trade balance is negative. Explain why. Answer: Again we begin by solving for optimal production. We have y 1 = 1 3 y 2 so that 1 9 y y2 2 = 4 10

11 from which it follows that and that y 2 = 3 y 1 = 1. Next, we determine optimal consumption. Evidently and c 2 = 4 c 1 c 2 = 4 5 c 1 so that c 1 = 20 9 and c 2 = Evidently the period 1 trade balance is y 1 c 1 = The reason, of course, is that production opportunities in the future have improved and so we produce relatively less today. 11

12 3. Suppose inflation π (measured in percent) and (log) output s deviation from trend y are governed by the following Lucas surprise supply function: y = π π e and that you evaluate inflation and log output outcomes according to the following loss function. L(y, π) = 1 2 (y y) (π π)2 (1) where π > 0 and y > 0. Inflation expectations are formed before inflation is chosen by the monetary policy maker. (a) Suppose you trying to hire a new governor of the Riksbank. You will be giving the governor full control over monetary policy and his or her salary will not depend on performance. Each candidate i has preferences described by L i (y, π) = 1 2 (y yi ) (π π)2. What value of y i would you most prefer to see in a good governor? Answer: We begin by finding the equilibrium for a given type of governor. She minimizes subject to 1 2 (y yi ) (π π)2 2 y = π π e. The associated first order condition is π π e y i + π π = 0. Imposing rational expectations so that π = π e, we have π = π + y i and, of course, y = 0. Evaluating this outcome from the point of view of your objective function, we have L = 1 2 (y) (yi ) 2. Notice that the first term is the same regardless of whom you hire as governor. So you want to minimize the second term. Evidently that happens when 12 y i = 0.

13 (b) Suppose again that you are trying to hire a new governor of the Riksbank. This time, however, all candidates have the same preferences as you do, except that they also care about their own salary S. Specifically, the person you hire maximizes L(y, π) plus S (measured in MSEK). You decide to write a performance contract specifying a basic salary S minus a penalty p for each percentage point that inflation exceeds π. How big should p be? Answer: Again we begin by finding the equilibrium. The governor maximizes 1 2 (y y)2 1 2 (π π)2 + S 100p(π π) subject to y = π π e. The first order condition is (π π e y) (π π) 100p = 0. Imposing rational expectations, we have Solving for inflation, we get y π + π 100p = 0. π = π + y 100p. Substituting this into your objective function, we have 1 2 (y) (y 100p)2. The first term we cannot control, but the second can be minimized. That happens when p = y 100. To get a sense of what this means, suppose that we would ideally like output to be 5 percent above its natural rate. Then p should be and hence the governor should lose SEK 500 of her annual salary for each percentage point that π exceeds π. 13

14 Part IV. Essay questions. Instructions This part contains three questions. Please answer just one of them. Your answer should not exceed one page. This part carries a maximum score of 25 points. 1. In my view, real business cycle theory does not provide an empirically plausible explanation of economic fluctuations. (N. Gregory Mankiw) Do you agree? Answer: Here you should mention the empirical successes of the basic model (relative volatility of investment and consumption, positive correlation between consumption, investment and output) and its failures (relative volatility of hours, correlation between hours and output per hour). For more credit, mention how the model can be extended to deal with the failures. You should also talk about the plausibility of the model. Can (detrended) Solow residuals really be thought of as shocks to technology? Aren t they at least partly determined by capacity utilization, which is a choice unrelated to the state of technology? 2. Tax rates alone account for most... differences in labor supply [among the major industrial countries]. (Edward C. Prescott) Do you agree? Answer: First of all, taxes alone don t explain labour supply. It is crucial what governments use the revenue for as well. In any case, it is striking how much explanatory power Prescott s equation H 1 H = α Y (1 θ) (1 τ) 1 α C has. It predicts differences between North America and continental Europe remarkably well. However, it fits Scandinavian data very badly. Presumably this is because taxes here are high, but other policies encourage labour supply (subsidies to childcare and homecare for the elderly, public pensions based on past earnings, benefits conditional on having a job). 14

15 3. What policies might be used to reduce the rate of unemployment? Answer: First, notice that not all such policies may be good. The question is not what policies would maximize welfare, but which policies would reduce the unemployment rate. Explanations as to why the policies might work earn extra credit. Mentioning skill mismatch (employers need skills that job seekers don t have), stuctural unemployment or frictional unemployment earns extra credit. Here are just some examples of policies that either (1) shrinks the labour force, (2) mitigates the mismatch problem or (3) makes it easier for employers and job seekers to find each other. Cut unemployment benefits. Weaken the legal rights of unions to diminish their bargaining power. Offer generous early retirement benefit to encourage people to drop out of the labour force. Subsidize education and training to make people more employable. Subsidize infrastructure to make it easier and (privately) cheaper to get from A to B. Dismantle legal barriers to mobility, e.g. join a common labour market with other countries. (E.g. a person with the skill set required of an oil rig worker could make a better living in Norway than in Sweden.) Subsidize information technology to make it easier for job seekers and employers to find each other. 15

16 FORMELSAMLING x α x β = x α+β ; (x α ) β = x (αβ) ; x α y α = (xy) α. If h(x) f(g(x)) then h (x) = f (g(x))g (x). If h(x) f(x)g(x) then h (x) = f (x)g(x) + f(x)g (x). If h(x) f(x)/g(x) then h (x) = [f (x)g(x) f(x)g (x)]/g 2 (x). If y = x/(1 x) then x = y/(1 + y). The Slutsky equation when income m is fixed: The Slutsky equation when m = p ω: x i p i = h i p i x i m x i. x i p i = h i p i + x i m (ω i x i ). The Cobb-Douglas (Wicksell) production (or utility) function: If Z(t) X(t) Y (t) then f(x) = x α 1 1 x α x 1 α 1 α 2... α n 1 n. Ż(t) Z(t) = Ẋ(t) X(t) + Ẏ (t) Y (t). If Z(t) X(t)/Y (t) then Ż(t) Z(t) = Ẋ(t) X(t) Ẏ (t) Y (t). More generally, if Z(t) X α (t)y β (t) then Ż(t) Z(t) = αẋ(t) X(t) + β Ẏ (t) Y (t). 16