AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Econ 06A - Political Economy II
January 2005
Page 1 of 7
Directions: This examination has two sections, Macro and Micro. You must answer both
sections and be sure to follow the directions in each section carefully. Each section receives
equal weight in the overall grading; therefore, you should plan to spend an equal amount of time
(i.e., about 2 hours) on each section (micro and macro) regardless of the number of questions in
each section. Please make sure that all math is intuitively explained, all diagrams are clearly
labeled, and all answers are responsive to the specific questions asked.
MACRO SECTION
This section has two parts, A and B. Answer one (1) question in each part for a total of two (2)
questions.
Part A – Choose one (1) of the following:
1.
Suppose that the saving function (relative to the capital stock) for a society is
gsK +δ = (r +δ) − (1 – δ)(1 – β)
where r is the net rate of profit, β is the weight on future consumption in the capitalists’
intertemporal utility function (0 < β < 1), δ is the depreciation rate of the capital stock
(0 < δ < 1), and there is no saving out of wages. You may assume that there is no continuous
technological change, i.e., labor and capital productivity (x and ρ) are constant. Analyze
(and interpret and explain) the effects of an increase in on the equilibrium of the model (for
r +δ, gK +δ , the real wage w, consumption per worker c, and the utilization rate u if
relevant) under each of the following assumptions:
a.
A classical-Marxian model with a fixed (“conventional”) profit share, .
b.
A classical-Marxian model with “full employment” or a constant rate of
unemployment (be sure to explain and derive what these assumptions imply for the
growth rate, gK).
c.
A Keynesian-Kaleckian model, in which capacity utilization u is variable, and
there is an independent investment function
giK +δ = α + η(r +δ)
(be sure to explain the rationale for this function and discuss the meaning of the
parameters α and η).
Finally, compare and contrast your results for the three models. How are they similar or
different, and why? What are the policy implications of the three models for the desirability
of increasing a society’s saving rate, and under what conditions would each model apply?
2. Consider a hybrid neo-Keynesian/Kaleckian macro model with no depreciation ( = 0) and
no government or foreign trade, which combines a Robinsonian investment function
gi = + r
(where , > 0)
with a Lance Taylor-type saving function that includes positive saving out of wages:
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(This question continues on the next page)
gs = [sr + s w(1
)]u
where 0 < sw < sr < 0 are the saving rates; is the profit share; r = u is the profit rate; u is
the utilization rate (defined as the output-capital ratio); and g is the rate of capital accumulation (growth rate), with superscripts s for saving and i for investment (each relative to the
capital stock), and equilibrium condition g = gs = gi. The profit share in turn is
determined by a fixed profit mark-up rate > 0 on unit labor costs (there are no raw
materials costs for simplicity).
a. Show how the profit share is re lated to the mark-up rate .
b. Find the reduced-form solutions for equilibrium u, r, and g as functions of . Also
derive the stability condition and use it as needed in signing your results. What is the
intuition for the stability condition?
c. Is this model necessarily stagnationist, or can it also be exhilarationist? Analyze and
discuss intuitively, making sure to define your terms. If you find that exhilarationism is
possible, be sure to explain how it can be consistent with the stability condition.
d. Are both cooperative and conflictive cases of stagnationism possible, or only one of
these, or neither? Analyze and explain intuitively, again being sure to define your terms.
e. Does this model exhibit a “paradox of thrift”? Analyze by considering the effects of a
rise in the saving rate out of profits, sr (do not consider a rise in sw).
Part B – Choose one (1) of the following:
1. This question concerns open economy growth models in the “post-Keynesian” tradition:
a. First, explain how Thirlwall’s model of “balance of payments constrained growth”
(BPCG) compares with the neoclassical (Houthakker-Magee) model of the conditions for
balanced trade in the long run. Show how they can both be viewed as special cases of the
same underlying model of the trade balance.
b. Then, discuss and evaluate the empirical evidence of regarding whether the international
adjustment process follows the predictions of either Thirlwall’s BPCG model or the
neoclassical model. Specifically, how do Alonso and Garcimarín test for which of these
two models fits the data better, and what results do they obtain?
c. Finally, discuss how the equilibrium growth rate is obtained in Setterfield and Cornwall’s
model of export-led growth with cumulative causation. Compare and contrast this model
with Thirlwall’s BPCG model: how are they similar and how are they different, both in
terms of their assumptions and their policy implications?
2.
This question is about the effects of “Marx-biased” technological change:
Define and explain what it means for technological change to be “Marx-biased.”
To what extent does the available empirical evidence support the assumption that technological change is normally Marx-biased?
b.
What is the “viability condition” for a Marx-biased technological change to be
adopted? How does this criterion relate to the difference between a “fossil” production
function and a “neoclassical” production function? Does this condition suggest any
economic incentives that would induce firms to seek Marx-biased innovations? Discuss
briefly.
a.
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c.
Compare the effects of a one-time Marx-biased technological change on the profit
rate, profit share, growth rate, and real wage in each of the following “closures” of a
classical growth model:
(This question continues on the next page)
i. Fixed real wage
ii. Fixed wage share
iii. Natural rate of growth (be sure to explain what this assumes)
Explain each case both mathematically and intuitively, and also compare and contrast the
results for the three different closures. How are they similar or different, and why?
MICRO SECTION:
This section has two parts, A and B. Answer two (2) question in Part A and one (1) question in
Part B for a total of three (3) questions.
Part A– Choose two (2) of the following:
1. Given a population in which members can play either strategy x or strategy y:
a. Write down the conditions necessary for x to be an Evolutionary Viable Strategy.
b. Explain what this means for the percent of the population which will play strategy x.
c. Now consider that a change in p, or the percent of the population playing x, can be
defined as
where bx and by are payoffs to strategies x and y, respectively,
is the frequency with which the population is updated, and
is impact of differences in the payoffs on the replication of the strategies.
Explain the conditions under which a superior strategy x (bx > by) will not produce a
significant increase of strategy x in the population.
d. Explain the significance of this insight for our expectations of the achievement of
economic efficiency.
2. Below is a Hawk-Dove Game.
a. Find the mixed-strategy Nash equilibrium p*. (Payoffs are symmetric. Those shown are
for the row player.)
Palyer 1
Player 2
Hawk
Dove
Hawk
½ (v-c)
v
Dove
0
v/2
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(This question continues on the next page)
b. Consider a population that consists of two groups (call them x and y, but they could be
“hawk” and “dove”) which have distinct characteristics and norms (the characteristics are
referred to as “strategies”). Payoff functions to the strategies of x and y are:
bx(p) = pΠ(x,x) + (1−p) Π(x,y) and
by(p) = pΠ(y,x) + (1−p) Π(y,y),
where p is the share of the population who are “x’s” and Π(⋅) defines the payoff to the
strategic interaction specified. What will be the equilibrium (p,p*) in the population?
c. What is the relation between the p* in part a. and the p* in part b? Are they the same
equilibrium? Different? Explain.
d. Suppose that, initially, the two populations (hawks and doves) are separate, but then a
small number of Hawks invade a population of Doves and multiply as in the replicator
equation
Explain the conditions under which a superior strategy x (bx > by) (i.e. playing Hawk)
will not produce a significant increase of strategy x in the population.
3. Contingent Renewal
a. Bowles’ contingent renewal model of firm behavior uses a Stackleberg equilibrium.
Explain this equilibrium concept and why it is appropriate to use in this model of capitallabor relations.
b. The equation below shows a worker’s expected utility function:
V = {u(w,e) – iZ} / (i+t(e)) + Z
where
w = the wage set by the employer,
e = effort per hour by the worker
t = the probability of termination in the next period (t = m ( 1-e)), where m is the
level of monitoring used by the firm.
i = the worker’s rate of time preference, and
Z= the worker’s fall back position, or what they would earn if terminated.
Using the solution to the worker’s maximization problem, outline two ways that unit
labor costs can be reduced without reducing the wage (given that Qe > 0).
c. Compare this to the neo-classical model of wage determination.
d. How do the two distinct models affect our predictions about capitalist choices of
technology?
Part B – Choose one (1) of the following:
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1. It was commonly assumed that treating preferences as endogenous would require welfare
analysts to make judgments that some human characteristics and the preferences they give
rise to are better than other human characteristics and the preferences they generate based
ultimately, only on the personal opinions of the analysts. Briefly explain the basis for this
(This question continues on the next page)
concern. Hahnel & Albert present a model of endogenous preferences in chapter 6 of Quiet
Revolution in Welfare Economics that purports to avoid this dilemma. Explain what they
argue is the key feature in their model that permits an “end run” around this seemingly
intractable problem, and evaluate their proposed “solution.”
2. Assume a two sector economy with the technology below:
a(11) = 0.3 a(12) = 0.2
a(21) = 0.2 a(22) = 0.4
L(1) = 0.1 L(2) = 0.2
(a) Suppose the conditions of class struggle are such that capitalists receive a 30% rate of
profit. With p(2) = 1, what will p(1) and the wage rate be? Show your work.
(b) Under the conditions in the question above, suppose capitalists in sector 2 discover
the new, capital-using, labor-saving technique below. Will they replace the old technique
with the new one? Show your work.
a(12)' = 0.3
a(22)' = 0.4
L(2)' = 0.16
(c) Assuming the capitalists in sector 2 do what you said they would, will they have
served the social interest or acted against the social interest? Show your work and briefly
explain your reasoning.
(d) Adam Smith believed that profit maximizing capitalists would always serve the social
interest when choosing among technologies. Explain the intuition for Smith’s belief.
Then explain the intuition for why capitalists sometimes make social counter productive
choices.
3. There are 1000 people. There is one produced good, corn, which all must consume. Corn is
produced from inputs of labor and seed corn. All 1000 people are equally skilled and
productive, and all know how to use the two technologies that exist for producing corn. We
assume each person needs to consume exactly 1 unit of corn per week, after which they want to
maximize their leisure. We assume people only accumulate corn if they can do so without loss
of leisure. There are two ways to make corn: a labor intensive technique (LIT) and a capital
intensive technique (CIT):
Labor Intensive Technique:
4 days of labor + 0 units of seed corn yields 1 unit of corn
Capital Intensive Technique:
1 day of labor + 1 unit of seed corn yields 2 units of corn
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We measure the degree of inequality in the economy (imperfectly) as the difference between
the maximum and minimum number of days anyone works, and the efficiency of the
economy as the number of days it takes on average to produce a unit of net corn. We
examine a situation where 50 of the 1000 people have 10 units of seed corn each, while the
other 950 people have no seed corn at all.
(This question continues on the next two pages)
Under the rules of autarky:
(a) What will each seedless person do?
(b) What will each seedy person do?
(c) What will the degree of inequality in the economy be?
(d) What will the efficiency of the economy be?
Imperfect lending without banks: Before we implicitly assumed that if borrowing and
lending were made legal all mutually beneficial loans would be made. Financial economists
explain this is a naïve and unwarranted assumption. It ignores the fact that there are
considerable “transaction costs” associated with lenders and borrowers finding one another
and successfully negotiating deals. Enthusiasts point out how banks reduce transaction costs
for borrowers and lenders by allowing lenders to simply deposit funds at a single location,
where the rate of interest on bank deposits is taken as a given, and by allowing borrowers to
apply at a single location, where the rate of interest on bank loans is taken as a given. Easy
to find, nothing to negotiate. So we overcome our naiveté and get “real” by assuming that
without the assistance of banks only half the mutually beneficial loans would be made. We
assume that only 25 of the 50 seedy would find borrowers, and the other 25 would fail to do
so without the mediation of banks.
(e) What will the rate of interest be?
(f) How many days will each of the seedless work?
(g) How many days will the seedy who do not find borrowers work, and how much corn
will they accumulate?
(h) How many days will the seedy who do find borrowers work, and how much corn will
they accumulate?
(i) What will be the degree of inequality in the economy?
(j) What will the efficiency of the economy be?
Lending with banks when all goes well: We open a bank and assume this permits all 50
seedy people to find borrowers simply by depositing their seed corn in the bank. The bank
will be able to charge an interest rate of 3/4 on loans of seed corn to the seedy, but to make a
profit suppose it only pays 2/4 or 1/2 on deposits. We assume no legal reserve requirement,
permitting the bank to loan out all 500 units of seed corn deposited by the seedy; we assume
no depositors panic, so the bank does not have to sell off its loan assets prematurely at a
loss; we assume all borrowers repay their bank loans at the end of the week; and we assume
the bank then pays all depositors all the interest it owes them, along with their principle.
(k) How many days will each of the seedless work?
(l) How many days will each of the seedy work, and how much corn will they accumulate?
(m) What will the bank’s profits be?
(n) What will be the degree of inequality in the economy?
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(o) What will the efficiency of the economy be?
Lending with banks when all does not well: Suppose the seedy must deposit their seed corn
in the bank before 12 PM on Saturday of the previous week in order to get their 1/2 weekly
rate of interest, and suppose the bank lends seed corn to the seedless borrowers beginning
Monday morning at 9 AM. Over the weekend a rumor spreads among the seedy depositors
that the weather bureau is predicting no rain for the week, in which case harvests from corn
grown in the CIT will be depleted to the point where borrowers will not only be unable to
pay interest owed the bank, they will not even be able to pay back all the principle they
borrowed. Our bank run model makes clear why rational depositors would switch from
“don’t withdraw” before the week begins but only at week’s end, to “withdraw”
immediately if they believe bad weather will prevent the seedless from being able to pay the
bank back the principle, much less interest on their loans the following Sunday. Suppose on
Sunday all the seedy run (rationally) to find an ATM machine and withdraw their 10 units
of corn from the bank -- leaving the bank with nothing to lend. And suppose the seedy had
lost the habit of searching for borrowers themselves, and the seedless had lost the habit of
searching for lenders without the convenience of a bank, so none of the seedy found
borrowers, and none of the seedless found lenders before the week’s work began on
Monday morning. However, to everyone’s surprise suppose a soaking rain begins at 2 AM
Monday morning, and by the time the work day begins Monday morning it is clear
productivity in the CIT during the week will be as high as always.
(p) How many days will each of the seedless work?
(q) How many days will each of the seedy work, and how much corn will they accumulate?
(r) What will the bank’s profits be?
(s) What will be the degree of inequality in the economy?
(t) What will the efficiency of the economy be?
(u) What conclusions can you draw from this exercise about the effect of banks on the
efficiency of the “real” economy?
(End of exam)