Department of Economics

Paul KleinOffice: Södra huset, A757Phone: 08-162136Email: paul.klein@ne.su.seURL: http://paulklein.ca/newsite/teaching/2201.php

Exam with suggested answersCourse name: Intermediate MacroeconomicsCourse code: EC2201Examiner: Paul KleinNumber of credits: 7.5Date of exam: October 25, 2016Time 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 thequestion, please provide definitions. If you find a question ambiguous, please spec-ify your interpretation. Please write legibly. Scientific (but not programmable) cal-culators are allowed. All questions must be answered in English except the essayquestion, 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 ques-tion 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, 90points.

If you have submitted acceptable answers to four out of five assignments, pleasesolve 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 beheld on November 16, 13:00-15:00 in B4.

Good luck!

Part I. Multiple choice questions.

Instructions

For each question, please indicate the best alternative. Each correct answer yields3 points. Full marks yields a bonus point. The maximum total score for this part is25.

1. A balanced growth path is, by definition, a situation where...

(a) consumption, output and the capital stock all grow at the same rate. X(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 sup-ply 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). X(d) increase subsidies on childcare (barnomsorg).

3. Which aphorism comes closest to capturing the truth about how a country bestachieves prosperity?

(a) “With law shall the land be built.” (Västgötalagen andmany other sources)X(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)

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4. According to the Kydland-Prescott model of real business cycles, a greaterthan expected improvement in technology leads to a rise in labour supply be-cause...

(a) the substitution and income effects cancel out.(b) it is not expected to last forever. X(c) leisure is an inferior good.(d) the endowment income effect dominates all the other effects because ev-

eryone is a net supplier of leisure.

5. If government consumption shocks were the only driving force behind the busi-ness cycle, the correlation between hours worked and output per hour wouldbe...

(a) close to +1.(b) close to −1.X(c) close to 0.(d) about +1/2.

6. When you see a country running a large current account deficit you concludethat 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.

X(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. X(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 be-cause...

(a) wages fall and hence the unemployed have weaker incentives to searchfor a job.

(b) wages rise and hence fewer vacancies are posted. X(c) the Beveridge curve shifts to the right.(d) the Beveridge curve shifts to the left.

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Part II. Short answer questions.

Instructions

This part contains five questions. Please choose three of them and answer onlythose. Each answer should cover no more than half a page. Each answer carries amaximum score of 8, though a particularly good answer may score a bonus point.The maximum total score for this part is 25.

1. “The Solow model is not a model of growth.” Discuss.Answer: This is true in the following sense: the long-run growth rate of out-

put is exogenous in the Solowmodel. However, the model does have somethingto say about growth in the short run. For instance, suppose half the capitalstock is destroyed. Then the model has definite implications for the speed ofrecovery.

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 competi-tive equilibrium level. However, if the employer is a monopsonist (perhaps abrukspatron) then an appropriately set minimum wage can actually raise em-ployment. A diagram may be used to show this. It should feature a marginalcost of labour curve which should be steeper than the labour supply curve.Finally, students get credit for mentioning the empirical work of Card andKrueger which suggests that minimum wage legislation has had little or noeffect 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 totalincome effect can dominate the substitution effect even if leisure is a normalgood. What determines the slope of the labour supply curve is (1) the impor-tance of unearned income and (2) the substitutability between consumptionand leisure. If a person has enough unearned income, the income effect ofa wage change is proportionally small (relative to total income) and so the

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substitution effect dominates. If leisure and consumption are good enoughsubstitutes, 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 andconsumption is one and that there is no unearned income (apart perhaps fromany transfer payment). Then if the tax revenue is spent on something thatis a poor substitute for consumption and so has no effect on the MRS betweenconsumption and leisure, then the tax has no effect on labour supply. The otherextreme 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 un-employed search less eagerly for a new job.” Discuss.

Answer: Thatmay be true, but that is not themainmechanism in theMortensen-Pissarides model that we have studied. The main mechanism is that high-er unemployment benefits strengthen the bargaining position of workers andhence raise wages, making it less profitable for firms to hire, thus reduc-ing the number of vacancies posted, hence increasing unemployment. Hage-dorn, Manovskii and Mitman argue that there is little evidence (in the Unit-ed States) for the eagerness-of-search mechanism but strong evidence for thebidding-up-wages-leading-to-fewer-vacancies mechanism.

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Part III. Mathematical problems.

Instructions

This part contains three questions. Please choose two of them (if you have not sub-mitted acceptable assignment answers) or just one (if you have). This part carriesa maximum score of 25 points. If you handed in acceptable answers to the assign-ments, you have automatically gained 13 points already.

1. Consider Solow’s growth model in continuous time where output is producedaccording to

Y (t) = Kα(t)L1−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 deprecia-tion rate is δ = 0.06. Capital’s share of income α is 1/3. The investment rate sis 0.3.

(a) Suppose you are given the capital/labour ratio k. What is then the capi-tal/output ratio (in terms of k and parameters)?Answer:

Y = KαL1−α

K

Y=K1−α

L1−α =

(K

L

)1−α

= k1−α.

(b) What is the long-run capital/output ratio in this model (in terms of pa-rameters only)?Answer: This is a standard formula and does not need to be derived,though of course it could be.(

K

Y

)∗=

s

n+ δ=

0.3

0.09=

10

3≈ 3.3333.

(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 = t0?

(The notation s is unfortunate, and I apologize.)Answer: It’s below, because 2.5<3.3333.

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(ii) Find the (instantaneous) growth rate of output at t = t0.Answer: Notice (or recall) that

Y (t)

Y (t)= α

K(t)

K(t)+ (1− α) L(t)

L(t).

Meanwhile,K(t)

K(t)= s

Y (t)

K(t)− δ

so thatK(t0)

K(t0)= 0.3 · 1

2.5− 0.06 = 0.06

and it follows that

Y (t)

Y (t)=

1

3· 0.06 + 2

3· 0.03 = 0.04.

(iii) What is the growth rate of output as t→∞?Answer: As t → ∞, the capital/output ratio tends to 10/3 and wehave

K(t)

K(t)= 0.3 · 3

10− 0.06 = 0.03

and henceY (t)

Y (t)= 0.03.

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2. Consider a country that exists for two periods, t = 1 and t = 2. It productionpossibilities are described by y1 ≥ 0, y2 ≥ 0, and

y21 + αy22 ≤ 4

where yt is output in period t; t = 1, 2. The country can borrow and lend ininternational capital markets, where the rate of return is r. Its preferencesare represented by

u(c1, c2) = ln c1 + β ln c2.

where ct 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 quarter-oval. The important thing is that it slopes down in (y1, y2)-space and that itis concave to the origin. As α increases, production opportunities in period2 diminish, making the economy relatively more efficient at producingnow as opposed to later.

(b) Write down a single–equation intertemporal budget constraint for this e-conomy.

c1 +c2

1 + r= y1 +

y21 + r

orc2 = (1 + r)y1 + y2 − (1 + r)c1.

(c) Explain why, in equilibrium, the slope of the PPF and the slope of thebudget line should be equal.Answer: By choosing y1 and y2, we determine the intercept of the budgetline. We want to maximize that intercept. It is easy to see geometricallythat the maximum is characterized by tangency between the PPF and thebudget line.Incidentally, the slope of the PPF is

dy2dy1

= − y1αy2

(d) Draw (sketch) a typical consumer indifference curve. Derive an expres-sion for its slope. Explain why, in equilibrium, the slope of an indifference

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curve should equal the slope of the budget line.Answer: The indifference curve need not be quantitatively consistentwith the preference specification, but it should be qualitatively consis-tent. In particular, it needs to slope down in c1, c2-space and be convex tothe origin. By choosing an indifference curve that is tangent to the budgetline, we choose one that is furthest from the origin and hence associatedwith the highest level of utility, among those that intersect the budgetline and is therefore attainable.To find an expression for the slope of an indifference curve, note that,along an indifference curve

ln c1 + β ln c2(c1) ≡ k.

Differentiating with respect to c1, we get

1

c1+β

c2· dc2dc1

= 0.

Solving for dc2/dc1, we getdc2dc1

= − c2βc1

.

(e) Write down all four equations that must hold in equilibrium.Answer:

• Production is feasible and there is no waste.

y21 + αy22 = 4

• The budget constraint is satisfied

c1 +c2

1 + r= y1 +

y21 + r

• The slope of the PPF equals the slope of a budget liney1αy2

= 1 + r

• The slope of an indifference curve equals the slope of a budget line

c2 = β(1 + r)c1.

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(f) Suppose α = 5/4, β = 4/5, r = 0. Show that the period 1 trade balance iszero.Answer: We begin by determining y1 and y2. Apparently, by the equalityof the slope of the PPF and the budget line,

y1 = α(1 + r)y2 =5

4y2.

Substituting this into the PPF, we have(5

4

)2

· y22 +5

4· y22 = 4

so thaty2 =

8√5

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andy1 =

2√5

3.

which is perhaps a bit unfortunate. Next, we solve for c1 and c2. Thebudget constraint now says that

c2 =6√5

5− c1

so that, at the optimum,4

5c1 =

6√5

5− c1

and hence thatc1 =

2√5

3

andc2 =

8√5

15.

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 isnegative. Explain why.Answer: Again we begin by solving for optimal production. We have

y1 =1

3y2

so that1

9y22 +

1

3y22 = 4

10

from which it follows thaty2 = 3

and thaty1 = 1.

Next, we determine optimal consumption. Evidently

c2 = 4− c1

andc2 =

4

5c1

so thatc1 =

20

9

andc2 =

16

9.

Evidently the period 1 trade balance is

y1 − c1 = −11

9.

The reason, of course, is that production opportunities in the future haveimproved and so we produce relatively less today.

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3. Suppose inflation π (measured in percent) and (log) output’s deviation fromtrend y are governed by the following Lucas surprise supply function:

y = π − πe

and that you evaluate inflation and log output outcomes according to the fol-lowing loss function.

L(y, π) =1

2(y − y)2 + 1

2(π − π)2 (1)

where π > 0 and y > 0. Inflation expectations are formed before inflation ischosen by the monetary policy maker.

(a) Suppose you trying to hire a new governor of the Riksbank. You willbe giving the governor full control over monetary policy and his or hersalary will not depend on performance. Each candidate i has preferencesdescribed by

Li(y, π) =1

2(y − yi)2 + 1

2(π − π)2.

What value of yi 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

1

2(y − yi)2 + 1

2(π − π)2

subject toy = π − πe.

The associated first order condition is

π − πe − yi + π − π = 0.

Imposing rational expectations so that π = πe, we have

π = π + yi

and, of course, y = 0. Evaluating this outcome from the point of view ofyour objective function, we have

L =1

2(y)2 +

1

2(yi)2.

Notice that the first term is the same regardless of whom you hire as gov-ernor. So you want to minimize the second term. Evidently that happenswhen

yi = 0.

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(b) Suppose again that you are trying to hire a new governor of the Riks-bank. This time, however, all candidates have the same preferences asyou 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). Youdecide to write a performance contract specifying a basic salary S minusa penalty p for each percentage point that inflation exceeds π. How bigshould p be?Answer: Again we begin by finding the equilibrium. The governor max-imizes

−1

2(y − y)2 − 1

2(π − π)2 + S − 100p(π − π)

subject toy = π − πe.

The first order condition is

−(π − πe − y)− (π − π)− 100p = 0.

Imposing rational expectations, we have

y − π + π − 100p = 0.

Solving for inflation, we get

π = π + y − 100p.

Substituting this into your objective function, we have

1

2(y)2 +

1

2(y − 100p)2.

The first term we cannot control, but the second can be minimized. Thathappens when

p =y

100.

To get a sense of what this means, suppose that we would ideally likeoutput to be 5 percent above its natural rate. Then p should be 5 · 10−4

and hence the governor should lose SEK 500 of her annual salary for eachpercentage point that π exceeds π.

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Part IV. Essay questions.

Instructions

This part contains three questions. Please answer just one of them. Your answershould 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 plau-sible explanation of economic fluctuations.” (N. Gregory Mankiw)Do you agree?Answer: Here you should mention the empirical successes of the basic mod-el (relative volatility of investment and consumption, positive correlation be-tween consumption, investment and output) and its failures (relative volatili-ty 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 shouldalso talk about the plausibility of the model. Can (detrended) Solow residu-als really be thought of as shocks to technology? Aren’t they at least partlydetermined by capacity utilization, which is a choice unrelated to the state oftechnology?

2. “Tax rates alone account for most... differences in labor supply [among themajor industrial countries].” (Edward C. Prescott)Do you agree?Answer: First of all, taxes alone don’t explain labour supply. It is crucialwhat governments use the revenue for as well. In any case, it is striking howmuch explanatory power Prescott’s equation

H

1−H=

α

1− α· (1− θ) · (1− τ) · Y

C

has. It predicts differences between North America and continental Europeremarkably well. However, it fits Scandinavian data very badly. Presumablythis is because taxes here are high, but other policies encourage labour supply(subsidies to childcare and homecare for the elderly, public pensions based onpast earnings, benefits conditional on having a job).

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3. What policies might be used to reduce the rate of unemployment?Answer: First, notice that not all such policies may be good. The questionis not what policies would maximize welfare, but which policies would reducethe unemployment rate. Explanations as to why the policies might work earnextra credit. Mentioning “skill mismatch” (employers need skills that job seek-ers don’t have), “stuctural unemployment” or “frictional unemployment earnsextra credit”. Here are just some examples of policies that either (1) shrinksthe labour force, (2) mitigates the mismatch problem or (3) makes it easier foremployers 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 outof the labour force.

• Subsidize education and training to make people more employable.

• Subsidize infrastructure to make it easier and (privately) cheaper to getfrom A to B.

• Dismantle legal barriers to mobility, e.g. join a common labour marketwith other countries. (E.g. a person with the skill set required of an oilrig worker could make a better living in Norway than in Sweden.)

• Subsidize information technology to make it easier for job seekers andemployers to find each other.

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FORMELSAMLING

• xα · xβ = xα+β; (xα)β = x(αβ); xαyα = (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)]/g2(x).

• If y = x/(1− x) then x = y/(1 + y).

• The Slutsky equation when income m is fixed:

∂xi∂pi

=∂hi∂pi− ∂xi∂m· xi.

• The Slutsky equation when m = p · ω:

∂xi∂pi

=∂hi∂pi

+∂xi∂m· (ωi − xi).

• The Cobb-Douglas (Wicksell) production (or utility) function:

f(x) = xα11 x

α22 . . . x1−α1−α2−...−αn−1

n .

• If Z(t) ≡ X(t) · Y (t) then

Z(t)

Z(t)=X(t)

X(t)+Y (t)

Y (t).

• If Z(t) ≡ X(t)/Y (t) thenZ(t)

Z(t)=X(t)

X(t)− Y (t)

Y (t).

• More generally, if Z(t) ≡ Xα(t)Y β(t) then

Z(t)

Z(t)= α

X(t)

X(t)+ β

Y (t)

Y (t).

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