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Economics Programs M.I.T. Undergraduate

M.I.T. Economics department committee (re-)organization. 1976-78

During my second year in graduate school at M.I.T. (1975-76), the economics department professors were engaged in a discussion about reforming the administration of their department. At the time I was completely unaware of this discussion that had been provoked by the following memorandum written by then Department Head, Professor E. Cary Brown, based on his experience with the growing overload of administrative chores and responsibilities in a department with the scale of that attained by M.I.T.’s economics department.

Brown’s memo to the faculty is followed by a transcription of a copy of the letter Brown wrote to Robert Solow, who as an administrative reorganization committee member, must have been asked for some further testimony. The entire committee’s (Peter A. Diamond, Stanley Fischer, Jerry Hausman, Paul Joskow, Robert M. Solow) report was completed two months after Brown’s memo. In the same departmental file from the M.I.T. archives, one finds a copy of the actual assignment of administrative responsibilities for the academic year 1977/78.

Many, if not most, of the administrative tasks had been allocated and faithfully executed before this “reorganization”. I know that Evsey Domar had long been covering the placement of new Ph.D.’s and also proudly serving as the departmental representative for library-related affairs. I sense reading these documents that the truly neglected child all along was the undergraduate program for which some arm-twisting was required to achieve equitable burden-sharing among the faculty. But perhaps there were other specific items that had been sore points too. Maybe Brown simply wanted an explicit organization chart to forestall “whataboutism” from the mouths of relatively uncooperative colleagues. But like I wrote above, this was a discussion that was invisible to me (appropriately so) at the time.

Cf. The committee assignments in the Harvard economics department during the 1972-73 academic year

__________________________

MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF ECONOMICS
CAMBRIDGE, MASSACHUSETTS 02139

March 12, 1976

Economics Department Faculty

Dear [blank]

For some time I have become increasingly dismayed at the increase in the administrative burden in the Department, and now find the present job as Head to be a nearly impossible one. If the job is to be made tolerable, it must have substantial additional faculty support in some form to cut it down to a scope manageable either by me or a successor.

There are two basic ways that this can be achieved: (1) by spreading the administrative activities and responsibilities more widely among the faculty; or (2) placing these tasks on essentially an associate departmental head, whose precise title could take various forms Executive Officer, Academic Officer (e.g., Tony French in Physics), or Associate Head. I personally would favor the Associate Head route, but regard it as an open question subject to further discussion and consideration, and to Administration approval. This new structure should be treated as an experiment, to last no longer than until the next Head is chosen, and to be reconsidered at that time.

My own thinking about the administrative tasks of the Department separates them into four major areas: undergraduate programs, graduate programs, research programs, and personnel and budgeting. While these can be headed by an administrator or by faculty, it seems to me that the first two programs should have formal faculty control regardless of the form the administrative reorganization takes. The graduate program nearly has that form now and largely runs itself, with the exception of a few odds and ends that now lie outside the responsibility of the graduate registration officers. The undergraduate program is a long way from this structure and will require a good deal of imagination, initiative and effort to resuscitate the Undergraduate Economics Association and provide more guidance and support for majors. The research programs (student and faculty) focus more or less clearly under the Committee on Economic Research. Personnel and budgeting are an administrative responsibility. They have involved increasing amounts of time as budgets have tightened, space has tightened, and the search for new faculty has expanded.

The administrative structure is an important matter to the Department. Because it involves departmental administration and the role of the Department Head, it concerns the Administration through Dean Hanham. He has asked me to appoint the following committee to consider these questions of reorganization and to make recommendations: Bob Solow, Peter Diamond, Stan Fischer, Paul Joskow, and Jerry Hausman. Please give your views to members of the committee as soon as you can.

Sincerely,
[signed “Cary”]
E. Cary Brown, Head

ECB/sc

__________________________

Brown to Solow

March 16, 1976

Professor Robert Solow
E52-383

Dear Bob:

I shrink from making organization charts, but the following diagram is intended to give some idea of the orders of magnitude of faculty involvement in departmental chores.

Chairman, Committee on Undergraduate Studies

  1. Faculty counselors (we have agreed with the UEA to keep members to 10 or less, and let faculty build up expertise by staying adviser for freshman, sophomore, junior, or senior year).

—10 faculty: 2 for each class. 4 for seniors

  1. Faculty adviser for humanities concentration in economics (advises and signs up students); also considers the eligibility of economics subjects, what we consider concentration, etc.
  2. Closely related to (2) is possible membership on the so-called Humanities Committee that approves and reviews the whole Humanities, Arts, and Social Science requirement and program. (We have no one on this year but as the largest concentration will surely need to have a presence.)
  3. Approval of transfer of credits from other schools to M.I.T.
  4. Advising with Undergraduate Economic Association in matters academic, professional, social.
  5. Undergraduate placement, while an Institute responsibility, could be supervised and assisted by a faculty member who would keep up to date on summer placement, interning possibilities, salaries. The experience our students have applying to graduate schools, actual jobs offered and taken.
  6. Design of curriculum, cooperative program, etc.
  7. Various activities, such as providing information to undergraduates in their choice of major (Midway in fall, seminar in spring), Open House activities, Alumni activities, etc.
  8. Relations with other Departments at undergraduate level, such as subject offerings, subject content, etc.
  9. Supervision and staffing of undergraduate subjects with multiple sections — 14.001, 14.002, 14.03, 14.04, 14.06, 14.30, 14.31.
  10. Catalog copy.

Chairman, Committee on Graduate Studies

  1. Graduate Registration Officers, so far one each for first two years, and one for thesis writers. Has been suggested that we have an additional adviser for foreign students and minority and women?
  2. Admissions Committee has, in the past, had three members.
  3. Placement, both summer and permanent.
  4. Supervision of core subjects.
  5. Ph.D. and M.S. requirements, program, size.
  6. Financial aid — coordinating various GRO; Admissions Committee, and Budget limitations.
  7. Graduate School Policy Committee meetings.
  8. Annual revision of brochure.
  9. Graduate Economics Association, Black Graduate Economics Association.
  10. Catalog copy.
  11. Various activities — professional and social that are not contained within a particular class.

Chairman, Committee on Economic Research (I faculty)

  1. Organized list of faculty projects requiring research assistants and the supply of them (both graduate and undergraduate). Assignment of R.A.’s.
  2. Assistance in research proposals.
  3. Inventory of internships and off-campus research.
  4. Supervision of unscheduled subjects, such as UROP, Undergraduate Seminar, and thesis.
  5. Supervision of M.I.T. Working Paper Series.
  6. Allocation of computer funds, developing rules, developing alternative sources.

Personnel and Budgeting (Administrative Officer and a large chunk of my time)

  1. Personnel
    1. Nonfaculty is supervised by the Administrative Officer.
    2. Faculty Personnel

(1) Employment — new Ph.D.’s and senior faculty
(2) Review and promotion
(3) Assignments, leaves, research

    1. Postdoctoral personnel
  1. Space allocations, revisions.
  2. Budget Proposals
  3. a. Proposals
    b. Implementation

Telephone
Xerox & Ditto
Supplies
Equipment

There may be other matters that I am leaving out – routine meetings average probably a day a week, and things like that. Consultations with faculty, students, and other Departments, would probably add a couple more days.

If there are questions, I’ll oblige, of course.

Sincerely,
E. Cary Brown, Head

ECB/sc

__________________________

MEMORANDUM

May 10, 1976

TO:       Department Faculty
FROM: Committee on Reorganization (PAD, SF, JH, PJ, RMS) [Peter A. Diamond, Stanley Fischer, Jerry Hausman, Paul Joskow, Robert M. Solow]

SUBJECT:         Reorganization

ECB’s [E. Cary Brown] letter of March 12, which created this committee, starts from the premise that the administrative burden on the Department Head has become essentially impossible. This seems clearly to be the case. It has happened because the department has increased in size and complexity without any corresponding adaptation of its administrative arrangements. Every new function has fallen into the Head’s lap. (Top that, anyone.) Apart from the sheer burden of work thus created, another problem is the difficulty of communications, because that is also time-consuming.

After some palaver and negotiation, we have a reorganizational package to suggest. It rests on two conditions; since it is something of an interconnected web, it will probably unravel if the two conditions can not be met. (1) Since the only way to correct an excessively centralized structure is to decentralize it, we propose to diffuse administrative responsibility more widely through the department; there will be at least one serious administrative post for everyone, or perhaps two minor posts instead, but everyone will have to participate. (2) The administrative load attached to the undergraduate program has increased with the size of the enrollment and the improvement of the curriculum; no one wants to manage an inadequately staffed program. We propose, therefore, that the normal teaching load for everyone in the department be agreed to be half graduate and half undergraduate teaching. This definition should be extended to everyone on the departmental budget: joint appointees, visiting professors, etc. As soon as there are a couple of exceptions to this understanding, there will be more. Then the management of the undergraduate program will break down, and it will revert or default to the Department Head, and that is what we are trying to stave off.

The particular organization we have in mind is as follows.

  1. The central functions (budgeting, space, leaves, relations with the MIT hierarchy, etc.) will be in the hands of the Department Head and an Associate Head namely PAD [Peter A. Diamond]). In addition, one of them (probably ECB [E. Cary Brown]) will be an ex officio member of the Committee on Undergraduate Studies to be proposed below, and the other will be an ex officio member of the Committee on Graduate Studies. The precise division of labor is obviously a matter of taste; for the moment, ECB [E. Cary Brown] will probably do most of the relations with the MIT structure and PAD [Peter A. Diamond] will concentrate on intra-departmental matters.
  2. There will be a Director of Undergraduate Studies (PT [Peter Temin]), who will be chairman of a Committee on Undergraduate Studies (with 2 or 3 additional members, possibly RD [Rudiger Dornbusch], PJ [Paul Joskow] and one other). This committee will be responsible for revisions of the undergraduate curriculum adding and subtracting subjects, staffing them, degree requirements, etc. In recent discussions with the Undergraduate Economics Association, the proposal has merged that there should be a larger number of Undergraduate Advisors (i.e., registration officers) than there is now, with each taking care of at most 10 students. That suggests we would need about 8 such advisors. The members of the Committee might serve as advisors, plus others. Merely serving as registration officer for 10 undergraduates is by itself not an onerous job.
  3. There seems to be no need for change in the organization of graduate studies in the department. We suggest that there be a Director of Graduate Studies (RSE [Richard S. Eckaus]) and a Committee on Graduate Studies which would, as now, consist of the other two Graduate Registration Officers. Things are going very well now with REH [Robert E. Hall] handling the first-year students. MJP [Michael J. Piore] the second-year students and RSE [Richard S. Eckaus] the thesis-writers. REH [Robert E. Hall] is prepared to take on the task or devising a scheme to keep track of post-generals students, and see that they find themselves a reasonable thesis topic in a reasonable amount of time. The scheme may need another person to look after it.
  4. We suggest the creation of Committee on Staffing whose functions would include looking after the hiring of assistant professors, the dovetailing of visiting professors with faculty leaves, and the rationing of visiting scholars. The picture we have is that the members of committee would do the interviewing and preliminary screening of new Ph.D.’s at the annual meetings, and decide which of them to invite to come and give seminars. At that stage and thereafter, the whole department faculty would be in on the act, and final decisions would be made, as they are now, in a department meeting. The main time-consumer for this committee would be the correspondence in connection with hiring. Since that would fall on the Chairman, that post would be a major one. For the other members of the committee, the burden would be relatively light. We suggest REH [Robert E. Hall] as chairman, plus perhaps 3 others.
  5. There seems to be no reason to change the way the Admissions Committee now functions.
  6. We see no need for major change in the Placement process. Our only suggestion are (a) perhaps to provide EDD [Evsey D. Domar] with another person to share the load, and (b) to have a pre-season department meeting, analogous to the post-generals meeting, at which each graduate student entering the market could be discussed by the full facuIty, and information and ideas collected.
  7. There are other details. RLB [Robert L. Bishop] is functioning as advisor to MIT undergraduates thinking about economics as part of their Humanities requirement, and we are happy to preserve that human capital. MAA [Morris A. Adelman] who has been our representative to CGSP is to begin a term on the CEP, which should count as a major administrative burden. We need his successor on CGSP.

One last point: we hope that each committee chairman will promptly send a written notice of each substantive decision to the Head and Associate Head for distribution to the department faculty, so that communications are well looked after. That plus rational expectations should do the trick.

Source: MIT Archives. MIT Department of Economics Records. Box 2, Folder “Department Organization”.

__________________________

DEPARTMENTAL ADMINISTRATIVE RESPONSIBILITIES:
ECONOMICS DEPARTMENT 1977-78
  1. UNDERGRADUATE COMMITTEE
Chairman: Peter Temin
Members: Cary Brown Senior Faculty Counsellor, Ex Officio
Jerry Rothenberg Senior Faculty Counsellor
Peter Temin Senior Faculty Counsellor
Rudiger Dornbusch Junior Faculty Counsellor
Jeffrey Harris Junior Faculty Counsellor
Jagdish Bhagwati Sophomore Faculty Counsellor (Fall)
Henry Farber Sophomore Faculty Counsellor (Spring)

Summer Jobs: Jeffrey Harris
Humanities Adviser: Robert Bishop
Transfer of Credits: Cary Brown

  1. GRADUATE COMMITTEE
Chairman: Richard Eckaus Thesis, Graduate Registration Officer
Members: Paul Joskow/Mike Piore Second Year Graduate Registration Officer
Marty Weitzman First Year Graduate Registration Officer
Jerome Rothenberg CGSP Representative
Stan Fischer, Ex Officio

Admissions Committee:

Chairman: Robert Bishop
Members: Frank Fisher and Lance Taylor

Placement: Evsey Domar
Harvard-MIT Theory Seminar: Eric Maskin
Theory Workshop: Kevin Roberts

  1. OTHER DEPARTMENTAL ACTIVITIES

Staffing Committee: Chairman: Rudiger Dornbusch

(For New Ass’t Profs.) Members:

Paul Joskow
Jerry Hausman
Stan Fischer, Ex Officio
(Added for Temporary Visitors: Robert Solow)

Independent Activity Period: Jeffrey Harris/Marilyn Simon
Unstructured Subjects Committee: Peter Temin, Undergraduate; Richard Eckaus, Graduate
Computer Allocation: Richard Eckaus

ADDENDUM: INSTITUTE COMMITTEES

CEP: Morris Adelman
Associate Chairman of the Faculty: Michael Piore
Visual Arts: Jerry Rothenberg
Library System, Chairman: Evsey Domar

Image Source:  For this portrait of members of the M.I.T. economics department in 1975 see the Economics in the Rear-view Mirror post that provides identifications.

Categories
Exam Questions Harvard

Harvard. General Examination in Microeconomic Theory. Spring, 1993

Economics in the Rear-view Mirror has been provided a copy of nearly all the 1990s general exams in micro- and macroeconomic theory from Harvard through the collegial generosity of Minneapolis Fed economist Abigail Wozniak. With this post you now have the Spring 1993 graduate general exams in microeconomic theory.

While these exams lie outside of my personal comfort zone as a historian of economics (1870-1970), for fledgling historians of economics of today and tomorrow these are indeed legitimate historical artifacts definitely worth transcription. I am rather slow in digitizing them because transcription of mathematics for this blog requires latex inserts. Latex expressions involve considerably longer roundabout production than the application of my talents for touch-typing/OCR to non-mathematical text. Patience! The Rest is Yet to Come! 

________________________________

Previously Transcribed Harvard Graduate General Exams

Spring 1989: Economic Theory

Spring 1991: MicroeconomicsMacroeconomics

Spring 1992: Micro- and Macroeconomics

Fall 1992:  Micro- and Macroeconomics

________________________________

Graduate Microeconomic Theory Sequence, 1992-93

Economics 2010a. Economic Theory

Michael D. Whinston and Eric S. Maskin

Covers the theory of individual behavior including the following topics: constrained maximization, duality, theory of the consumer, theory of the producer, behavior under uncertainty, consumer choice of financial assets, externalities, monopolistic distortions, game theory, oligopolistic behavior, asymmetric information.

Prerequisite: Economics 2030 or equivalent; can be taken concurrently.
Half course (fall term). Tu., Th., 10-11:30.

Economics 2010b. Economic Theory

Andreu Mas-Colell and Stephen A. Marglin

General equilibrium, stability, pure and applied welfare economics, uncertainty, descriptive and optimal growth theory, income distribution, methodology.

Prerequisite: Economics 2010a.
Half course (spring term). Tu., Th., 10-11:30.

Source: Harvard University, Faculty of Arts and Sciences. Courses of Instruction 1992-1993, p. 248.

________________________________

HARVARD UNIVERSITY
DEPARTMENT OF ECONOMICS

Economics 2010b: FINAL EXAMINATION and
GENERAL EXAMINATION IN MICROECONOMIC THEORY

Spring Term 1993

For those taking the GENERAL EXAM in microeconomic theory:

  1. You have FOUR hours.
  2. Answer a total FIVE questions subject to the following constraints:

— at least ONE from Part I;
— at least TWO from Part II;
EXACTLY ONE from Part III.

For those taking the FINAL EXAMINATION in Economics 2010b (not the General Examination):

  1. You have THREE HOURS
  2. Answer a total of four questions subject to the following constraints:

— DO NOT ANSWER ANY questions from Part I;
— at least TWO from Part II;
— at least ONE from Part III.

PLEASE USE A SEPARATE BLUE BOOK FOR EACH QUESTION

PLEASE PUT YOUR EXAM NUMBER ON EACH BOOK

Part I (Questions 1 and 2)

  1. Suppose that there are J firms producing good \ell differentiable cost function c(w,q) where w is a vector of input prices and q is the firm’s output level. The differentiable aggregate demand function for good \ell is x(p), where p is good \ell’s price. Assume c(w,q) is strictly convex in q and that (p)≤0. Also assume that partial equilibrium analysis is justified.
    1. Suppose that all factor inputs can be adjusted in the long-run, but that input k cannot be adjusted in the short-run. Suppose that we are initially at an equilibrium where all inputs are optimally adjusted to the equilibrium level of output \bar{q} and factor prices \bar{w} so that, letting z_{k}\left( \bar{w} ,\bar{q} \right) be the conditional factor demand function for factor k, we have z_{k}=z_{k}\left( \bar{w} ,\bar{q} \right). What can be said about the short-run versus long-run output response of the firm to a differential change in the price of good \ell? What does this imply about the short-run versus long-run equilibrium response of p to a differential exogeneous shift in the demand function (hold the number of firms fixed in both cases)? (Hint: Define a short-run cost function c_{s}\left( w,q,z_{k}\right)  giving the minimized cost of producing output q given factor prices w when factor k is fixed at level z_{k}).
    2. Now suppose that all factor inputs can be freely adjusted. Give the weakest possible sufficient condition, stated in terms of marginal and average costs and/or their derivatives, that guarantees that if the price of input k\left( w_{k}\right) marginally increases, then firms’ equilibrium profits decline for any demand function x\left( \cdot \right) with x^{\prime }\left( \cdot \right)  \leq 0. Show that if your condition is not satisfied, then there exist demand functions such that profits increase when the price of input k increases. What does your condition imply about the firm’s conditional factor demand for input k?
  2. A. Consider a one-shot two-player game in which player 1 has a set of possible moves M1 (with n1 elements) and player 2 has a set of possible moves M2 (with n2 elements). Players move simultaneously. How many strategies does each player have?

B. Now suppose that the game is changed so that player 1 moves before 2, and 2 observes 1’s move, but that the game is otherwise the same as before. That is, the sets of moves are still M1 and M2, and player 1’s and 2’s payoffs as functions of moves \psi_{1} \left( m_{1},m_{2}\right) \text{ and } \psi_{2} \left( m_{1},m_{2}\right), respectively, are unchanged. How many strategies does each player have in the altered game?

C. The game of part B may have multiple subgame-perfect equilibria. Show, however, that, if this is the case, there exist two pairs of moves \left( m_{1},m_{2}\right)\text{ and } \left( m^{\prime }_{1},m^{\prime }_{2}\right) (where either m_{1}\neq m^{\prime }_{1}\text{ or } m_{2}\neq m^{\prime }_{2} ) such that either

(*) \psi_{1} \left( m_{1},m_{2}\right)  =\psi_{1} \left( m^{\prime }_{1},m^{\prime }_{2}\right)
or
(**) \psi_{2} \left( m_{1},m_{2}\right)  =\psi_{2} \left( m^{\prime }_{1},m^{\prime }_{2}\right).

D. Suppose that, for any two pairs of moves \left( m_{1},m_{2}\right)\text{ and } \left( m^{\prime }_{1},m^{\prime }_{2}\right)  such that m_{1}\neq m^{\prime }_{1}\text{ or } m_{2}\neq m^{\prime }_{2}, (**) is violated, i.e., \psi_{2} \left( m_{1},m_{2}\right)  \neq \psi_{2} \left( m^{\prime }_{1},m^{\prime }_{2}\right). In other words, player 2 is never indifferent between pairs of moves. Suppose that there exists a pure-strategy equilibrium in the game of part A in which \pi_{1} is player 1’s payoff. Show that in any subgame-perfect equilibrium of part B, player 1’s payoff is at least \pi_{1}. Would this conclusion necessarily hold for any Nash equilibrium of part B? Why or why not?

E. Show, by example, that the conclusion of part D may fail if either

(a) \psi_{2} \left( m_{1},m_{2}\right)  =\psi_{2} \left( m^{\prime }_{1},m^{\prime }_{2}\right)  holds for some pair \left( m_{1},m_{2}\right)  ,\left( m^{\prime }_{1},m^{\prime }_{2}\right) with m_{1}=m^{\prime }_{1}\text{ and } m_{2}=m^{\prime }_{2}; or

(b) we replace the phrase “pure-strategy equilibrium” with “mixed-strategy equilibrium.”

Part II (Questions 3, 4, & 5)

QUESTION 3 (General Equilibrium with Gorman Preferences)
(20 points)

Suppose you have a population of consumers i = 1,….,I. Ever consumer i has an endowment vector of commodities \omega_{i} \in R^{I} and preferences expressed by an indirect utility function v_{i}\left( p,w_{i}\right).

(a) (5 points)

Let \left(\bar{x}_{1},\cdots,\bar{x}_{I}\right) be a Pareto optimal allocation. The utility levels of this allocation are \left(\bar{u}_{1},\cdots,\bar{u}_{I}\right). The second welfare theorem asserts the existence of a price vector \bar{p} and wealth levels \left(\bar{w}_{1},\cdots,\bar{w}_{I}\right) supporting the allocation. What does this mean? Express \left(\bar{u}_{1},\cdots,\bar{u}_{I}\right) in terms of the indirect utility functions.

Assume for the next two parts of this question (b and c) that the indirect utility functions take the (Gorman) form v_{i}\left( p,w_{i}\right)  =a_{i}\left( p\right)  +b\left( p\right)  w_{i}. Note that b\left(\cdot\right) does not depend on i. In the following, neglect always boundary allocations. Use of pictures is permissible and helpful.

(b) (5 points)

Show that for the above family of utility functions all the Pareto optimal allocations are supported by the same price vector.

(c) (5 points)

Use the conclusion of part (b) to argue that the Walrasian equilibrium allocation is unique. (Assume preferences are strictly convex.)

For the last part of the question (d) assume that indirect utilities are of the form v_{i}\left( p,w_{i}\right)=b_{i}\left(p_{i}\right)w, that is, the preferences on commodity bundles are homothetic (but possibly different across consumers).

(d) (5 points)

Argue by means of an Edgeworth box example (or in any other way you wish!) that the multiplicity of Walrasian equilibria is possible even if preferences are restricted to be homothetic.

QUESTION 4 (Revelation of Information Through Prices)
(20 Points)

Suppose there are two equally likely states s_{1},s_{2} and two traders. In each state there is a spot market where a good is exchanged against numeraire. The utilities of the two traders are (the second good is the numeraire):

STATE 1 STATE 2
TRADER 1 2 ln x11x21

4 ln x11 + x21

TRADER 2

4 ln x12 – x22

2 ln x12 + x22

The total endowment of the first good equals 6 in the first state and 6+\varepsilon    in the second state. All the endowments of this good are received by the second trader. Assume that the endowments of numeraire for the two traders are sufficient for us to neglect the possibility of boundary equilibria. The price of the numeraire is fixed to 1 in the two states. The prices of the non-numeraire good in the two states are denoted \left( p_{1},p_{2}\right)  .

(a) (5 points)

Suppose that when uncertainty is resolved both traders know which state of the world has occurred. Determine the spot equilibrium prices \left(\hat{p}_{1}\left(\varepsilon\right) ,\hat{p}_{2}\left(\varepsilon\right)  \right) in the two states (as function of the parameter \varepsilon).

(b) (5 points)

We assume now when a state occurs Trader 2 knows it while Trader 1 remains uninformed (i.e. s/he must keep thinking of the two states or equally likely). Under this information set up determine the spot equilibrium prices \left( \bar{p}_{1}\left(\varepsilon\right) ,\bar{p}_{2}\left(\varepsilon \right)\right) in the two states.

(c) (5 points)

We are as in (b), except that now we allow Trader 1 to deduce the state of the world from prices. That is, if p_{1}\neq p_{2} then Trader 1 is actually informed while if p_{1}=p_{2}, s/he is not informed. A system of equilibrium spot prices \left( p^{\ast }_{1}\left(\varepsilon\right) ,p^{\ast }_{2}\left(\varepsilon\right) \right) is a rational expectation equilibrium if at the equilibrium Trader 1 derives information from \left( p^{\ast }_{1}\left(\varepsilon\right) ,p^{\ast }_{2}\left(\varepsilon\right) \right) in the manner described. Let \varepsilon \neq 0. Exhibit a rational expectations equilibrium. Comment.

(d) (5 points)

Show that if \varepsilon = 0 then there is no rational expectations equilibrium.

QUESTION 5 (20 Points)

There are three participants in a public good decision problem with two outcomes. If the public good project is not carried out then the utility is zero for everybody. If it is carried out then the utility is 3 for the “project-lovers” and -1 for the “project-haters.” The cost of the project is zero.

We consider first the following decision mechanism. People are asked if they are PL (project-lovers) or PH (project haters). If at least one participant announces PL the project is carried out and the self-declared PH are exactly compensated for their loss. The resources for the compensation comes from a tax imposed on the self-declared PL (equal across them).

(a) (5 points)

Show that the above mechanism is not straightforward. Define your terms.

(b) (5 points)

Suppose now that participants know each others characteristics (i.e. if they are project-lovers or project-haters). Consider the situation where everybody self-declares truthfully. Argue that this is an equilibrium (i.e. it does not pay to any participant to deviate) if there is one but not if there are two PLs. Which are the equilibrium situations in the latter case?

We now change the set-up somewhat. Suppose that the designer knows how many PLs there are and that the participants know that the designer knows (or, simply you can assume that both designer and participants have this information). Say that the number of PLs is \alpha \in \left( 1,2,3\right)  . (Hence there is at least one PL.) Then the decision mechanism is as above except that for the project to be carried out it is now required that at least \alpha self-declare as PL.

(c) (5 points)

Show that for this mechanism it does not always pay to self-declare truthfully (that is, the truth is not a dominant strategy).

(d) (5 points)

Suppose that it is understood (Precisely, it is common knowledge) that no participant will ever use a dominated announcement. Show then that it cannot hurt to self-declare truthfully (technically, the truth is dominant after one round of deletion of dominated strategies. There is a subtle point here—that you may want to discuss—namely, if “dominated” should be understood as “weakly dominated” or “strongly dominated.” The distinction does not matter for the case \alpha =1 but it does for the case \alpha =2.)

Part III (Questions 6 and 7)

  1. (a) How does the following idea (or vision, in Schumpeter’s sense of the term) get reflected in the neo-Keynesian model presented in this course?

…there is a subtle reason drawn from economic analysis why…faith may work. For if we act consistently on the optimistic premise, this hypothesis will tend to be realized; whilst by acting on the pessimistic premise, we keep ourselves for ever in the pit of want. (Keynes, Essays in Persuasion, pp. vii-viii)

(b) Why does Knight’s dictum [following] fail to characterize the neo-Keynesian model?

…competition among even a very few [entrepreneurs]will raise the rate of contractual returns [wages] and lower the residual share [profits], if they know their own powers. If they do not, the size of their profits will again depend on their “optimism,” varying inversely with the latter. (Knight, Risk, Uncertainty, and Profit, p. 285.)

(c) Is it true, as Joan Robinson once wrote, that in a neo-Keynesian conception of the world businessmen are free to make the rate of profit anything they wish?

(d) More generally, how can investment demand be exogenous in a model where income and expenditure must be equal as a condition of equilibrium? What features of the theory allow investors’ preferences and investment demand to play a role in neo-Keynesian theory which differs from the role played by consumers preferences and consumption demand in neoclassical theory?

  1. Economic theories are, among other things, theories of knowledge—implicitly if not explicitly. What is the neoclassical theory of knowledge? Which do you regard as the more serious of the many objections to this theory of knowledge? Why in your view has the theory been able to survive the objections?

Source: Department of Economics, Harvard University. Past General Exams, Spring 1991-Spring 1999, pp. 84-88. Private copy of Abigail Waggoner Wozniak.