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Exam Questions M.I.T. Suggested Reading Syllabus

M.I.T. Core Economic Growth and Dynamics. Readings and Final Exam. Solow, 1968

 

The reading list and examination questions for the “Economic Growth and Short-run Fluctuations” course taught by Robert Solow in the core graduate macro sequence has been posted earlier for 1966. There were many changes in the readings chosen between 1966 and 1968.

Solow’s 1973 course material for a later revised version (Growth and Capital Theory), that was moved to be the final course in the core macro sequence has also been posted.

Here a glimpse at what students thought about this course (as well as the other courses and instructors in the core theory courses, both micro and macro).

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R.M. Solow
Spring 1968

READING LIST
14.452

As a background text you should have a copy of R.G.D. Allen, Macro-Economic Theory (Macmillan, 1967). For review, read Chapters 1, 3, 7, 8.

ECONOMIC GROWTH

  1. Factual Basis

Kendrick & Sato, “Factor Prices, Productivity and Growth”, American Economic Review, December 1963.
Bureau of the Census, Long-Term Economic Growth, 1860-1965  (This is an excellent compendium of time series. You should spend a few hours with it, and might like to buy a copy from Supt. of Documents, Government Printing Office, Washington, D.C. 20402, $2.75)
Thurow & Taylor, “The Interaction between the Actual and Potential Rates of Growth,” Review of Economics and Statistics, November, 1966.

  1. One-Sector Real Theory

Allen, Chaps. 11, 14.
Hahn & Matthews, “The Theory of Economic Growth: A Survey”, Economic Journal, December 1964, Parts I, II except pp. 812-21.
Modigliani, “Comment” in Behavior of Income Shares (NBER), pp. 39-50.
(Optional: Johnson, “The Neo-Classical One-Sector Growth Model…,” Economica, August, 1966, pp. 265-79 only).

  1. Technical Progress

Allen, Chaps. 13, 15.
Solow et al., “Neoclassical Growth with Fixed Factor Proportions,” Review of Economic Studies, April 1966, pp. 27-89 only).

  1. One-Sector Monetary Theory

Tobin, “Money and Economic Growth”, Econometrica, October 1965.
Sidrauski, “Inflation and Economic Growth,” J.P.E., December, 1967.
Johnson, pp. 279-87 in article cited above.
See also Tobin-Johnson exchange in Economica, February, 1967.

  1. The Golden Rule and Optimal Growth

Marty, “The Neoclassical Theorem”, A.E.R., December 1964.
Diamond, “National Debt in a Neoclassical Growth Model”, A.E.R., December 1965, esp. pp. 1126-1135.
Koopmans, “Objectives, Constraints, and Outcomes in Optimal Growth Models,” Econometrica, January, 1967.

  1. Two (or more) Sector Real Theory

Hahn & Matthews, pp. 812-21.
Allen, Ch. 12.
(Optional: Shell & Stiglitz, “Allocation of Investment in a Dynamic Economy,” Quarterly Journal of Economics, November, 1967).

  1. Income Flows in Long-Run

Thurow, “A Policy Planning Model of the American Economy,” dittoed.

SHORT-RUN FLUCTUATIONS

  1. Cyclical Mechanisms

Samuelson, “Interaction between Multiplier Analysis and the Principle of Acceleration”, Review of Economics and Statistics, 1939, reprinted in A.E.A., Readings in Business Cycle Theory.
Metzler, “The Nature and Stability of Inventory Cycles”, Review of Economics and Statistics, 1941.
Kaldor, “A Model of the Trade Cycle”, Economic Journal, 1940, reprinted in Hansen and Clemence, Readings in Business Cycles and National Income and in Kaldor, Essays on Economic Stability and Growth.

  1. Income Analysis Models

Klein, “The Econometrics of the General Theroy,” Ch. IX in The Keynesian Revolution, SECOND edition.
Okun, “Measuring the Impact of the 1964 Tax Reduction,” xerox.
Surte, “Forecasting and Analysis with an Econometric Model,” A.E.R., March, 1962.
De Leeuw & Gramlich, “The Federal-Reserve-MIT Econometric Model,” Federal Reserve Bulletin, January, 1968.

  1. Inflation

Johnson, “A Survey of Theories of Inflation,” in Essays in Monetary Economics.
Solow, “Recent Controversies in the Theory of Inflation,” dittoed.
Solow & Stiglitz, “Output, Employment and Wages in the Short Run,” dittoed.

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FINAL EXAMINATION
14.452
May 23, 1968

Please answer each question in a separate examination booklet. Indicate on the front page of each booklet whether you are seeking only a grade in 14.452 or a grade in the general examination in economic theory. Those who seek only a grade in 14.452 should answer two questions in Part I and two questions in Part II. Those who are taking the general examination and economic theory should answer two questions in Part II and two in Part III.

Part I

  1. Construct a difference-equation model embodying the following assumptions:
    1. Consumption is a linear function of disposable income lagged one time-unit;
    2. Tax revenue is proportional to national product;
    3. Investment is the sum of a component proportional to the current change in consumption and the component proportional to national product lagged one time-unit;
    4. Imports are proportional to national product lagged one time-unit; exports constant;
    5. Government purchases are constant.

Write down formally the conditions for and an oscillatory response of the model to disturbance. When are the oscillations damped? How do variations in the tax rate affect these conditions? Suppose part of government purchases were made negatively proportional to the last observed change in national product?

  1. Why is technical progress an important part of the usual model of economic growth? Could increasing returns to scale play the same role? What is the special role of purely labor-augmenting (i.e. Harrod-neutral) technical progress?
  2. Imagine a planned economy choosing among steady states in the one-sector model, without technical progress. The planner values both consumption per head and capital per head (as a measure of national strength, say) and his preferences can be expressed by a system of conventionally-shaped indifference curves in consumption per head and capital per head.

Use this indifference map and the requirements for a steady state to show how the optimal steady-state is chosen. Prove that the optimal capital per head will exceed the “Golden-Rule” (maximal consumption per head) level. Show what happens to the optimal position if the rate of population growth increases. Discuss briefly the case of a one-time upward shift in the production function.

 

Part II

  1. In the generalized multiplier-accelerator model, the equation \frac{dK}{dt}=I\left( Y,K \right) means that “investment decisions are always carried out”, so that when I\left( Y,K \right)\ne S\left( Y \right) “unintended consumption or saving” occurs. Replace the above equation with \frac{dK}{dt}=S\left( Y \right), and interpret and analyze the resulting model. Compare its behavior with this with the case analyzed in class.
  2. Suppose I =I(Y,K) and S= S(Y) are the schedules of desired investment and saving. In what sense is (I-S) a measure of excess demand in the aggregate commodity market?
    How is it that no specific supply variables (labor force, for example) appear in this measure? Under what circumstances is it natural to suppose that \frac{dY}{dt} responds to (I-S)? (Y = real output, P = commodity price level). Under what circumstances is it natural to suppose that \frac{dP}{dt} responds to (I-S)?
  3. Consider it a one-sector non-monetary model of growth under the following assumptions:
    1. The production function in intensive form is q= Akb;
    2. The wages equal to the marginal product of labor;
    3. Investment demand is such that the after-tax return on capital is always at a target level r*;
    4. There is a tax on profits at rate t in the government spends all its revenue on consumption;
    5. The savings rates from wages and after-tax profits are both equal to a constant s.

Find the tax rate that will permit a steady-state at full employment. When will it be between zero and one? How does it change if this changes? Interpret.

  1. Considered a one-sector growth model, with two factors of production (capital and labor), constant returns to scale, and no technical progress. Suppose that the propensity to save out of profits and capital gains is equal to one, and the propensity to save out of wages and transfer payments (taxes = negative transfers) is zero.

Money, which is non-interest-bearing government debt, is the only alternative asset to capital. The desired money-capital ratio is of the form \frac{m}{k}=L\left( {f}'\left( k \right)+{{\left( {{\dot{p}}}/{p}\; \right)}^{e}} \right) where m is the real per capita stock of money,k is the capital-labor ratio, and {{\left( {{\dot{p}}}/{p}\; \right)}^{e}} is the expected rate of inflation which is equal to the actual rate \left( {{\dot{p}}}/{p}\; \right) in the steady-state.

  1. Government purchases are zero and the budget deficit, which is equal to the excess of transfers over taxes, is financed by issuing money.
    1. Describe the steady-state characteristics of the model.
    2. Find the rate of inflation that maximizes steady-state consumption per head.
    3. Suppose that {{\left( {{\dot{p}}}/{p}\; \right)}_{0}} is the rate of inflation in (b) that maximizes steady state consumption per head. Would a higher rate of inflation lead to a higher or lower long-run capital-labor ratio?

 

Part III

  1. Write a comprehensive essay on the subject of “The Problem of Weights in National Income and Index-Number Construction”.
    Explain the criteria which are used, should be used (for what purpose?) and why.
  2. Discuss the economic effects of an increase in the stock of money. Include an evaluation of the positions of several (not less than two) prominent economists familiar to you. How would you test the correctness of their positions?
  3. Discuss the effects of inflation on the level of real investment.

 

Source: Duke University, David M. Rubenstein Library. Economists’ Papers Archives. Papers of Robert M. Solow, Box 67, Folder “Exams”.

Image Source:  Robert Solow (right) from MIT Museum website.