AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
January 2013
Advanced Heterodox Theory
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[Contains corrections of typos in Macro section]
Instructions: This exam has two sections, Macro and Micro. You must answer both sections;
follow the directions in each section carefully. Each section receives equal weight in the grading;
therefore, you should spend an equal amount of time (about 2 hours and 30 minutes) on each
section (Macro and Micro). Please make sure that all math and graphs are intuitively explained,
all diagrams are clearly labeled, and all answers are responsive to the specific questions asked
(no credit for extraneous material). The time limits suggest the expected length and depth of your
answers. Only the calculators provided by the proctor are permitted; no other electronic devices
are allowed. All answers are expected to demonstrate mastery of the material at the PhD level.
MACRO SECTION (2 hours and 30 minutes total)
Directions: Choose any two (2) questions. 1 hour and 15 minutes per question.
1. Answer the following questions concerning Hein and Stockhammer’s post-Keynesian “story”
for a Phillips Curve/NAIRU model:
a. On the aggregate demand side, the saving and investment functions are as follows:
hz

 hz
g  g 0  g1 z  g 2   i 
and
   i (1  sR )
v

 v
where  = S/K is the saving-capital ratio, h is the profit share, z is the utilization rate
(ratio of output/potential output), v is the capital-potential output ratio, i is the interest
rate,  is the debt-capital ratio, sR is the rentiers’ saving rate (0 < sR < 1), and g = I/K is
the investment-capital ratio (accumulation rate, or growth rate of capital stock). First,
state the assumptions and explain the rationale for each equation. Then, find the stability
condition, solve for the short-run equilibrium utilization rate z*, and find the effect of an
increase in the interest rate z*/i. What are the “normal” and “puzzling” cases for this
derivative, and what is the intuition for them? (In this part, you may ignore expected
inflation and treat i as exogenously set by central bank policy.)
b. On the aggregate supply (distribution and pricing) side of the model, p is the price level
(so p̂ is the inflation rate, with superscripts e for expected and u for unexpected), expected inflation equals one-period lagged inflation ( pˆ e  pˆ t 1 ), and e is the employment rate
(which, for simplicity, is in a constant proportion to utilization e = xz with x > 0). The
profit share is h = m/(1+m), where m is the mark-up rate on unit labor costs (there are no
raw materials costs for simplicity).
The firms’ target for the profit share is hFT  h0 , and the actual (realized) profit share
is h  h0  h2 pˆ u .
The workers’ target for the wage share is (1  h)WT  W0  W1e , and the actual (realized) wage share is 1  h  W0  W1e  W2 pˆ u .
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Solve for the short-run Phillips Curve and also find the solution for the medium-run
equilibrium NAIRU employment rate, eN. Represent these on a pair of graphs showing
income distribution (1 – h) and unexpected inflation ( pˆ u  pˆ ) on the vertical axes.
i. What is it that reconciles the distributional targets of the workers and firms when
these are inconsistent in the short run? in the long run?
ii. How does an increase in unexpected inflation p̂ u affect the distribution of income
between wages and profits, and between rentiers’ and firms shares of the profits?
c. What would be the effects of an increase in firms’ monopoly power (an increase in h0) on
(i) inflation in the short run and (ii) the NAIRU employment rate eN in the medium run?
What is the intuition for each of these effects? How would the economy adjust to the new
medium-run equilibrium? Analyze graphically and explain what must be assumed about
(1) monetary policy and (2) whether the short-run equilibrium is “normal” or “puzzling”
in order for the economy to converge to the new steady state at a higher h0 (say, h0).
d. Suppose that the firms’ target profit share is an increasing function of the interest rate,
hFT  h0  h1i . First, briefly discuss the rationale for this assumption. Then, analyze
(graphically and intuitively) how this would affect the stability of the economy’s adjustment toward the NAIRU employment rate eN.
2. Analyze and explain the effects of an increase in the saving rate (either  or s, depending on
the notation of the model) on long-run economic growth in any three (3) of the following
four models. If relevant to the model, also analyze and explain the effects on income distribution, and distinguish short-run versus long-run effects (and show adjustment dynamics).
NOTES: Mathematical solutions and graphs are expected for parts a. and b.; answers to c.
and d. can be mostly graphical and intuitive, but you should define the variables and explain
key equations as needed. For all models, be sure to discuss intuitively why the long-run equilibrium growth rate rises, falls, or remains unchanged (i.e., explain the causal mechanism).
Typo fixed in 2.c. below:
a. A Classical-Marxian model (Foley & Michl version) with full capacity utilization (u = 1)
and full employment or a constant unemployment rate (gK = n). The saving function is
gK +  = (r +) – (1–)(1– ).
where gK is the rate of capital accumulation, 0 <  < 1is the depreciation rate, r is the net
profit rate, and 0 <  < 1 is the weight on future consumption in the capitalists’ intertemporal consumption function.
b. An investment-constrained neo-Keynesian growth model—use the Foley & Michl version, in which u < 1 is the ratio of actual output to potential or full-capacity output, the
investment function is giK +  =  + (r +),  and  are positive parameters, and the
saving function is the same as in part a. The distributional closure is w  (1   )ux . Be
sure to include an analysis of the stability condition in your solution.
c. Dutt’s (2006) model of growth determined by both aggregate demand and aggregate
supply, with endogenous “animal spirits” ˆ   (l  n) and productivity growth
aˆ   (l  n) ; the saving function is gs = su and the investment function is gi =  + u.
d. Aghion and Howitt’s model of endogenous growth with neo-Schumpeterian technological change, in which the saving function is g = s–1 –  (0 < s < 1, 0 <  < 1) and the
innovation or R&D function is g  g~ ( ) ( g~  0 ).
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3. Suppose a country’s economy is described by the following functions (with all variables in
growth rate form):
imports:
m = m(e + p*  p) + my
exports:
x = x(e + p*  p) + xy*
y   ( x x  a a)
prices:
p=+w–q
output:
labor productivity (Verdoorn’s Law):
q = q0 + y
balance-of-payments equilibrium (assuming no capital flows): p  x  p*  e  m
a. First, show how the appropriate equations can be used to solve for the export-led, cumulative causation (ELCC) growth rate yE. Which equations and what assumptions are
required to obtain this solution? Which equation(s) is (are) ignored and why?
i. Find and interpret the condition for stability of the equilibrium at y = yE.
ii. What is implicitly assumed about the balance of payments in this model? What
would have to happen if the country’s growth led to a current account deficit?
b. Second, show how the appropriate equations can be solved for the balance-of-paymentsconstrained growth (BPCG) rate yB. Again, be sure to indicate which equations and what
assumptions are required, and discuss which equation(s) is (are) ignored and why.
i. If the real exchange rate is constant in the long run (i.e., long-run relative purchasing
power parity [PPP] holds), which equations do not matter to the long-run solution and
why not?
ii. What is implicitly assumed about (the growth rate of) domestic expenditures a in this
model?
c. Suppose the country succeeds in increasing the income elasticity of its export demand x
through export-promotion efforts. What are the predicted effects on growth in each of the
two models, ELCC and BPCG (assuming PPP in the latter case)? Even if the growth
effects are similar, are the causal mechanisms different? Discuss in depth.
4. Consider a “conflicting claims” model of inflation combined with a neo-Kaleckian model of
aggregate demand. The wage share is  = a0W/P, where W is the nominal wage, a0 is the
labor coefficient (hours per unit of output), and P is the price level. The profit share is  = 1
– . The price is set via mark-up pricing: P = (1 + z)a0W (labor is the only variable cost,
there are no raw materials, and the mark-up rate is z > 0). The capacity utilization rate is
proxied by the output-capital ratio, u = Y/K. Answer the following questions:
a. First, assume that wage and price increases are governed by the reaction functions
Wˆ   ( w  )  u and Pˆ   (   f ) , where w and f are the workers’ and firms’
respective targets for the wage share, with ,, > 0. Briefly explain the behavior represented by these equations and especially the rationale for the u term.
b. Suppose that labor productivity grows at the exogenously given rate  â0   . Find the
equation for the “distribution curve” (DC, or ˆ  0 ) and determine its slope in u  
space. Does DC necessarily slope upward or downward, or can it slope either way, and if
so what is the condition for a positive or negative slope? Solve and draw all possible
cases on an appropriate graph (or graphs), given the functions as specified in part a.;
explain the intuition for each possible case.
(Question 4 continues and Question 5 is found on the next page)
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c. On the aggregate demand side, the economy is closed (no trade), and there is no government or depreciation of capital for simplicity. There are positive savings out of wages,
but at a lower rate than out of profits, so the saving function is  = S/K = [sr + sw(1)]u
with 0 < sw < sr < 1. The investment function is g = I/K =  +  + u, with , ,  > 0.
i. Solve the aggregate demand side of the model for the goods market equilibrium condition (“IS curve”). Find an explicit (reduced form) solution for the equilibrium utilization rate u as a function of the profit share .
ii. What do you have to assume for stability of the goods market and an economically
meaningful solution?
iii. Is aggregate demand (measured by u) wage-led or profit-led, or can it be either? If it
can be either, find and interpret the condition for wage-led vs. profit-led demand.
Explain your result in terms of the parameters of this specific model.
d. Combine the two curves (IS and DC) on a series of diagrams in u   space. Show all
possible cases (in terms of the relative slopes of the curves) given the functions specified
above (show only possible cases). Analyze (graphically) the conditions on the slopes of
the two curves for the economy to be stable or unstable, assuming that output (goods
market) adjustment is instantaneous but wage/price (distributional) adjustment is slow
and gradual. What is the intuition for the unstable case(s), if any are possible?
e. Suppose that the labor union movement is weakened by new legislation, so that the workers’ target for the wage share w falls. Analyze the effects using IS and DC curves for all
possible, stable cases, and explain.
5. First, explain in detail (a) the original neoclassical-Keynesian synthesis model of the 1940s60s, and (b) a typical “new consensus model” (NCM) of the 1990s-2000s. How do they each
model key features of the macroeconomy such as aggregate demand, aggregate supply, labor
markets, and monetary policy? (You may limit your discussion to closed economy versions
of these models.) Be sure to compare and contrast these synthesis/consensus models: what
do they have in common and how do they differ? Then, discuss in depth the main criticisms
that post-Keynesian or heterodox (PKH) economists would make of these models (both old
synthesis and new consensus). What kind of automatic adjustment mechanism does each
model have for restoring full employment or a NAIRU? Without developing a full-blown
alternative model, indicate how PKH economists would modify the key equations of the
modern NCM approach (what different assumptions would they introduce?). Are there any
parts of the NCM that have moved closer to a PKH point of view? [You need not give an
exhaustive list of criticisms and alternatives; rather, you should focus on a few of the most
important points and modifications for each relationship from the PKH perspective.]
(The Micro Section starts on the next page)
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MICRO SECTION (2 hours and 30 minutes total)
This section has two parts A and B; you must answer both parts A and B and there is some
choice in each part.
Part A - Problems. Choose one (1) of the following questions. [1 hour and 30 minutes]
1) Bargaining and Institutions:
PLAYER A
PLAYER B
Left
Right
Left
ΔA, ΔB
X, x+εB
Right
x+εA, x
ΔA, ΔB
The above box represents a typical coordination problem, where ΔA, ΔB < x represent the
“breakdown” values which occur when the coordination fails, and εA, εB represent the
relative advantage of player A and B, respectively, when they succeed in an (asymmetric)
bargain, and ΔA > ΔB. Let p be that probability A will play Right.
a) Find p*, the probability that makes B indifferent between playing Left and Right. When
will B play left?
b) Explain and show the relationship between the breakdown value and p*.
c) Explain how, according to Knight, this situation of an individual actor playing Left, or
Right, might be turned into a general expectation of behavior, an institution that generates
a “class”-type pattern of inequality.
d) Use this model to explain any one empirical outcome seen in a reading in the course.
e) Suppose that a new institution is available such that the payoffs are now:
PLAYER A
PLAYER B
Left
Left’
Right’
ΔA, ΔB
x+ εA’, x
Right
x+εA, x
ΔA, ΔB
And εA’> εA, p = probability that B will play L’. Will A always adopt the new
institution? Explain.
(Question 1 continues on the next page)
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f) Suppose that a different new institution is available such that the payoffs are now as
below, and p = probability that A adopts the new institution (plays L’):
PLAYER A
PLAYER B
Left
Right’
Left’
ΔA, ΔB
X, x+ εB’
Right
x+εA, x
ΔA, ΔB
Will B ever be able adopt the new institution? Explain.
g) Compare the two cases. Which player is more likely to switch institutions? Give an
intuitive explanation of this outcome.
2)
Contract Enforcement
A population of individuals faces a prisoners’ dilemma-type situation, with payoffs as in the
box below and a > b > c > d. One possible solution to this dilemma is to “inspect” the possible
trading partner and use local information on player reputation to decide how to play.
PLAYER 1
PLAYER 2
Cooperate
Defect
Cooperate
b, b
d, a
Defect
a, d
c, c
Players who inspect are called “Inspectors.” They pay a cost of δ to inspect and find a cooperator. The alternative behavior is to play defect. There are α Inspectors in the population.
a) Write down the expected payoffs for each type of individual (Inspectors and nonInspectors).
b) Find the equilibrium share of Inspectors in the population.
c) Is this equilibrium stable? How many total equilibria are there? Explain.
d) What can you say about the Pareto efficiency of this equilibrium?
e) What happens to the equilibrium if δ increases? What does this imply for which
equilibrium is likely to be achieved and Pareto efficiency?
f) Could δ be a quasi-parameter as defined by Avner Greif. Explain.
g) Relate this model to one historical example from Greif or another relevant source.
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3) Chris (C) and Pat (P) are partners in a household with one child. Chris earns an income of
$400 per week and Pat earns an income of $200 per week.
They are each trying to allocate 50 hours of free time weekly between play time with their
child (K), and personal leisure (L) (time spent working in the market is exogenous). Thus, the
time constraint is given by 50= Ki + Li .
Play time is a public good, i.e., Chris and Pat derive utility from the amount of time each
parent spends playing with their child.
In the event of divorce, social norms require that Chris and Pat individually spend 20 hours
of play time with their child. Each no longer derives utility from their partner's play time with
their child (i.e. play time is no longer a public good).
Their utility functions take the following form:
1
m
1
U C  ln 400  ln K C  ln K P  ln LC ,
4
4
2
1
m
1
U P  ln 200  ln K P  ln K C  ln LP ,
2
4
4
where m is an indicator variable which takes the value 1 if the couple stays married, and 0 if
the couple decides to divorce.
a) What are the divorce threat points (m = 0, those that would be used for the cooperative
Nash game)?
b) What is the equilibrium allocation under a non-cooperative marriage? Compare to the
divorce threat points. Why are these different?
c) How will the threat points change if Pat is altruistic, giving a weight of 0.3 to Chris’
utility? How will this change the Nash bargaining equilibrium (in general, do not attempt
to solve for it)? Explain this outcome.
d) How can a Nash Cooperative Bargaining model of marriage be used to explain rising US
and British divorce rates as women entered the labor force in the 1970s? Explain.
e) How might women’s increased labor force participation affect non-cooperative
bargaining outcomes? Explain.
f) Compare conclusions you would draw from two different Nash Cooperative bargaining
models of the US/Britain dynamic in d) —one using a divorce threat point and one using
the non-cooperative equilibrium as a threat point (the so-called “harsh words and burnt
toast” equilibrium).
(Micro Part B is on the next page)
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Part B - Essay. Choose one (1) of the following. [1 hour]
1) Explain the importance of the “Constitutional Conundrum” to economic analysis. Explain
the implications for this for neo-classical microeconomics. Under which conditions would
the neo-classical model be expected to accurately predict outcomes? Under which conditions
not? Make explicit reference to models and evidence in the area of heterodox
microeconomics.
2) In 1981, Douglass North wrote “competition in the face of ubiquitous scarcity dictates that
the more efficient institutions will survive and the inefficient ones will perish.” Evaluate this
proposition in such a way as to offer an explanation of persisting underdevelopment. Make
explicit reference to the concepts, models, and evidence in the area of heterodox
microeconomics.