AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Advanced Heterodox Theory
June 2012
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General Instructions: This examination has two sections, Micro and Macro. You must answer
both sections; follow the directions in each section carefully. Each section receives equal weight
in the overall grading; therefore, you should spend an equal amount of time (about 2 ½ hours) on
each section, regardless of the number of questions in each. Make sure that all math is intuitively explained, all diagrams are clearly labeled, and all answers are responsive to the specific questions asked. The time limits should suggest the expected length and depth of your answers. The
standard for passing this exam is demonstration of “mastery” of the material.
MICRO SECTION
(2 hours and 30 minutes total)
Part A – Problems. Choose one (1). [1 hour and 15 minutes]
1) Consider a production function Q = qE, a utility function U = C – E2 (there are only variable
inputs of labor effort, E, and the producer consumes the good she produces in amount C) and
an economy composed of 3 individuals with the above functions. Two are tenants and the
other their landlord, whose income is his own production (governed by the above production
function) plus a share, α, of the two tenants’ crops. For each of the tenants, C = (1–α)Q. Let
q = 1.
1.1 What is the landlord’s optimal effort level (farming his own land)?
1.2 Assuming that the landlord has the power to determine α, what value would she select?
(Give both FOCs and a numerical value.)
1.3 Indicate the levels of utility achieved by all three individuals.
1.4 Since none of the tenants can obtain capital to buy land from the landlord, protests ensue,
as a result of which there is a land redistribution (costless!), in which everyone gets one
acre of the landlord’s 3 acres, including the former landlord. As a result, how much does
each farmer work and what is their level of utility?
1.5 Explain this result and its relevance to the Second Fundamental Theorem of Welfare
Economics.
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2) Two fishers, Eye (i) and Jay (j), fish in the same lake, using their labor and their nets. They
consume their catch and do not engage in exchange. They do not make agreements about
their actions, yet each one’s action affects the other. Specifically:
yi = αi (1–Bej)ei , where yi = amount of fish caught by Eye over some period
αi>0 = constant which varies with the size of Eye’s nets
ei and ej = respectively the share of the 24-hour day each spends fishing,
B > 0 is the impact of one agent’s actions on the other.
Fishers have analogous production functions, yi, and utility functions such that:
Ui = yi – ei2, Ue < 0, Uy > 0
2.1 Solve for the best response functions of the two actors and graph them.
2.2 Indicate any Nash equilibria. Are they/is it Pareto Optimal? What accounts for
this?
2.3 Suppose the state wishes to determine the Pareto Optimal outcome. Write down
the state’s optimization problem and find the new FOCs for determining the
optimal levels of ei and ej. Compare these to the FOCs from the individual
decisions. Explain the difference.
2.4 If the state wants to use a tax to get individuals to choose the optimal outcome,
what should the tax rate be?
2.5 Show how the existence of altruism might affect this outcome, and link this to at
least one relevant empirical paper.
3) Let a standard prisoner’s dilemma illustrate the exchange problems created where incomplete
contracts create the possibility of cheating (Defect). Note: a > b > c > d and a + d < 2b.
Cooperate
Defect
Cooperate
Defect
b, b
a, d
d, a
c, c
Some argue that, in this context, institutions (like the use of repetition and retaliation) can
permit decentralized interactions to generate more efficient results. Define the probability, ρ,
that the game (exchange interaction) will be terminated after this round, and the share of the
population = τ will be playing tit-for-tat. All others play defect.
3.1 Write down payoff functions for the two types of agents.
3.2 Find the equilibrium share of tit-for-tatters mixed population, τ*. Are there any pure
population equilibria?
3.3 Which equilibria are stable? Show both graphically and mathematically. Explain the
relation between the two methods.
3.4 If ρ increases, show how this affects τ*.
(Question 3 continues on the next page!!!)
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3.5 Discuss some empirical evidence about the use of such institutions in facilitating
exchange.
3.6 Could τ be a quasi-parameter, in the Greif-ian sense? If an increasing share of tit-fortatters in the population causes probability of termination to fall (say exchange becomes
more stable in a population where more people play tit-for-tat), what would Greif say
about the long run stability of τ*. Explain.
Part B – Essay. Choose one (1) of the following. [1 hour and 15 minutes]
1)
Explain the important of the “Constitutional Conundrum” to economic analysis. Define
institutions and explain how these relate to this problem. Outline 3 explanations of why
institutional change might be difficult, even when institutions fail to implement a Pareto
Optimal outcome.
2)
Drawing on Bowles, Knight, and Greif, carefully explain a “Bowlesian” theory of
underdevelopment and offer relevant examples to support the theory.
3)
Bowles offers a theory of class. Explain the fundamental economic problem which results
in the emergence of classes. What might have determined who ended up in which class
position as exchange expanded? What is the role of credit markets and rationality in this
process? What implications does this have for the link between income distribution and
efficiency in this theory.
(The Macro Section Starts on the Next Page)
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MACRO SECTION
(2 hours and 30 minutes total)
This section has two parts, A and B. There is some choice in each part.
Part A – Shorter Answers. Choose two (2) questions [70 minutes total; 35
minutes each]
These questions should be answered primarily with graphs and intuitive explanations, but
you should give any key equations or math if necessary to support your answers and
subject to the time constraints; you do not need to give complete math for each model.
1. Does the balance-of-payments-constrained growth (BPCG) model support the idea that
“mercantilist” trade policies (i.e., active export promotion combined with import restrictions)
can be successful in stimulating long-run economic growth? Why or why not? Be sure to
highlight which parameter(s) of the model have to be influenced by government policy in
order for such policies to be successful, especially in the context of a simple version of the
model in which purchasing power parity holds and there are no net capital or financial flows
in the long run.
2. Can an aggregate demand stimulus lead to more rapid long-run economic growth, and if so
under what assumptions or conditions? Analyze and explain in terms of one (1) of the
following models: Dutt’s (2006) model of “Aggregate Demand, Aggregate Supply and
Economic Growth”; or the model of export-led cumulative causation (ELCC, originally
attributed to Kaldor and later developed by Setterfield and Cornwall among others). Be sure
to explain as specifically as possible how supply-side limitations on long-run growth are
relaxed by the aggregate demand stimulus in the model you have chosen.
3. Does more rapid economic growth (represented by the rate of capital accumulation, gK+)
require a more unequal distribution of income (represented by a higher profit share, ), or
can it be achieved with greater distributional equity (a lower )? Compare and contrast the
implications of a classical-Marxian growth model (use the version with a conventional wage
share, 1   ), and a neo-Keynesian growth model (with variable capacity utilization u and the
profit share is determined by the mark-up rate  so that  = /(1+ )). What is (are) the
crucial difference(s) in assumptions that account for the different implications?
4. What are the effects of Marx-biased technological change on the profit rate in each of the
following three “closures” of a classical-Marxian model of income distribution: (a) fixed or
conventional real wage; (b) fixed or conventional wage share; (c) full employment. If there
is a case in which the profit rate can fall, what must happen to the real wage in that case, and
what solutions could be used (either by corporations or the government) to restore profitability?
(Section II, Part B begins on the next page)
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Part B – Longer Answers. Choose one (1) question [80 minutes]
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 [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 (0 < sr < 1; there are no savings out of wages)
Investment function: g = I/K = f0 + f1r
(f0, f1 > 0)
Trade balance: b = B/K = b0 + b1q – b2u
(b1, b2 > 0)
ˆ
Wage adjustment: W   ( w   ) where w is the workers’ target wage share
Price adjustment: Pˆ   (     q ) where  reflects the degree of competition in domestic markets ( is inversely related to industrial concentration) 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 parameters. You may assume that z, W, a0, E, and P* are exogenously given in the short run.
HINT: 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 u/ (get an 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, assuming that demand is wage-led in the
short run; your answer to this part should be graphical and intuitive (math is not expected). Be sure to state if the outcome including medium-run, open economy effects is
wage-led, profit-led, or can be either.
i. A currency depreciation policy (rise in the monetary authority’s target q )
ii. An increase in the monopoly power of firms (fall in the degree of competition, )
(Section II, Part B, # 2 and 3 are on the next page)
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2. Is the NAIRU a stable equilibrium for (un)employment? And is the NAIRU unique, or is it
endogenous? Analyze using the post-Keynesian model of either Hein and Stockhammer
(chapter 5 in their 2011 edited book) or the version in Hein’s 2008 book (where he uses the
term SIRE = stable inflation rate of employment). Give a full derivation and explanation of
the model you use, including math as well as graphs and intuition. Be sure to discuss the role
of income distribution (the wage or profit share) in your model, and analyze whether (or
under what conditions) central bank monetary policy is stabilizing or destabilizing, and what
factors (if any) make the NAIRU endogenous in the medium run in your model.
3. Answer the questions below with reference to the following version of Hein’s neo-Kaleckian
model:
mark-up pricing: p = (1 + m)w/y where m is a constant (interest-inelastic) mark-up, w is
the nominal wage rate (per hour), and y is labor productivity (output/worker hour)
profit share:
h = m / (1 + m)
profit rate:
r = hu/v
saving rate:
 = S/K = (hu/v) – i(1 – sz)
investment rate: g = I/K =  + u + h – i
a. Interpret the saving function (what are the two sources of saving in this equation, and
which terms represent them?) and the investment function (what is the rational for each
term?). State briefly (and define any variables not defined above).
b. Solve for the short-run equilibrium rates of capacity utilization and capital accumulation
[growth rate], u* and g*. Be sure to find the short-run stability condition and state any
other necessary assumptions.
c. What are the effects of increasing the mark-up rate m on equilibrium utilization u* and
growth g* in the short run? Solve for the appropriate derivatives and determine whether
utilization and growth are wage-led or profit-led or can be either (if “either” then state
and interpret the sign condition).
d. During the recent financial crisis and recession, the Fed and some other central banks
adopted monetary stimulus policies consisting of reductions in interest rates. Is an
interest rate cut (reduction in i) necessarily expansionary in the short run, and how is this
related to Hein’s distinction between the “normal” and “puzzling” cases? Find the
derivatives u*/i and g*/i and interpret intuitively. Be sure to state in words the
conditions for the puzzling case to result, in terms of this specific model, and what these
imply for monetary stimulus policy. How would you determine empirically which case
applies?
e. Does this model exhibit a Keynesian “paradox of thrift” for increases in the rentiers’
saving rate, sz, either in the short run or the long run or both? First, analyze the short-run
effect on utilization by finding and interpreting the derivatives u*/sz. Second, analyze
the long-run effect on the steady-state equilibrium growth rate g (i.e., find and interpret
 g s z ). Compare and contrast your results for the short and long run and discuss. (You
may wish to discuss stability of the long-run equilibrium briefly, but a full long-run
stability analysis is not required here.)
(End of Exam)