AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Econ 01A - MA Theory
January 2006
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Instructions: You must answer both the macroeconomic and microeconomic sections of
this exam. Each section receives equal weight in the grading. Plan to spend about two
hours on each section. Make sure you follow the directions in each section carefully.
MICROECONOMICS SECTION
Directions: Answer all questions from part A (short-answer questions) and from part B
(long-answer questions). Please show all your work. 3 short questions + 2 long
questions (answer all questions, total of 5)
Part A: Answer ALL questions: (20 minutes in each – 60 minutes total))
1. Assume there are only two goods in the economy – food and cars.
a. Show that it cannot be the case that both goods are luxury goods.
b. Let there be two individuals in the economy, Shelby and Chris. Shelby
and Chris’s demand function for food are given by
QSF (PF) = 100 - 5PF
QCF(PF)= 200 – 4PF
respectively.
Find the aggregate demand function for food and depict this graphically.
c. Using the aggregate demand function you found in (b), is the demand for
food elastic? What does your answer depends on? Here ignore the
proportion aggregate demand curve where Shelby’s consumption is zero.
2. Suppose Beth is considering opening a bagel shop, which is risky. With
probability 0.5 the business will succeed, resulting in profits of $5,000; with
probability 0.5 the business will be a failure and produces losses of $2,000.
Beth’s initial wealth is $5,000.
a. What is the expected value of the business venture?
b. Beth’s utility function for income is U(x) = x1/2. Is she risky averse?
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c. What is Beth’s expected utility if she opens the bagel business? Should
she undertake the project?
3. Graph a typical indifference curve for the following functions. Calculate the
marginal rate of substitution for each function. Are these indifference curves
convex?
a. U = 4X + 2Y
b. U = (XY)1/2
c. U = lnX + lnY
Part B: Answer ALL questions (30 minutes each – 60minutes total) question)
1.
A firm’s production function for hand-squeezed orange juice uses two inputs,
oranges and labor. Let x1 denote the kilograms of oranges used and let x2 denote
the hours of labor used in squeezing. The production function for orange juice is
Y = x11/3x21/3
Where Y is measured in liters of orange juice. Let w1 denote the cost of a
kilogram of oranges and let w2 denote the wage for an hour of labor.
a. Set up the profit function for this firm. Maximize with respect to x1 and x2.
Find the demands for x1 and x2 and find the firm’s profit maximizing level of
output.
b. Ignore for now your answer to part (a). Minimize the firm’s cost of using x1
and x2 subject to producing a given Y*. What are the conditional factor
demand functions of x1 and x2 subject to producing Y*? What is the cost
function that minimizes the cost of producing Y* at prices w1 and w2?
c. Use the cost function that you derived in part (b). Add a fixed cost of F =
100, and assume that w1 = 3 and w2 = 2. Write down the total cost function
C(Y), the average fixed cost function, the average variable cost function, and
the marginal cost function. Graph these. On this graph, denote the firm’s
supply curve.
d. Using the input prices and fixed cost from (c), and assuming that the prices of
output is given by p = 20, what are firm’s profits? Redraw graph from (c), and
shade the area depicting producer surplus and firm’s profit.
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2.
Joe enjoys only two things in life, eating tacos at Taco Bell and talking with
friends on his cell phone. Currently, Joe has $20 dollars per month to spend on
these two goods. Suppose Taco Bell is charging $0.50 per taco and his cell phone
company is charging $0.25 per minute.
a. Write down Carlo’s budget constraint, and depict graphically his budget set.
Label the slope.
b. Suppose the phone company introduces a new pricing plan where each minute
after 50 minutes now costs $0.10. Draw Joe’s new budget set, labeling the
slope of each segment.
c. Return to the case of no discount pricing. Initially, Joe was consuming 20
minutes of cell phone time and 30 tacos per month. The price of tacos then
drops to $0.25 while the price of minutes increased to $0.50. Draw Joe’s new
budget set. If Joe’s preferences are well-behaved, did the change in prices
make Joe better off? Why?
d. Return the case where the price of tacos is $0.50 each and the price of cell
phone minutes is $0.25. Again assume that with these prices Joe chooses to
purchase 20 minutes of cell phone time and 30 tacos. Draw Joe’s indifference
curve through this point, and label it “A”. Suppose the phone company in an
effort to please its current customers begins offering the first 30 minutes of
phone time for free. On the same graph, draw Joe’s new budget set. Shade
the area of the available goods space that makes Joe better off. Do you know
whether Joe will consume more cell phone minutes?
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MACROECONOMICS SECTION
Directions: Answer one (1) question from Part A, one (1) question from Part B and three
(3) short answer questions from Part C. Please define all variables, explain all models
carefully, and label all graphs used to illustrate your answers.
PART A. Answer one (1) question (about 40 minutes)
1. (a) Explain carefully the essential differences between the Classical and New
Keynesian (or "Neoclassical synthesis") theories of aggregate supply (AS) and
aggregate demand (AD)? (Discuss how these relationships are derived and illustrate
using diagrams)
(b) What do the above differences suggest about the role of policy in the Keynesian
and Classical models of AD/AS?
(c) Use both the classical and the Keynesian models of AD/AS to show the effects of
an unfavorable supply shock such as a rise in the price of oil. What are the effects of
this shock in both the short run and the long run? (Illustrate your explanations using
graphs; note that the “long run” in this context is the same as what Blanchard calls the
“medium run”).
(d) Should the central bank intervene to offset the short-run effects of a supply shock
that you found in part (c)? Analyze the costs and benefits of central bank intervention
in this situation and evaluate under what conditions it would or would not be justified.
2. Consider the following IS-LM model:
C = 200 + 0.25Yd
T = 200
I = 150 + 0.25Y − 1000i
G = 250
(M/P)d = 2Y − 8000i
(M/P)s = 1600
where C=consumption, Yd = disposable income, Y = national income, T = taxes,
I = investment, i = interest rate, G = government expenditures, (M/P)d = real money
demand, (M/P)s = real money supply. Answer the following questions:
(a) Solve for the IS and LM equations.
(b) What are the equilibrium levels of Y and i?
(c) Now suppose that government spending increases to G = 400. What are the
effects on equilibrium Y and i?
(d) What happens to equilibrium investment (I) and consumption (C) after the fiscal
policy change in part (c)?
(e) How would your answer to part (d) change if (i) there was no “accelerator
effect”? (ii) the central bank targeted the interest rate instead of the money supply?
[Answer this part (e) qualitatively; no calculations are required.]
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PART B. Answer one (1) question (about 40 minutes)
1. (a) Derive and discuss the implications of the Solow (neoclassical) growth model for:
(i) the relationship between the rate of saving and the level of GDP per capita (i.e.,
output per worker) and (ii) the rate of population growth (assumed to be the same as
the growth rate of the labor force) and the level of GDP per capita. (Hint: you can
consider the Solow model with population growth or the Solow model with
technological change).
(b) Would your answers to part (a) change if the observed relationships were not with
the level of GDP but rather with its growth rate? Explain your answer.
(c) Can this model explain persistent differences in growth rates? Discuss.
(d) The Solow model can be criticized on several grounds. Discuss in detail at least
three of these criticisms.
2. (a) Discuss in detail at least two assumptions of the Solow growth model that can be
considered unrealistic.
(b) Discuss in detail two implications of the Solow growth model that are
controversial or unrealistic.
(c) How do the endogenous growth models try to remedy the possible weaknesses of
the neoclassical model? Explain in detail.
(d) Analyze the effects of an increase in a country’s saving rate using: (i) the Solow
model; (ii) an endogenous growth model. Explain carefully and illustrate using
graphs. Discuss the similarities and differences carefully.
3. Considering an open economy IS-LM model for a small country with perfect capital
mobility, answer the following questions:
(a) Explain the (uncovered) interest rate parity condition and discuss how it is used in
this model.
(b) Compare the effects of a fiscal expansion (e.g., an increase in government
spending) on equilibrium output (Y) and the interest rate (i) under a flexible exchange
rate vs. a fixed exchange rate. In the flexible case, does the home currency appreciate
or depreciate, and does the exchange rate change make the fiscal stimulus more or
less effective for increasing Y? Explain.
(c) Now compare the effects of a foreign interest rate shock (an increase in the
foreign interest rate i*) under a flexible vs. a fixed exchange rate. Which exchange
rate system is preferable in this situation and why?
PART C. Short Answer Questions: Choose three (3) questions. (about 40 minutes
total; each answer should be about 2 paragraphs maximum)
1. Define “procyclical” and “countercyclical” time series variables. How can one
determine if a variable is procyclical or countercyclical?
2. Analyze the effects of an increase in the money supply using an aggregate supply/
aggregate demand model. Be sure to show (and explain) both the short-run and
“long-run” (what Blanchard calls “medium-run”) effects and explain how the
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economy gets to the long/medium-run equilibrium. Is money “neutral” in the short
run? in the long/medium run? Explain.
3. What do you understand by the term “growth accounting” and what are the main
findings of growth accounting exercises with US or OECD data (or, if you prefer any
other country’s data)?
4. What is the Fisher equation and what does it imply for the long run relation between
the nominal interest rate and the rate of growth of money supply?
5. Briefly compare the policy implications of any three of the following: (a) the original
(Keynesian) Phillips Curve model, (b) the expectations-augmented Phillips Curve
model with adaptive expectations, (c) the expectations-augmented Phillips Curve
model with rational expectations, and (d) the Phillips Curve model with “near rational
behavior” due to Akerlof et al. No math is required (just draw diagrams and
discuss).
6. Explain the relationship between the effectiveness of monetary policy and the interest
elasticity of money demand. What about the relationship between Fiscal policy and
the interest rate elasticity of demand? Are the two relationships different? Why?
7. Can faster growth of labor productivity (an increase in γ = ∆A/A, where A = Y/N is
labor productivity) reduce the “natural rate of unemployment” (uN) in an
expectations-augmented Phillips Curve model? Be sure to highlight the assumptions
about expectations under which this is possible and prove your result mathematically.
8. Discuss how the behavior of unemployment has differed between the United States
and Europe. Describe the reasons that may explain these differences in the behavior
of unemployment.
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