Tag: Varian

Categories
Economics Programs Economists M.I.T.

M.I.T. Department of Economics Annual Report by E. Cary Brown, 1975-1976

The following annual report of the M.I.T. department of economics was most likely written for the care and feeding of administrators and the members of the department’s visiting committee. This report covers what was my second year of graduate school, so for folks from that time it reads like an annual Holiday newsletter to the family.

_______________________

Department of Economics
1975 – 76

Undergraduate Program

The long-run impact of the past year’s changes in the Institute Requirement in the Humanities, Arts, and Social Sciences is not yet clear. Unquestionably they have increased the Department’s enrollment, but the precise amount is uncertain because simultaneously a major revision was made in the two introductory economics subjects. In the past year enrollments were larger than previously, but smaller than in the transition of the previous year. Nearly 200 of the Class of 1976 concentrated in economics for their Humanities, Arts, and Social Sciences Requirement. Of all students presently enrolled, 327 (primarily juniors and seniors) have elected to concentrate in economics.

Undergraduate majors remain steady in numbers. As in 1974-75, 20 degrees were awarded. In the spring term the Undergraduate Economics Association was reactivated. Its weekly meetings with faculty led to several proposals for revision of the undergraduate program, and several student-faculty socials were organized.

Graduate Program

Enrollment has been remarkably steady in the graduate program. The number of applications for admission was virtually identical to the average of the previous six years. Next year’s entering class of 32 will be slightly larger than average, and will have fewer foreign students and more women, reflecting a shift in the percentage of applications from these groups. Four students from minority groups are expected to be in this class.

Financial support for the graduate student has changed very little over the last several years. We are still fortunate in having from one-third to one-half of the entering students on National Science Foundation Fellowships. For the whole student body, there has been an increase in the support by US foundations (other than NSF) and a decrease in support provided by M.I.T.

The number receiving the Doctor of Philosophy increased somewhat in the past year to 21. For the first time, two American blacks received degrees.* The class fared well in placement, their median salary offer totaling 24 percent above that of 1971. Like the past average, 86 percent went into teaching and 14 percent into non-teaching positions.

*Samuel Myers, Jr. Ph.D. thesis: “A Portfolio Model of Illegal Transfers”, supervised by Robert Solow.
Glenn Loury. Ph.D. thesis: “Essays in the Theory of the Distribution of Income”, supervised by Robert Solow.
See: William Darity Jr. and Arden Kreeger, “The Desegregation of an Elite Economics Department’s PhD Program: Black Americans at MIT“, History of Political Economy 46 (annual suppl.)

The Graduate Economics Association awarded the outstanding teacher in the Department prize to Professor Stanley Fischer.

PUBLIC SERVICE ACTIVITIES

The faculty has always been involved in public service activities tying research to the public interest. In connection with M.I.T.’s participation in the Bicentennial Celebration, Professor Jagdish N. Bhagwati set up a recent conference on the New International Economic Order: Professor Ann F. Friedlaender is planning one for this fall on Air Pollution and Administrative Control. Through the German Marshall Fund, Professor Richard S. Eckaus is organizing a fall conference on economic problems of Portugal. Professor Franco Modigliani arranged a conference through the Bank of Finland on International Monetary Mechanisms.

Various Congressional committees and government agencies have been advised. Professor Peter A. Diamond served on the Consultant Panel on Social Security for the Congressional Research Service. Professors Rudiger Dornbusch and Fischer and Institute Professor Paul A. Samuelson prepared a report for the US Department of Commerce on international financial arrangements. Professor Robert E. Hall was a member of the Advisory Committee on Population Statistics, Bureau of the Census. Professor Jerry A. Hausman served on the Econometrics Advisory Committee to the Federal Energy Administration. Institute Professor Modigliani was a consultant and member of the Committee on Monetary Statistics, Board of Governors of the Federal Reserve System. Institute Professor Samuelson consulted with the Board of Governors of the Federal Reserve System, the US Treasury, and the Congressional Budget Office. Professor Charles A. Myers was a member of the National Manpower Policy Task Force. Institute Professor Robert M. Solow served as Deputy Chairman, Federal Reserve Bank of Boston.

Several faculty members have been involved with the National Academy of Sciences and its related organizations. Professor Eckaus prepared a report, Appropriate Technology for Developing Countries, for the Board on Science and Technology for Developing Countries of the National Academies of Science and Engineering. Professor Franklin M. Fisher served on a National Academy panel on the Effects of Deterrence and Incapacitation; Professor Friedlaender was on the Executive Committee, Assembly of Behavioral and Social Sciences, National Research Council; Institute Professor Modigliani was on the Finance Committee; Institute Professor Samuelson served on the Editorial Board of the Proceedings; and Institute Professor Solow chaired the Steering Committee on Environmental Studies.

Professor Eckaus led an OECD Mission to Portugal that included Professors Lance Taylor and Dornbusch.* Professor Paul L. Joskow was a consultant to OECD in energy. Professor Evsey D. Domar was a member of a delegation of economists sent by the American Economic Association to the Soviet Union. Institute Professor Modigliani, who gave much time to the problems of stabilization in Italy, was a member of the Board of Directors of the Italian Council for Social Sciences.

*Along with several graduate students among whom were Paul Krugman, Andrew Abel and Jeffrey Frankel. Paul Krugman has written a short note about this experience with a picture!

The Brookings Institution Panel for Economic Activity included Professors Dornbusch and Hall, with Institute Professors Modigliani, Samuelson, and Solow as senior advisors to it. Professor Friedlaender served on the examining committee, Graduate Records Examination, Educational Testing Service. Institute Professor Modigliani served on the Committee on Economic Stabilization, Social Science Research Council. Professor Fisher is a member of the Board of Governors of Tel Aviv University. Institute Professor Solow continues as Trustee for the Institute of Advanced Study.

RESEARCH

International topics seem to dominate the research interests of the faculty. Professor Bhagwati, in addition to his work in developing countries and international trade theory, has given attention to a proposal for applying taxation to the brain drain. Professor Eckaus studied the role of financial markets and their regulation and the behavior of income distribution in economic development. Professor Taylor had three major areas of research: the development of nutrition planning models in Pakistan, international food aid and reserve policies, and growth and income distribution in Brazil.

Professor Morris A. Adelman’s continuing research on the world oil market, Professor Joskow’s analysis of the international nuclear energy industry, and Professor Martin L. Weitzman’s examination of OPEC and oil pricing involve applied microeconomics with international implications.

Research in various applied microeconomics areas was responsible for the second largest fraction of faculty effort. Institute Professor Solow continued to research the economics of exhaustible resources, and Professor Weitzman completed his analysis of the optimal development of resource pools. Professor Joskow has explored the future of the electric utility industry and its financing, the future of the US atomic energy industry, and the pattern of energy consumption in the US. He is developing a simulation model of the energy industry, and is reviewing the regulatory activities of government agencies in general and the health care sector in particular. Professor Hausman examined the Project Independence Report and is analyzing the choice of new technologies in energy research.

In the transporation field, Professor Friedlaender surveyed the issues in regulatory policy for railroads and alternative scenarios in federal transporation policy. Professor Jerome Rothenberg examined such problems in urban transportation as pricing policies, demand sensitivity to price, and modeling locational effects. Professor William C. Wheaton considered an optimal pricing and investment policy in highways under a gasoline tax.

Inextricably intertwined with urban transportation are questions of urban location and housing. Professor Rothenberg carried out research in such aspects of this problem as microeconomics of internal migration, supply-demand for housing in multizoned areas, the impact of energy costs on urban location, and the development of a model of housing markets and of metropolitan development and location that can be applied to general policy questions. Professor Wheaton developed an equilibrium model of housing and locational choice based on Boston experience.

Institute Professor Modigliani also conducted research on the housing market, but his interest comes primarily from the side of stabilization policies and similar macroeconomic problems. He also participated in a review after 20 years of his life cycle hypothesis of saving, made monetary policy prescriptions for both the US and Italy, reflected on the description of financial sectors in econometric models, and explored more deeply the application of optimal control to the design of optimal stabilization policies in economic models. Institute Professor Samuelson reviewed the art and science of macromodels over the 50 years of their development. Professor Friedlaender completed a quarterly macromodel of the Massachusetts economy. Professor Hall developed a model to deal with income tax changes and consumption.

Public economics has both macro and micro aspects, both of which are represented in the Department’s research. With Visiting Professor James A. Mirrlees, Professor Diamond theorized about public shadow prices with constant returns to scale, and about the assignment of liability. He also has generalized the Ramsey tax rule and continued his research into an optimal Social Security system. Professor Hausman is reexamining the cost of a negative income tax; Professor Rothenberg analyzed the distributional impact of public service provision; and Professor Wheaton explored intertemporal effects of land taxes, fiscal federalism in practice, and the financial plight of American cities.

Besides such theoretical research, there was significant research of an entirely pure nature. Professor Robert L. Bishop reexamined the measurement of consumer surplus. Professor Fisher extended his exploration of the stability of general equilibrium and of aggregate production functions. Professor Weitzman investigated the welfare significance of national product in a dynamic economy. Professor Hal R. Varian further explored the theory of fairness, non-Walrasian equilibria, and macromodels of unemployment and disequilibrium. Professor Hausman examined the econometric implications of truncated distributions and samples, of probit models, and of simultaneous equation models. In historical research, Professor Domar was concerned with serfdom, while Professor Charles Kindleberger investigated the role of the merchant in nineteenth-century technologic transfer.

Publications

Professor Bhagwati edited Taxing the Brain Drain: A Proposal and Brain Drain and Taxation: Theory and Empirical Analysis, and coauthored Foreign Trade Regimes and Economic Development: India. Professors Dornbusch and Kindleberger published numerous papers on implications of the new international monetary exchange structure for exchange rates, price stability, international trade, and international capital movements. Professor Weitzman continued his study of the Russian economy with a paper on the new Soviet incentive model.

With Visiting Professor of Management Ezio Tarantelli*, Institute Professor Modigliani published Labor Market, Income Distribution and Private Consumption (in Italian) and various papers on stabilization policy in Italy. He also wrote papers on inflation and the housing market and edited New Mortgage Designs for Stable Housing in an Inflationary Environment. Professor Hall’s labor market research resulted in papers on persistence of unemployment, occupational mobility, and taxation of earnings under public assistance. Professor Michael Piore wrote on labor market stratification and the effect on industrial growth of immigration from Puerto Rico to Boston. Professor Fisher had several publications on indexation and adjustment of mortgages to inflationary episodes. In the realm of economic history, Professor Temin published Reckoning with Slavery and Did Monetary Force Cause the Great Depression?

*Ezio Tarantelli was the victim of a Red Brigades’ assassination in 1985.

Institute Professor Samuelson published theoretical papers on factor price equalization and trade pattern reversal. In the realm of pure research, he put out papers on nonlinear and stochastic population analysis, optimal population growth, and the optimal Social Security system implied in a lifecycle growth model. He also brought out the tenth edition of his famous text, Economics: An Introduction Analysis.

FACULTY

Visiting Professor John R. Moroney was here from Tulane University; Visiting Professor Mirrlees came in the spring term from Nuffield College, Oxford University. Regular faculty on leave were Professors Fisher and Joskow in the fall and Professor Weitzman in the spring.

It is a pleasure to report the promotion to Associate Professor of Jerry A. Hausman. A new appointee, Professor Jeffrey E. Harris, with the unusual background of an M.D. and a Ph.D. in economics, will provide long-sought coverage in health economics.

Professor Kindleberger will retire as Ford Professor and become a Senior Lecturer on a half-time basis. Since 1948, when he came as an Associate Professor, Professor Kindleberger has been an effective teacher, scholar, participant in faculty governance, and counselor to governments and the public. He has trained the leading international economists of the next generation; he has produced a dozen books and more than a hundred articles in international trade and finance and in economic history. He epitomizes the highest kind of academician.

Several honors were bestowed on members of the Department. Institute Professor Modigliani will complete his year as President of the American Economic Association. Professor Myers received a Distinguished Alumni award from Pennsylvania State University. Professor Fisher was F.W. Paish Lecturer to the Association of (English) University Teachers of Economics. Institute Professor Solow received a D. Litt. from Warwick University, and Institute Professor Samuelson, a D.Sc. from the University of Rochester.

EDGAR CARY BROWN

Source: MIT Libraries, Institute Archives and Special Collections. MIT Department of Economics Records, Box 1, Folder “Annual Report 1975-6”.

Image Source: Building E52, Alfred P. Sloan Jr. Building, later Morris and Sophie Chang Building

 

https://mitmuseum.mit.edu/collections/subject/building-e52-alfred-p.-sloan-jr.-building-later-morris-and-sophie-chang-building-52

Categories
Courses Exam Questions Problem Sets Syllabus

MIT. Core Microeconomic theory III. Hal Varian, 1975

Hal R. Varian, chief economist at Google since 2007, was a 28 year old assistant professor at M.I.T. in 1975 when he taught my cohort the third in a sequence of four half-term courses that constituted MIT’s required core of graduate microeconomic theory. He assigned draft chapters from his graduate textbook Microeconomic Analysis (published in 1977). For this post I have transcribed the course outline, five problem sets and the final examination for the course.

Core microeconomic theory at MIT in 1974-75:

14.121 (linear models and production) was taught by Martin Weitzman,
14.122 (competitive and noncompetitive market structures) taught by Robert L. Bishop,
14.123 (theory of the consumer and resource allocation) was taught by Hal Varian,
14.124 (capital theory, uncertainty and welfare economics) was taught by Paul Samuelson.

_______________________

14.123—Microeconomic Theory III
Theory of the Consumer and Resource Allocation

Professor Hal R. Varian, E52-353, 3-2662
Spring, 1975

Feb. 5 advanced placement exam
Feb. 10 utility; demand; expenditure
Feb. 12 indirect utility; Slutsky equation
Feb. 17 no class
Feb. 19 no class
Feb. 24 demand functions; duality
Feb. 26 expected utility; properties
Feb. 28 general equilibrium; existence
Mar. 3 welfare theory
Mar. 5 the core of an exchange economy
Mar. 10 general equilibrium and production
Mar. 12 dynamics and general equilibrium
Mar. 17 malfunctions of the market mechanism
Mar. 19 final exam

Course text will be lecture notes available from me. Malinvaud and Arrow and Hahn are highly recommended secondary reading. There will be four or five problem sets and a problem session on Fridays, 9-10:30.

_______________________

 

14.123 Spring, 1975
Professor Hal R. Varian

Consumer Theory I

  1. Consider a consumer with a Cobb-Douglas utility function:
    u(x,y) = a ln x + (1-a) ln y.
    Calculate:

    1. demand functions for x and y
    2. the indirect utility function
    3. the expenditure function
    4. the Hicksian demand functions.
  2. In a general equilibrium analysis, we cannot take income as an exogenous variable in the demand function since income, y = p.w, depends on the vector of relative prices. Derive the Slutsky equation for Dpm(p, p.w) in this case.
  3. At a general equilibrium price vector p*, we have aggregate supply equal aggregate demand:
    Σ mi(p*, p*.w) = Σ wi. Show that if all agents have identical marginal propensities to consume each good (Dymi(p*, p*.w) = Dymj(p*, p*.w) for all i and j) then all aggregate demand curves must be downward sloping at equilibrium. More generally, show that Dp(Σ mi(p*, p*.wi)) is negative semi-definite.
  4. Define eij = (-pj/xi) Dpjmi(p,y) be the cross price elasticity of good i with respect to price j, and ri = pi mi(p, y)/y, the income share of commodity i.
    Show that r1e11 + r2e21 +r3e31  = r1.

_______________________

14.123 Spring, 1975
Professor Hal R. Varian

Consumer Theory II

  1. A consumer is found to have a utility function of the form
    u = -1/x1 – 1/x2.

    1. Starting from the utility function, compute the market demand functions for the consumer when he has income y and faces prices p1 and p2.
    2. Use the market demand functions to show that the indirect utility function is
      u = -( √(p1) + √(p2))2/m.
    3. Compute the expenditure function from the indirect utility function.
    4. Compute the consumer’s compensated and market demand curves from the expenditure function.
  2. Suppose at prices (p1, p2) = (5,10) and income y = $100, a rational consumer consumes the bundle (6,7). Assume that we have measured the following derivatives:

∂H1/∂p1 (p1, p2, ū) = -2
∂H1/∂p2 (p1, p2, ū) = +1
∂M1/∂y (p1, p2, y) = 2/7

where H1 and H2 are the Hicksian demand functions for goods 1 and 2 and M1 is the Marshallian demand function for good 1. Find an estimate of the consumption bundle of the consumer at (p1, p2) = 5,11).

  1. Suppose a consumer has an expenditure function of the form e(p, u) = u.g(p). Show that his utility function is homogenous of degree one. Suppose e(p,u) is of the form e(p,u) = h(u)g(p). How does the consumer’s behavior differ?
  2. Suppose a consumer has a differentiable expected utility function for income with Dyu(y) strictly positive. Show that he will always take a small enough bet as long as it has positive expected value.

_______________________

 

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium III

  1. Show that Walras law holds for a production economy with fully distributed profits.
  2. Prove the theorem that a general equilibrium is pareto efficient for an economy with production.
  3. Suppose we have a productive economy with two agents. The producer has a production function x = q1/2 where x is output and q is labor.
    The consumer has a utility function u(x,q) = x1/2(1-q)1/2. Calculate the general equilibrium real wage and equilibrium level of profits.

_______________________

 

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium Theory and Welfare Economics I

  1. Show that any solution to

max Σ ai ui(xi), ai>0
s.t. Σ xi ≤ w

is necessarily pareto efficient.

  1. Suppose we have two agents with indirect utility functions

v1(p1, p2, y) = ln y –a ln p1 – (1-a) ln p2
v2(p1, p2, y) = ln y –b ln p1 – (1-b) ln p2

and initial endowments

w1 = (1,1)
w2 = (1,1)

Calculate the market clearing price.

  1. We have two agents with utility functions

u1(x1, y1) = a ln x1 +(1-a) ln y1
u2(x2, y2) = b ln x2 + (1-b) ln y2

and initial endowments

w1 = (1,0)
w2 = (0,1)

Calculate the market equilibrium prices in terms of the parameters a and b.

_______________________

 

14.123 Spring, 1975
Professor Hal R. Varian

General Equilibrium Theory and Welfare Economics II

  1. Two agents with strictly convex preferences have equal initial endowments
    w1 = w2. They trade to an arbitrary allocation in the Core (w1,w2), (x1,x2). Prove that this allocation is necessarily fair:

    1. Draw an Edgeworth box and give a geometric argument;
    2. give an algebraic argument in the general case (there is a one-line proof.)
    3. Show in a three person economy there are allocations in the equal division core that are not fair.
  2. Suppose we have n agents with identical, strictly convex preferences and we have some initial bundle of k goods to be divided among them. Let x be a fair allocation; show that x must give the same bundle to each agent. (Recall that a fair allocation is one that is strongly pareto efficient and such that no agent prefers any other agent’s bundle to his own.)
  3. Show that under appropriate assumptions of convexity, every pareto efficient allocation is necessarily a solution to a problem of maximizing a weighted sum of utilities. What is the economic interpretation of the weights?
  4. Suppose we are at a market allocation that is considered good. Since it is a market equilibrium it is pareto efficient and therefore maximizes a certain weighted sum of utilities Σ ai* ui(x). Accordingly, we will use Σ ai* ui(x) to evaluate small projects. Suppose we are considering a small project that will change x = (x1,…, xn) to x´= (x1´,…, xn´). Show that it should be undertaken if and only if it increases national income; that is, iff Σ p.(xi´-xi) >0.

_______________________

 

14.123 FINAL EXAMINATION
March 19, 1975

Professor H. Varian

Answer any 2 out of 4. All questions have equal weight. Good luck!

  1. A consumer has a utility function of the form u(x1, x2) = ln x1 + x2. He faces prices p1 and p2 and has income y. Calculate:
    1. his Marshallian demand functions for each good
    2. his indirect utility function
    3. his Hicksian demand functions
    4. his expenditure function.
  2. There are two consumers A and B with the following utility functions and endowments:

UA(XA1, XA2) = a ln XA1 + (1-a) ln XA2 , WA = (0,1)
UB(XB1, XB2) = min (XB1, XB2) , WB =(1,0)

Calculate the market clearing prices and the equilibrium allocation.

  1. We have n agents with identical strictly concave utility functions, u1(x1),…,un(xn). There is some initial bundle of goods w. Show that equal division is a pareto efficient allocation.
  2. A consumer has a differentiable expected utility function u(y) with u´(y) > 0. (There are no conditions on u´´(y)). His initial level of wealth is w and he is contemplating a bet which gives him $e with probability p > ½ and he loses $e with probability 1-p. (Notice the bet has positive expected value.) Show that he will always take the bet if e is small enough. (Hint: try Taylor series.)

 

Source: Personal copies.

Image Source: Detail from 1976 departmental group photo.

Categories
Economists M.I.T.

MIT. Department of Economics Group Photo, 1976

Back Row:  Harold FREEMAN, Hal VARIAN, Jerome ROTHENBERG, Peter DIAMOND, Jerry HAUSMAN

4th Row: Paul JOSKOW, Anne FRIEDLAENDER, JOHN R. MORONEY (VISITOR TO DEPARTMENT)

3rd Row: Stanley FISCHER, Jagdish BHAGWATI, Rudiger DORNBUSCH, Robert SOLOW, Robert HALL

2nd Row: Edward KUH, Morris ADELMAN, Abraham J. SIEGEL, Richard ECKAUS, Martin WEITZMAN

1st Row: Evsey DOMAR, Paul SAMUELSON, Charles KINDLEBERGER, E. Cary BROWN, Franco MODIGLIANI, Sydney ALEXANDER, Robert BISHOP

1976_MITEcon_blogCopy

Apparently didn’t get the memo and/or not pictured: Michael PIORE, Frank FISHER, Peter TEMIN.

Thanks to Robert Solow, the photo-bomber standing to Solow’s left in the picture has been identified as a guest from Tulane University, John Moroney. It is possible that I forgot some other person not included in this faculty picture.

I note that the entire front row has gone to that great Department of Economics in the Cloud.

Source: A graduate student buddy of mine who entered the MIT Ph.D. program in 1975/76.

______________________

If you find this posting interesting, here is the complete list of “artifacts” from the history of economics I have assembled of which this is the 250th. You can subscribe to Economics in the Rear-View Mirror below. There is also an opportunity for comment following each posting….