AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Advanced Macroeconomic Theory
January 2014
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General Instructions: You must answer both sections, I and II; follow the directions in each section carefully. Each section receives equal weight in the overall grading, so plan to spend equal
time (about 2 hours and 30 minutes) on each. Make sure all math and graphs are intuitively explained, all diagrams are clearly labeled, and all answers are focused on the specific questions
asked (there is no credit for extraneous material). Time limits suggest the expected length and
depth of answers. No calculators or electronic devices of any kind are permitted. Answers are
expected to demonstrate mastery of the material at the PhD level.
SECTION I
Directions: There are two parts, A and B. You must answer both parts; there is some
choice in Part B. Allocate 1 hour and 15 minutes for each part.
Questions for Section I begin on the next page 
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Part A – Mandatory Question (no choice)
1. There are many versions of a “new consensus” or “New Keynesian synthesis” macro
model that have the following basic structure (where time subscripts and lags of variables
are deliberately omitted, so that you can make suggestions about adding them later):
Aggregate demand (1):
y = a0 – a1(i – pe) + η
Aggregate supply or Phillips curve (2):
p = pe + b0 + b1 y + ε
Monetary policy or Taylor rule (3): i = i0 + pe + c1y + c2(p – p*) + ν
where y is an output variable (depending on the model, it could be the output gap or capacity utilization rate, and it could possibly be replaced by the employment rate in some
equations), i is the nominal interest rate, p is the inflation rate (log change in the price
level), pe is the expected inflation rate, p* is the target inflation rate of the central bank,
b0 is a parameter reflecting labor-management bargaining, and η, ε, and ν are shocks to
aggregate demand, aggregate supply, and monetary policy, respectively. You may
assume that ai, bi, ci > 0 for all parameters shown above.
a. What changes or modifications of this basic model (including additional variables
that should be added, ways of specifying some of the variables or coefficients,
particular lag structures, etc.) would be recommended by various alternative
macro theories? Be sure to consider the new consensus theory itself as well as
neo-Kaleckian models and the work of Akerlof et al. on near-vs.-full rationality,
Ball and Moffitt on “wage aspirations,” Hein and Stockhammer on NAIRU models/stories, and Svensson on inflation targeting. Discuss the rationale for each of
the recommended changes or additions to the basic model and their main implications.
NOTE: You do not need to give complete details for each of these
approaches, nor do you need to create one big synthetic model; rather, you
should indicate what specific modifications to the basic equations are
implied by each approach, and discuss their motivations and implications.
b. Are there any additional modifications to the basic macro model given above that
you would recommend based on the experience of the financial crisis and “Great
Recession” of 2008-9 and the subsequent slow recovery of the U.S. economy?
What important features of the recent crisis and policy responses are ignored or
assumed away in this model, which are important for explaining both the origins
of the crisis and the prolonged, slow recovery from the recession? Be as specific
and detailed as possible about any further changes you think the model needs.
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Part B – Choose one (1) of the following two questions:
1. Consider an open economy neo-Kaleckian model characterized by the following equations (there is no government sector and no depreciation of capital for simplicity):
Mark-up pricing: P = (1 + z)Wa0 (z > 0 is the mark-up rate, W is the nominal wage, and
a0 is the labor coefficient [labor hours/output])
Real exchange rate: q = EP*/P (E is the nominal exchange rate in domestic/foreign
currency; P* is the foreign price level)
Wage share:  = Wa0/P
Profit rate: r = (1 – )u (where u = Y/K is a proxy for the capacity utilization rate)
Saving function:  = S/K = srr (the saving rate out of profits is 0 < sr < 1; there are no
savings out of wages)
Investment function: g = I/K = g0 + g1u + g2π
(g0, g1, g2 > 0)
(b1, b2 > 0)
Trade balance: b = B/K = b0 + b1q – b2u
Wage adjustment: Wˆ   ( w  ) where w is the workers’ target wage share
(note  = 0)
Price adjustment: Pˆ   (     q ) where  reflects the degree of competition ( is
inversely related to concentration or monopoly power), and ,  > 0
Exchange rate adjustment (“crawling peg” managed exchange rate): Eˆ   ( q  q ) ,  > 0
a. Let  = EP*/ Wa0 be the real exchange rate in terms of unit labor costs. Demonstrate that q = .
b. Solve mathematically for the short-run equilibrium level of u; find an explicit
(reduced form) solution for the equilibrium utilization rate u as a function of , ,
and other exogenous (in the short run) variables and parameters. Be sure to use q
=  to substitute for q where necessary.
c. Is aggregate demand (measured by u) wage-led or profit-led, or can it be either, in
the short run? Find the appropriate derivative (again, get a reduced, explicit solution) and analyze its sign. If the sign is ambiguous, find and interpret the condition for wage-led vs. profit-led demand in terms of the parameters of this model.
Find and use the stability condition as needed.
d. Show the derivation of the two demarcation curves (isoclines) for income distribution and the real exchange rate in the medium run, ˆ = 0 (DC curve) and q̂ =
0 (FE curve). Draw on a diagram. Find the slopes and relate to the stability of the
medium-run equilibrium for  and q.
e. Analyze the effects of each of the following on medium-run equilibrium q, , and
u, assuming (if this was not found in part c.) that demand is wage-led in the short
run; your answer should be mainly graphical and intuitive (full math is not required in this part). Analyze and discuss intuitively whether the medium-run outcomes including open economy effects are wage-led, profit-led, or can be either.
i. A currency appreciation policy (a fall in the monetary authority’s target
for the real exchange rate, q ).
ii. An increase in the bargaining power of labor, as indicated by a rise in the
workers’ target wage share, w.
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2. Analyze the effects of the parameter changes indicated below in particular “closures” of a
model of growth and distribution, assuming an inverse wage-profit relation given by
1 a
w  1 r
a0 a0
where w is the real wage, r is the rate of profit, a0 is the labor coefficient (hours per unit
of output), and a1 is the capital coefficient (capital per unit of output). Combining math,
graphs, and intuition, determine and explain the impact of the following changes on the
endogenous variables w, r, profit share , and/or accumulation rate g (as appropriate to
each model) in each of the following cases (do NOT analyze consumption per worker c):
a. A fall in the wage share (rise in  ) in a Classical-Marxian model with an exogenously given wage share ( 1   ), where capital accumulation is determined by the
function g = αr (where 0 < α < 1; you may assume no minimum profit rate, rmin =
0, for simplicity).
b. A rise in the growth rate of labor supply in a Classical-Marxian model with a constant unemployment rate (full employment/natural rate of growth, g = n) where
the growth of labor supply is exogenous (n = n0) and you may use the same accumulation function as in part a.
c. An increase in “animal spirits” in a Neo-Keynesian model, in which the classical
accumulation function is replaced by a saving function   S/K = srr and an independent investment function g  I/K = f0 + f1r, f0, f1 > 0 (you may model the increase in animal spirits as a rise in f0).
d. A rise in the mark-up rate τ in a Kalecki-Steindl model, allowing for variable
capacity utilization u = Y/Y* (where Y is actual output and Y* is potential output),
with 0 < u < 1, and the investment function is g = g0 + g1r + g2u (g0, g1, g2 > 0),
while the saving function is the same as in part c. For this model, you may assume
that prices are set by P = (1+)Wa0, where W is the nominal wage rate, and the
inverse w-r relation (with w = W/P) is modified to incorporate variable utilization.
e. Finally, discuss (compare and contrast) what your results show about the relationship between distribution (the wage share) and growth (the rate of capital accumulation) in these four models. Are more equitable distribution and more rapid
growth positively or inversely related in each one? What different assumptions
account for the different implications in this respect?
Section II begins on the next page 
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SECTION II
Directions: This section consists of two (2) problems; there is no choice and you must answer
all questions for each problem. Each of the ten questions (five per problem) carries the same
weight. Allow 1 hour and 15 minutes per problem or approximately 15 minutes per question.
Problem 1. Consider the following version of the Ramsey growth model. The production
, where
technology of firms is given by a Cobb-Douglas production function
0
1. The aggregate supply of labor (population size) is growing at a constant rate
0.
Markets are perfectly competitive.
A representative infinitely-lived household is maximizing its lifetime utility subject to the
typical budget constraint (and the no Ponzi game condition):
1
. .
∙
∙
→ max
,
where is per capita assets. As usual, one unit of labor is supplied by each person inelastically at
the market wage rate , and assets earn the market interest rate . Capital depreciates at rate .
1. Write down the profit-maximization problem of the representative firm and derive the
corresponding first order conditions.
2. Write down the first order conditions for the utility-maximization problem of the
representative household and derive the consumption Euler equation.
3. Using the equilibrium conditions in factor markets derive the law of motion for capital
stock per person, . Draw a phase diagram showing the co-evolution of and . Is the
equilibrium dynamics in this model qualitatively different from the standard Ramsey
model with the CRRA instantaneous utility function?
4. Find the steady-state values of , , and per capita output . Find the steady-state level of
the savings rate,
1
/ . How does it depend on ρ?
5. Now consider the “centralized” version of this economy. Formulate the lifetime utility
maximization problem subject to the economy’s resource constraint and derive the law of
motion for consumption per capita. How does it compare to that in the decentralized
equilibrium? Is the decentralized equilibrium Pareto optimal? If not, why?
Problem 2 for Section II is on the next page 
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Problem 2. Consider the following version of the Malthusian model. Assume that output is
produced with labor, , and land, , whose supply is fixed. The production function is
and the income of each worker is the average output
/
. Assume
further that it takes units of the output good to raise one child. Hence, the budget constraint of
the household is
. Preferences are given by
1
ln
̃
ln
,
where ̃ is an exogenous parameter that may be thought of as subsistence consumption level.
That is, subsistence consumption enters the utility function but not the budget constraint. Note:
when answering the questions below, assume that parameters and initial conditions guarantee
that subsistence consumption ̃ is always feasible on the equilibrium path.
1. Solve the utility-maximization problem of the household to derive the optimal values of
consumption and fertility rate.
2. Derive the dynamic equation for population
. Calculate the steady-state
level of population . How does it depend on the subsistence consumption parameter ̃ ?
3. Derive the conditions on parameters which guarantee that 0
1 and assume
that those conditions hold. Sketch the diagram showing the evolution of population over
time and mark the steady state.
4. Derive the dynamic equation for income per capita
and calculate the
steady-state level of income per capita . Sketch the diagram showing the evolution of
1.
income per capita assuming that 0
5. Assume that the economy is in the steady state found in parts 2 and 4. Consider an
increase in the amount of land . How will this affect the population size and income per
capita in the short run? How will this affect the steady-state values and ? Demonstrate
these effects graphically using the diagrams from parts 3 and 4.
End of Exam