AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Econ 06A - Political Economy II
January 2006
Page 1 of 6
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 (Spend about 2 hours on this section)
Choose two (2) of the following macro questions:
1. Both David Ricardo and Karl Marx had theories of a falling tendency of the rate of profit.
What is the driving force behind the falling tendency of the profit rate in each theory? In
which one is technological change a cause of the problem, in which one is it a potential cure,
and why? And what happens to the real wage when the profit rate falls in each theory? In
your answer, be sure to refer to Casarosa’s interpretation of Ricardo, and for Marx think
about the distributional “closure” required for the profit rate to fall. What are the offsetting
factors or counteracting tendencies that can prevent the profit rate from falling in each
theory? Discuss the two theories in detail, and compare and contrast their assumptions and
implications.
2. In the past decade (i.e., since the mid-1990s), the United States economy can be characterized by the following “stylized facts” (compared with previous decades, i.e., 1970s-80s):
1) Increased inequality (higher profit share π)
2) Lower inflation rate
3) Faster growth of labor productivity
4) Generally better macroeconomic performance (higher growth rates, a lower unemployment rate, and a higher profit rate)
a. Show how the first three facts can be analyzed using a conflicting claims model of
inflation to determine the profit share π (or wage share ψ = 1−π). Which of these three
changes is the cause, and which two are the effects? Develop a model and analyze.
b. Then, use a neo-Kaleckian/structuralist macro model to analyze the effects of the rise in π
(or fall inψ) on capacity utilization u (which you may assume is positively related to
employment), the profit rate r, and growth rate g. Under what sorts of assumptions (e.g.,
about parameter values) will the model generate result 4)?
NOTE: For this question, you should present equations, graphs, and intuition for your
models, but logical explanations of how these models can be applied to the above facts are
more important than complete mathematical derivations.
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3. Is a redistribution of income toward profits good or bad for economic growth (measured by
the gross rate of capital accumulation, gK +δ)? Analyze each of the following cases:
a. A classical-Marxian model with a fixed (“conventional”) wage share (analyze a rise in
π ).
b. A classical-Marxian model with full employment (analyze a change in the natural rate of
growth (n) that would make the profit share (π) increase—would this require a rise or
fall in n?)
c. A neo-Keynesian/Kaleckian model, in which capacity utilization u is variable, and there
is an independent investment function of the form
giK +δ = α + η(r +δ) + λu
(where α, η, λ > 0; analyze a rise in π ).
For all three models, you may assume that the saving function (relative to the capital stock) is
gsK +δ = (r +δ) − (1 – δ)(1 – β)
where r is the net rate of profit, δ is the depreciation rate of the capital stock (0 < δ < 1), β is
the weight on future consumption in the capitalists’ intertemporal utility function (0 < β < 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 and γ = χ = 0. Give
complete mathematical derivations to prove your results and illustrate each case on an
appropriate diagram. Finally, compare and contrast your results for the three models: under
what conditions (assumptions) is there a positive or negative relationship between the real
wage and the growth rate, and why? Try to generalize from your results!
MICRO SECTION
(Spend about 2 hours on this section)
This section has three parts (A, B, and C). Answer one (1) question in each part for a total of
three (3) micro questions (be sure to answer all sub-parts of each question you choose!).
Part A - Answer one (1) of the following:
1.
A firm's output in time t is a positive function of the amount of two different kinds of
labor done: x(t) = x(LD1(t),LD2(t)) for t = 1,2. Both first partials of x(t) are positive.
The amount of each kind of labor done is a function of the number of hours of that kind
of labor and of the employee's effort level: LD1(t) = LD1(h1(t),e(t));
LD2(t) = LD2(h2(t),e(t)) for t = 1,2. Both first partials of all LDs are positive.
Effort is a positive function of employer bargaining power:
e(t) = e(BP(t)) for t = 1,2. The first derivative of e w.r.t. BP(t) is positive.
Employer bargaining power in period 2 is negatively affected the more of characteristic
C employees have in period 2: BP(2) = BP(2)(C(2)). The first derivative of BP(2) w.r.t.
C(2) is negative.
Performing hours of type 1 labor in period 1 has no effect on characteristic C in period 2.
However, performing hours of type 2 labor in period 1 increases characteristic C in
period 2: C(2) = C(2)(h2(1)). The derivative of C(2) w.r.t. h2(1) is positive.
Assume both society and the employer have a 10% rate of time discount. Assume the
price of x is 1 in both time periods. Assume the retention rate for employees from period
1 to period 2 is 80%. Finally, assume the hourly wage rate for each kind of labor is set
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exogenously in its labor market, and does not change from period 1 to period 2, i.e:
W1(1) = W1(2) = W(1) and W2(1) = W2(2) = W(2).
a) Formulate the profit function for the firm.
b) Write out two first order conditions, FOCs, for maximizing profits: the first order
condition for profit maximization regarding the amount of type 1 labor to hire in period 1,
and the first order condition for profit maximization regarding the amount of type 2 labor
to hire in period 1.
c) Interpret all the terms in each FOC: Specifically state if a term refers to an effect in
period 1 or 2; if the term is a part of traditional analysis or only appears in a conflict
theory of the firm analysis; if the term is positive or negative, if the term is a private
benefit or private cost to the employer; and if the term is a social benefit or social cost to
society.
d) Explain what the FOC for each type of labor implies about how many hours of each
type of labor a profit maximizing employer will hire compared to what traditional
analysis would predict.
e) Explain what the FOC for each type of labor implies about how many hours of each
type of labor a profit maximizing employer will hire compared to the amount that is
socially efficient.
f) How would an increase in the employer's rate of time discount affect any inefficiency
in the use of either type of labor? Briefly explain.
g) How would an increase in the retention rate of employees affect any inefficiency in the
use of either type of labor? Briefly explain.
h) Give a real-world example of a kind of labor activity that would be like type 2 labor.
2.
(1+r)pA + wL = p are the price equations for an economy with one primary input,
homogeneous labor. If b is the real wage bundle then w = pb and the price equations can
be rewritten as: (1+r)pA + pbL = p, or as: (1+r)p[A+bL] = p. Let [A+bL] = A* =
(a(1)*, a(2)*) so the price equations can be rewritten as: (1+r)pA* = p. Assume A* is
non-negative and indecomposable and that dom(A*) < 1.
a) Is good 1 a basic or a non-basic good? How do you know?
b) Is good 2 a basic or a non-basic good? How do you know?
c) Will the rate of profit in the economy, r, be positive? How do you know?
d) What are the true social opportunity costs of producing a unit of each good in this
economy? [Hint: They are easily expressed using vectors and matrices in the model
above.]
Suppose capitalists in sector 1 discover a new capital-using, labor-saving technology
where a(11)' = a(11), a(21)' > a(21), L(1)' < L(1), and pa(1)*' < pa(1)*.
e) Will capitalists in sector 1 replace a(1)* with a(1)*' ? How do you know?
f) What will happen to the prices of the two goods? How do you know?
g) What will happen to the uniform rate of profit in the economy? How do you know?
h) What will happen to the efficiency of the economy? How do you know?
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Instead, suppose capitalists in sector 2 discover a new capital-saving, labor-using
technology where a(12)' < a(12), a(22)' = a(22), L(2)' > L(2), and pa(2)*' < pa(2)*.
i) Will capitalists in sector 2 replace a(2)* with a(2)*' ? How do you know?
j) What will happen to the prices of the two goods? How do you know?
k) What will happen to the uniform rate of profit in the economy? How do you know?
l) What will happen to the efficiency of the economy? How do you know?
Part B - Answer one (1) of the following:
1. 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-ej)ei , where yi = amount of fish caught by Eye over some period
αi = constant which varies with the size of Eye’s nets (let αi = αj = 1, for simplicity)
ei and ej = respectively the share of the 24-hour day each spends fishing.
Fishers have analogous production functions, yi, and utility functions such that:
Ui = yi –ei2
Assume that the strategy set for the fishers is to work 8 or 6 hours per day, and a full day is
24 hours.
a. Write down the payoff matrix for the resulting game (in net utilities).
b. Indicate any Nash equilibria. Are they/is it Pareto Optimal? What accounts for this?
c. Suggest one way to improve the outcome. Explain how it works.
d. Fishing is not very important in most economies today. Why do we study this problem?
2. 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.
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 fallback position, or what he/she would earn if
terminated.
b. Assume workers’ utility functions were such as to define the following labor extraction
function (Best Response Function): (1-e) = β/w for w ≥ w, where w is the reservation
wage. The reservation effort level associated with w is e. Let w = 1.5, β= 1. What is e?
Graph e = e(w). Explain its shape.
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c. The firm has the production function Q = Q(he), where h = hours hired, output is sold at
p, and the firm maximizes profit. Use the firm’s first order conditions to calculate w*
and e*.
d. Using the worker’s BRF and also the FOCs from the full equation in from part b., outline
two ways that the firm could reduce unit labor costs (labor costs per unit of output)
without reducing the wage (given that Qe > 0), linking these directly to variables in the
BRF. Graph the new labor extraction functions.
e. How might these dynamics change if the firm were worker-owned?
3. Modeling of household behavior has changed significantly in the past two decades.
a. Explain the difference between the cooperative bargaining and non-cooperative
bargaining approaches to modeling household behavior. What assumptions underlie each
model and what aspects of household behavior does each model best capture?
b. Using a Nash cooperative bargaining model, explain the impact of an increase in
women’s cash earnings on household behavior.
c. Traditional female contributions to households, such as childcare and home production
are also valuable. (Valued, for example, at the cost of replacing them in the market.)
Explain why these contributions do not produce bargaining outcomes equivalent to those
resulting from an equal amount of cash earnings.
Part C: Answer one (1) of the following:
1.
For either question 2 or 3 in Micro Part B above, discuss:
a. How the assumptions of the model differ from those of their neo-classical “cousin”—
i.e. either the neoclassical model of household decision-making (unitary model) or the
neoclassical model of wage setting.
b. How the conclusions differ.
c. How the differences in assumptions and conclusions are related.
2.
Regarding the "existence" and "optimality" theorems of welfare economics:
a) State each theorem for a private enterprise market economy.
b) For which theorem(s) is it necessary to assume convexity regarding consumer
preferences and production technologies? Briefly explain why.
c) For which theorem(s) is it necessary to assume absence of external effects? Briefly
explain why.
e) For which theorem(s) is it necessary to assume absence of public goods? Briefly
explain why.
d) For which theorem(s) is it necessary to assume that markets are competitive? Briefly
explain why.
e) If we use a "purposeful preference molding" or "informed self-development" model of
endogenous consumer preferences, what are the implications for each theorem? Briefly
explain why.
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f) If we use a "myopic habit formation" model of endogenous consumer preferences,
what are the implications for each theorem? Briefly explain why.
g) State each theorem for a participatory economy.
h) For which theorem(s) is it necessary to assume convexity regarding consumer
preferences and production technologies? Briefly explain why.
i) For which theorem(s) is it necessary to assume absence of external effects? Briefly
explain why.
j) For which theorem(s) is it necessary to assume absence of public goods? Briefly
explain why.
k) For which theorem(s) is it necessary to assume that markets are competitive? Briefly
explain why.
l) If we use a "purposeful preference molding" or "informed self-development" model of
endogenous preferences, what are the implications for each theorem?
m) If we use a "myopic habit formation" model of endogenous preferences, what are the
implications for each theorem?
3.
According to the welfare theory developed in Quiet Revolution in Welfare Economics,
economists should examine different economic systems for their particular "biases"
because: (1) This will reveal the kinds of inefficiencies we can expect in different
economies; and (2) since people do, to some extent, recognize the preference
development as well as the preference fulfillment effects of their choices, this will tell us
what kinds of deformed preferences and inefficiencies will grow over time in different
economies. One can interpret the model of a participatory economy as an attempt to
eliminate biases generated by private enterprise and markets.
a) Explain how "bias" can be rigorously defined.
b) If an economy contains a bias what are the predictable effects if people recognize the
preference development as well as the preference fulfillment effects of their choices?
Briefly explain.
c) What kind of biases do markets generate? Briefly explain.
d) What specific feature(s) of a participatory economy seek to avoid these biases?
e) What kind of bias is created when production is carried out by privately owned
enterprises? Briefly explain.
f) What specific feature(s) of a participatory economy seek to avoid this bias?
(End of exam)