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Harvard. General Examinations in Micro- and Macroeconomic Theory, Fall 1992

 

 

The following general examinations for microeconomic and macroeconomic theory (Fall 1992) have been transcribed from a collection of general exams at Harvard from the 1990s provided to Economics in the Rear-view Mirror by Abigail Waggoner Wozniak (Harvard economics Ph.D., 2005). Abigail Wozniak was an associate professor of economics at Notre Dame before being appointed a senior research economist and the first director of the Federal Reserve Bank of Minneapolis’ Opportunity & Inclusive Growth Institute. Economics in the Rear-view Mirror is most grateful for her generosity in sharing this valuable material.

The “Wozniak collection” is over 90 pages long, so it will take some time for all the exams to get transcribed.

Transcriptions are available for:

Spring 1991 General Examinations in Microeconomic Theory and Macroeconomic Theory.

___________________

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

GENERAL EXAMINATION IN MICROECONOMIC THEORY
FALL 1992

Instructions:

  1. You have FOUR
  2. Answer a total of FOUR questions subject to the following constraint:
    There are four sections (I, II, III, IV). You must answer ONE question from each section.
  3. Please use a separate blue book for each question.
  4. Please put only your EXAM NUMBER on the blue book.

 

PART I

  1. Suppose that the consumption set is X=\left\{ x\in \mathbb{R}_{+}^{2}:{{x}_{1}}+{{x}_{2}}\ge 1 \right\} and the utility function is u(x) = x2.
    1. Represent graphically the consumption set and the indifference map.
    2. State and show that the locally cheaper consumption test for demand fails at the price/wealth combination (p, w) = (1, 1, 1).
    3. Show that market demand is not continuous at the above price/wealth combination. Interpret economically.
  2. An individual has Bernoulli utility indicator u and initial wealth w. Let lottery L offer a payoff of G with probability q and a payoff of B with probability 1 – q.
    1. If the individual owns the lottery, what is the minimum price s/he would sell it for?
    2. If s/he does not own it. What is the maximum price s/he would be willing to pay for it?
    3. Are buying and selling prices equal? Give an economic interpretation for your answer. Find conditions on the parameters of the problem under which buying and selling prices are equal.
    4. Let G = 10, B = 5, w = 0 and u(x) = x0.5. Compute the buying and selling prices for this lottery and this utility indicator.

 

PART II

Consider a market with three identical firms. The three firms set quantities as strategies and do so simultaneously. Each firm has marginal cost c, and market price is

p=1-\sum\limits_{i=1}^{3}{{{q}_{i}}}, where qi is firm i’s quantity.

  1. What are the Cournot equilibrium quantities and prices in this model?
  2. Suppose that firms 1 and 2 consider merging to form a single firm, which would have access to the two firms’ technologies. The merged firm, if it forms, would compete as a Cournot duopolist with firm 3. Assuming that the owners of firms 1 and 2 split the merged firm’s profit equally, would they find such a merger advantageous?
  3. Now suppose that firm 1 sets its quantity (as a Stackelberg leader) first and that firms 2 and 3 then follow and set quantities simultaneously. The model is otherwise the same as before. Suppose that firms 1 and 2 contemplate forming a merged firm that would act as a Stackelberg leader vis a vis firm 3. Will the merged firm’s profit be higher or lower than the sum of firm 1’s and 2’s profits in the pre-merger equilibrium? The question should be answered without making any mathematical computations.

 

PART III

Consider the country of Ec, a country with a small open economy. Ec’s economy produces two outputs, x and y, from two immobile factors, capital (K) and labor (L). The prices of x and y, px and py, are determined on the world market and are not affected by anything that happens in Ec. The aggregate production function in Ec for x is fx(K,L) and that for y is fy(K,L). Both of these functions are homogeneous of degree one in (K,L), continuous, differentiable, and have strictly convex upper contour sets. Let the input price of K  in Ec be r and that for L be w(these are prices in Ec, not world prices).

  1. Display the set of efficient production plans in an Edgeworth Box. Argue that the contract curve must lie either all above, all below, or be coincident with the diagonal in the interior of this box.

Now assume that production of x is more capital intensive than is production of y in the sense that for any given ratio of input prices, r/w, the cost minimizing way to produce any given amount of output involves a strictly larger capital-labor ratio, K/L, in the production of x than in the production of y.

  1. What can you say about the shape of the contract curve now? How do the slopes of the isoquants of the two production processes vary at various points on the contract curve?

Now assume that Ec has a perfectly competitive economy.

  1. Show that there is a unique equilibrium input price ratio r/w.
  2. Prove that if the world price of the capital intensive good (px) rises, then the equilibrium input price ratio, r/w, increases.
  3. Prove that if the endowment of labor in Ec increases, the output of good y increases and output of good x

 

PART IV

  1. How is it that, even in a world of linear technologies, different theories of growth and distribution lead to different theories of value, i.e., different theories of relative prices? Doesn’t this violate the non-substitution theorem, which shows that, for a given cost of capital, the technology which minimizes costs will be chosen irrespective of demand? Is the existence of different theories of value compatible with the idea that competition eliminates any difference between price and cost of production? How does utility maximization enter into neoclassical and non-neoclassical theories of value?
  2. Overheard in the corridors of Littauer:
    “I took the best road home yesterday.”
    “How do you know that?”
    “If there had been a better one I would have taken it.”
    Analyze the above dialogue from the point of view of both partisans and critics of revealed preference theory.

 

Source: Department of Economics, Harvard University. Past General Exams Spring 1991-Spring 1999, pp. 72-77. Copy provided to Economics in the Rear-view Mirror by Abigail Wozniak.

___________________

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

GENERAL EXAMINATION IN MACROECONOMIC THEORY
FALL 1992

Instructions:

  1. You have FOUR
  2. Answer a total of SIX questions subject to the following constraint:
    There are four sections (I, II, III, IV). You must answer ONE question from each section.
  3. Please use a separate blue book for each question.
  4. Please put only your EXAM NUMBER on the blue book.

 

PART I

  1. Answer the question, “Does money affect output?” Support your answer with both theoretical arguments and empirical evidence. Discuss the strengths and weaknesses of this evidence. Finally, include a detailed discussion of one theory that supports your position.
  2. The response among pundits to the recent reduction in German interest rates has been overwhelmingly positive. Evaluate this response in light of the Mundell-Flemming model. How does foreign monetary policy affect domestic output in the model? What other channel might American commentators have in mind. Speculate about the cause of this difference and give an opinion as to who is correct.

 

PART II

Problem 1

Consider the following dynamic version of the Mundell-Fleming model:

{{\dot{e}}}/{e}\;={{i}^{*}}-i

i=\alpha y-\beta m

\dot{y}=\gamma \left( d-y \right)

d=\lambda y-\theta e+g

where

e is the exchange rate (measured so that an appreciation of the domestic currency is an increase in e),
i* is the (exogenous) world interest rate,
i is the domestic interest rate,
y is output,
m is (exogenous) real money balances,
d is demand,
g is a measure of (exogenous) fiscal policy,
and \alpha >0,\,\,\beta >0,\,\,\gamma >0,\,\,0<\lambda <1,\,\,\theta >0.

  1. Give an interpretation of each equation.
  2. Write the model using two variables and two laws of motion. Identify the state (non-jumping) variable and the costate (jumping) variable.
  3. Draw the phase diagram, including the steady-state conditions, the implied[?] dynamics, and the saddle-point stable path.
  4. Describe the effects of a sudden, permanent increase in g. Compare the results to the standard (static) Mundell-Fleming model.
  5. Describe the effects of a sudden, permanent increase in Compare the results to the standard (static) Mundell-Fleming model.

 

Problem 2

Suppose that the representative consumer maximizes the following intertemporal utility function:

{{E}_{t}}\sum\limits_{j=0}^{\infty }{{{\left( 1+\rho  \right)}^{j}}U\left( {{C}_{t+j}},{{G}_{t+j}} \right)}

where C is consumption,

G is (exogenous) government spending,

\rho is the subjective rate of discount,

The consumer has random earnings, and she can borrow and lend at the constant real interest rate r.

  1. What is the consumer’s intertemporal first-order condition? Explain.
  2. In this problem, what variable follows a random walk (that is a martingale)? What variable doesn’t? Explain.
  3. Suppose that government spending follows a predictable pattern: in particular, suppose that (for some political reason) G fluctuates as a sine wave. What is the implied pattern of consumption?
  4. Describe the equity-premium puzzle.
  5. Suppose now that government spending is countercyclical (that is, the government increases G when the economy goes into a recession). How might this model help resolve the equity-premium puzzle? What condition would you need for the utility function U(.)?

 

PART III

  1. What implications for the conduct of monetary policy follow from the fact that many of the familiar variables that economists have urged central banks to adopt as their operating targets—for example, prices, or real interest rates, or measures of money other than the monetary base—are inherently endogenous in the sense that a central bank typically cannot set any of these variables directly via its open market operations? Use a specific model of your choice to illustrate what role a variable like the price level or the real interest rate, or a measure of money other than the monetary base, can plausibly play in the monetary policymaking process even when it is clearly endogenous.
  2. “Whether or not debt-financed government spending ‘crowds out’ private capital formation depends on whether or not the economy’s private resources are already fully employed. At less than full employment, deficit spending will crowd out investment even if it raises output (which it may or may not do). By contrast, the mechanisms that cause this decline in investment at less than full employment are not operative when the economy is fully employed.” Do you agree or disagree with this statement? Explain your reasoning as explicitly as possible.

 

PART IV

  1. Suppose that the government wishes to minimize the present value of costs, zt, which are given for period t by {{z}_{t}}=a\cdot {{\left( {{\pi }_{t}} \right)}^{2}}-b\cdot \left( {{\pi }_{t}}-\pi _{t}^{e} \right)+\left( {c}/{2}\; \right){{\left( {{\pi }_{t}}-\pi _{t}^{e} \right)}^{2}}
    where a, b, c, > 0 are constants, {{\pi }_{t}} is the inflation rate for period t, and \pi _{t}^{e} is the inflation rate that people expected at the start of period t.

    1. If the government takes \pi _{t}^{e} as given, then what value of {{\pi }_{t}} minimizes the cost zt for period t?
    2. If the government acts as in part I., and everyone knows it, then what is the full equilibrium under conditions of rational expectations? Explain the costs that are borne in this equilibrium. How are they affected by an increase in the parameter a, which measures the cost of inflation? Explain the results.
    3. If the government can commit to an inflation rate for period t, then what rate should it commit to? Explain how the costs in this situation compare with those from the equilibrium in part 2.
    4. Can the equilibrium described under 2. still apply if the government takes account of costs in future periods as well as for period t?
  2. Consider the neoclassical growth model for a closed economy of Solow, Cass, Koopmans, et al.
    1. If we think of all countries as closed, does this model imply convergence in the sense that poor countries tend to grow faster per capita than rich countries? Discuss in your answer the distinction between absolute convergence—where the poor grow faster than the rich—and conditional convergence—where a poor country grows faster for given values of some exogenous variables.
    2. How do the rates of convergence in this model relate in a general way to the diminishing returns to capital and to the behavior of the saving rate? How would the rate of convergence be affected by allowing for some capital mobility across countries?
    3. If poor countries tend to grow faster per capita than rich countries does it follow that the dispersion of per capita incomes across countries will tend to narrow over time?

 

Source: Department of Economics, Harvard University. Past General Exams Spring 1991-Spring 1999, pp. 78-83. Copy provided to Economics in the Rear-view Mirror by Abigail Wozniak.

Image Source: Harvard Class Album 1946.