An analog model for studying economic development problems

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Economic Development Program C/58-6

AN ANALOG UDEL FOR STDYING ECONOMIC DEVELOPMENT PRBLElS

Edward P,, Holland

Center for International Studies Massachusetts Institute of Technology

Cambridge, Massachusetts January 1958

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Abstract

AN ANAWOG DDE FOR STUDEIE 'CW01MIC DEVEZOPMENT PEOBEMS

by

Edward

Peck

Holland

Submitted to the Department of cnomics and Social

Science on January 13, 1958, in partial fulfillment of

the requirements for the degree of Doctor of Philosophy.

This thesis

Is

the formulation of a dynamic macro-econoic model

which will later be simulated with the electro-nechanical analog at

the Massachusetts Institute of Technology for the putpose of studying

the

starting of economic

development in underdeveloped countries.

In Part I the economic problem is described, and the

applica-bility of control-system concepts and analysis are discussed.

Although

some of the methods of control-system engineers are unsuitable for use

on this problem, the technique of analog simulation promises to be

fruitful. This technique is briefly explained.

In Part II the model is formulated in detail In words and

equa-tions and is translated into block diagrams corresponding to the analog

setup.

The model represents production and consumption of several kinds

of goods with a flexible price for each, which depends on costs,

capac-ity, and demand.

Demands depend on consumers! incomes and preferences.

Capacity in each sector depends on the history of capital creation,

which is motivated partly by profits and partly by government programs.

Exports,

imports, and foreign finance also affect the system in ways

that depend on tariff and exchange-rate policies

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Part

III includes a discussion of the procedure of trying out

various development

plans

repetitively with successive adaptation of

policies for each. Although the projected study will not be

quanti-tatively predictive, it is felt that it will give useful insight into

qualitative modes of behavior of real economic

systens and into the

questions of what variables are strategic for control and which are

good indicators of the corrective measures that are needed. It is

concluded that analog simulation of this model is feasible and worth

while, and that the same technique could be used advantageously for

Max F. Millikan

Professor of Economics

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3 CONTENTS

PART I: IETRMUCTION

Chapter Page

I PROBLEMS OF DEVELOPMENT POLICY 6

2 SUITABILITY OF CONTROL-SYSTEM APPROACH 13

Difficulties of Analysis 13

The Control-System Approach 16

Analog Simulation ₂₁

PART II: FORMULATION OF TE MODEL

3 GENERAL DESCRIPTION OF THE SYSTEM 28

Concepts 28

The Model 32

Fig. 1 - Supply and Demand Interactions 33 Fig. 2 - General Outline of Interdependences 38

4 CONSUMERS' JOINT DEMAND FUCTION 39

General 39

Choice 1: Food, Other Goods, and Savings 41

Elasticity Relations ₄₁

Choice 2: Low-cor, High-cor, and Imported Consumer Goods 44

Growth and Developing Tastes 45

APPENDIX TO CHAPTER 4 47

Fig. 3 - Consumers' Joint Demund Function 53

5 AGRICULTURE AND LOW-CAPITAL PRODUCTION 54

A. Agriculture (Sector 2) 14

Short-Run Supply; Capacity Changes

B. Low-cor Consumer Goods (Sector 4) 60

Short-Run Supply; Changes in Minimum Price; Capacity Changes; Overhead Costs; Investment Decisions; Investment Restraint and Augmentation

APPENDIX TO CHAPTER 5 ₇₀

Fig. 4 - Agriculture (Sector 2) 71

Fig. 5 - Low C.O.R. Consumer Goods (Sector 4) 74 Fig. 6 - Additions to Sector 4 for Imported Materials 75 6 INDUSTRIAL PRODUCTION AND PUBLIC 09ERHEAD

A. High-cor Consuror Goods (Sector 1) 76 Short-Run Supply; External Economies; Profits

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B. Capital Goods ₈₂

C. Public Overhead Capital 85

D. Government Expenses ₈₉

APPENDIX TO CHAPTER 6 ₉₀

Fig. _{7 - High C.O.R. Export and Consumer Goods (Sector 1)} ₉₂ Fig. 8 - _{Short-Run Supply Price Computer (Sector 1 or 3)} ₉₃

Fig. 9 - Capital Goods (Sector 3) 96

Fig. 10 - Public Overhead Capital (Sector 5) 98

7 FOREIGN COMRCE AND PAYMENTS ₉₉

Imports ₉₉

Exports ₁₀₀

Balance of Payments ₁₀₁

APPENDIX TO CEAPTER 7 _1W

Fig. 11 - Foreign Markets

8 INCOMIE, FINANCE, AND CONTROL _106i

A. Income 106

B. Finance and Control of the Investment Pattern 110

APPENDIX TO CHAPTER 8 ₁₁₄

Fig. 12 - Income Accounts ₁₁₆

Fig. 13 - Sample Program ₁₁₇

Fig. 14 - Price and Inflation Indexes ₁₁₈

Fig. 15 - Investment Controls ₁₁₉

PART III: PlANS FOR STUDY

9 PERIENTAL APPROACH ₁₂₁

A. Numerical Data ₁₂₁

B. Development Program Comparianna 122

C. Crises and Readjustments 12

D. Nature of Results Sought ₁₂₈

10 COWLUSIONS AND RECOMMENDATIONS ₁₃₁

BIBLIOGR/APHY ₁₃₄

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PAT I

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Chapter 1

PRBIEW OF DEVBWPMBNT POLICY

This thesis is the foundation for a larger study, in which n electro-mchanical analog will be used to simalate an underdeveloped economy. In the thesis, the model of the econozy is formulated in economic terms and then translated into a worhing specification of

the analog setup. Also. the method of investigation by means of the analog is outlined.

In the larger study, the problem of initiating economic devel-opment will be investigated from the dynamic macro-eceonce stand-point. The study will have two aims: Primarily it will be an at-tempt to gain significantly better understanding of the dynamic economic problems involved in starting economic development Sec-cndarily, it will be a test of the usefulness of simulation tech-niques for studying economic dynamics. This thesis fulfills a pre-liminary objective by providing a model which is better suited to the study than any directly soluble model and which can be simulated with existing equipment.

In the next chapter the technique of analog simulation ill be explained, wad its suitability for the problem at hand will become apparent. First, however, the economic problem is described sad discussed in the remainder of this chapter*

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In the kind of country to which the study is relevant, output per capita is initially quite low and is mainly agricultural and

handicraft products. The cenoW operates by tradition, with no tendency to develop nw products or more productive techniques. Food production is limited by the area of land cleaed, and the labor force on the farms is much more than is needed for the crop that is prduced . The problem of concern is hov to bring about what Roatco has med "the take-off," which he defines as an in-terval of two or three decades:

a . . during which the rate of investmnt inereases in such a way that real cutput per capita rises and this initial increase carries with it radical change in production techniques and the disposition of income f los _{which perpetuate the new scale of investant and} perpetuate thoby the rising trend in anita cut-put. . . .

This, of course, is not a purely economic phenomenon:

a , . The

take-off

requires . . . a society prepared to respond actively to new possibilities for productive enterprise; and it is likely to j4"ire political, social and institutional clanges. Q

Some theorists maintain that initiation of economie develop-mt is purely a noneconomie problem. In this view, economic growth is like the growth of a plant. To encourage it, one tries to establish

. W. Rostos, "The Take-off into Belf-Sustained Greath, "The Reenooic Journal, March 1956, p. 25.

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a favorable environment, but does not tamper with the process itself. Remove joint family obligations, religious prohibition of interest

charges and other commercial practices, and legal obstacles to free trade between regions and groups, and soanhow modify people's atti-tudes of disdain for money-makers, and the economy will thrive. Others have noted, however, cases where the beginnings of economic

progress seem to have induced some of the appropriate changes in aiistr, ucture, cultre., and evn religlis ds4etrines .

No doubt the truth is that certain noneconomic conditions-as well as certain economic conditions--have to be established beforo the process of take-off can fully succeed, but that some of these conditicns can be established during the take-off, rather than all having to be accomplished beforehand. The great importance of

non-economic factors is not denied in this study. Neither is the in-portance of establishing economic preconditions, which may take a long time and without which the take-off may be impossible. Study of these aspects, however, is left to others. This study is direct-ed solely to the economic dynmics of the take-off. Any notion that this aspect of the problem is clear and simple is vigorously denied.

Apart from this question, however, is the question of laissez-faire versus central planning, or rather of degree in between. Faith in the "invisible hand" is not so widespread in advanced countries as

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it was before the Great Depression, and there probably never was unch of it in the underdeveloped countries. Russia-however mch we may despise their flouting of personal freedom-has demonstrated

one way of bringing an underdeveloped nation up to advanced indus-trialism in forty years. Earlier, Japan had demonstrated another

Iy, with lose central control but with the government actively manipulating the economic incentives and deterrents. In countries where economic development is a popular objective today, it is taken

for granted that governmnt responsibility extends at least to the mnipulation of foreign commerce, the tax structure, and the money system, to the over-all planning of development patterns on a see-toral level, and usually also to the actual building and operation of public transportation, power, comunication, Irrigation, and other such system. There is no real question whether the govern-ment should exercise controls to try to steer developgovern-ment. There are, however, plenty of questions about what kinds of manipulation will be most conducive to progress . These are the questions on which this study is focused.

The problem is to find a combination of programs and policies which will lead into continuing growth of real disposable income per person. What is sought are guides for deciding how much rela-tive emphasis to give at any time to building up food production, or consumer-goods industries, or capital-goods industries, or trans-portation services; whether to combat inflation by encouraging more

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handicraft production, more industrial manufactures, or more imports of consumewr goods; whether to try to balance the foreign account by protective tariffs, encouragement of export industries, or adjust-ment of the exchange rate.

The situation presents many dilesms For example: An import surplus is one of the chronic problem of a country trying to start

consumers' development. An obvious remedy is a high tariff or a quota

on/im-port&. However, a by-product of such action is the diversion v2 some of the demand to the doesatic markot, where it adds to the in-flationary pressure which is also a normal concomitant of a

develop-mwnt effort. If home prices become inflated, the adverso balance of payments is likely to get worse instead of better. How can the proper remedy be chosen in a given case?

Another example: An antidote to inflation is increased pro-duction of consumer goods, cometitively priced. To increase the capacity of consumr-goods manufaoturing industries requires making investment expenditures, which increase demd right away, while the increase in supply will not occur until later. Hence what may be deflationary later an has inflationary effects in the short run. Will the long-run benefits erase the damge that has been done in the short run? (The investmnt may very well involve increased capital-goods imports, which further complicate the problem by dis-turbing the balance of payments .)

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Two of the most difficult aspects of the problem faced by the makers and executors of development policy are, first, the conflict between inediate symptoms and ultimate effects of any action and, second, the sultidimensional nature of both the goals and the ef-fects of various actions. Whether their decisions are actually effective toward any particular goals, they cannot tell by watch-ing the imediato conequonces, which often takethe form of crises in the balance of payments, inflation, anddlstortions in the goods and factor price patterns. What to do in such circumstances sust be decided on the basis of some sort of theory (explicit or Intui-tive), for policies based solely on alleviating the short-run

dif-ficulties will probably not lead to long-run progress.

The need for a different theoretical technique than those that are currently conventional in economics arises from the complex nature of the system and the problem to be dealt with. The ques-tiens posed _{above clearly call for a mltisectoral model, with} flexible prices, capacity limits, capital formation, foreign com-merce, and various controls. _{Time-delays and time-spreads are} basic to the physical processes of capital-formation and capital attrition; output in various sectors is limited by past capital formation; supply prices at capacity are determined differently than below capacity; and there is contInuous interaction between production of various sectors, Income, demnd, prices, foreign con-merce, and the balance of payments. These interactions are too

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significant to allow reaching valid conclusions from analyzing parts of the system separately with all else assumed constant; the non-linearities invalidate linearized analysis; and the time-spreads and irreversibilities in the system, together with the dynamic character of the forces applied to it, make comparative statics of little use.

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Chapter 2

SUITABIITY OF CONTROL-YST3M APPROACH

Difficulties of AnalysiS

Adequate analysis of economic take-off problems, as indicated

in Chapter 1, requires recognition of varios nonlinearities and

tL.-snpread eflct in a compXa ot o2 ±nterdependent relation-shipa. The nature of those relatimships has frequent3y been de-soribed and is fairly well agreed upon, Differences of opinion center mainly on the question of which ones cam be safely ignored or grossly simplified beocnse the dynamic behavior of the whole systen cannot be dealt with by verbal reasoning or direct nathemat-ical solution.

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acarse, every method of study involves ignoring or simplifying relationships, but in this problem heretofore it has had to be done too drastically.

From a postulated set of relationships to general conclusions about the system's modes of behavior is basically a matter of de-duction: given a set of assumptions, to what conclusions do they

lead? Verbal logic9 however, proves inadequate for two reasons.

First, most of the relations are not syllogisms stating that some-thing does or does not happen depending on whether a certain combina-tion of condicombina-tions Is or is not met. Most are magnitude relations, in which the agnitude of one variable depends on the mgnitude of

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several others, and moms involve effects distributed through time. A second reason that verbal logic is inadequate is that the system involves many feedback loops. These are sets of relations in circular chains such that the dependent variable of a relation enters other relations fhich in turn affect the independent variables of the first . Some feedback loops and mutually determined variables can be dealt with verbally, but not such a complex network as this problem involves, especially when the loops also include time-lags, delays, and nonlinearities. Verbal analysis can best handle those chains of emuse and effect that proceed minly in one direction, where a few premises lead to proof of a first proposition, which is then caubined with another premise to prove a second proposition, and so =, with each stop finished before the next is taken and no effects coming back "upstream." As Susanne Langer puts it:

. . . all

language

has a form which requires us to string out our ideas even though their objects rest one within the other; as pieces of clothingthat are actually worn one over the other have to be strung side by side on the clothesline. This property of verbal symbolism is known as discursiveness; by reason of it, only thoughts which can be arrged in this peculiar order can be spoken at all. 0 a

Various nathematical techniques also have shortcomings for the problem at hand. This is partly because of limitations of the mathe-smatics and partly because the relative merits of different results

1_{Susanne K. Langer, Philosophy in A NOw Eey, Cambridge:}

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Cannot be evaluated by a single criterion. Linear (or even non-linear) programming is an excellent technique for maximizing or minimizing a single criterion under conditions of general equilib-rium. The quantities in the general equilibrium may be expanding thrcugh time, but the situation is essentially what Baumol describes as "statics involving time"1 rather than dynamics. The circuit is not closed through incomes, consumer preferences, and market prices, with positive profits affecting investment and with inflation

limit-ing the rate of investment that is tolerable.

Models which are more dynamic have been offered under the gen-eral headings of Business Cycle Theory, or Fluctuations and Growth. Most of the dynamic mechanisms that are significant in business cycles are also significant in the take-off process, and a really adequate dynamc model should be suitable for studying both phe-nmena. An interesting collection and comparison of models of this type is presented by R . . D. Allen.2 Models included are those of Saselson, Bioks, Goodwin, Kalecki, and Phillips. A more sophisti-cated and elaborate ne has more recently been forsmlated by Smith-ies. 3 All of these deal with income and product interchSngeably,

1_{W. J. Baumol, Economic} _{as, New York:} _acaillan_Uz _Co.,

1951, pp. 1-3.

2fR. 0. D. Allen, athemtical Economdcs, Londcon: Macmillan a Co., 1956, Chapters 7 and 8 and pp. 285-289.

SFor the primary references on all six models, see "Dynamic Economic Models" in Bibliography.

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11.e., with fixed prices, or deal solely with incom, disregarding physical quantities and prices. None are open to foreign comerce, or distinguish between different kinds of goods, or have output limited by capacity (although galecki and Smithies at least go so far as to make investmnt sensitive to some relation between output and capacity). _{These criticisms are no reflection en the authors;} they reflect, rather, on the limitaticns imposed by mathematical method which are chosen to allow solution for general rather than particular cases. _{The article by Smithies in particular offers a} untuber of examles of the disparity between the ele nts the author considers relevant and those to which he is limited by the msthe-mtics. For example, after explaining and justifying the assump-tion that profits have a dominant influence on investment, he finds it necessary to assume that profits are a fixed proportion of gross national product. Given a technique that permitted it, Dr. Smithies surely would have preferred to allow for some of the factors that

ake profits high at some times and nngative at others.

The Control_ stem Aroach

In the search for more effective ways to deal with dynamic economic systems, several people have noted the strong similarity between such system and feedback control systes in engineering. The spectacular development of control system engineering since the beginning of World War IX certainly shculd have produced some tools

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that could be adapted to similar systems outside of engineering. One of the keys to this tremendous development was the use of the laplace transform to study systems in terms of their "frequency response spect1um" from which their dynamic behavior under any conditions culd be deduced. In Tustin's book, which is a great pioneering of fort to make the techniques of his field (electrical engineering) ivailable to economists, this technique is the most

pt allen also presents it in his chapter n closed-loop

system J1afortunately, as they both point cut, there are sericus doubts abirt the usefulness of this analysis to economics, because it appli ae only to linear system. The engineer often takes pains to deslgn his system to be linear, just so that he can analyse it betteA, but this choice is not open to the economist. He knows that the xconoeg has important nemlinearities, and he cannot change them. Other parts of Tustin's and Allen's expositions, however, offer om tools that are more certain to be helpful. Just the symbolism of drawing feedback relationships in block-diagram form is a great help for tracing information from one relation to another and for

seeing which variables are independent relative to the system as a whole or any part of it . For the discursive form of language and

Arnold Tustin, The Eschanism of Economic stem, Cambridge: Harvard University Press, 1953.

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algebra, it substitutes a pattern of relations that can be se like a nap. Simply translating an economic model into this form can give new insight into its character, as shown by Allen's diagrammatic comparison of the several models mentioned before.I

There still reains the problem of analyring a complex dynamic nonlinear system. All attempts to get direct rathematical solutia

seem to fail. How to break through this nathematical barrier is sug-gested by Allen in discussing the advantages of same other engineer-ing approaches to control-system problems:

0 . . the

engineer

does not often attempt general

solu-tionas; he aims at computing (by numerical or graphical methods) particular solutions, usually a whole string of them. . . . As economic models become more complex, and have a greater empirical content, to make them applicable to the real world, the answers to general questions be-come less possible. The economist may need, therefore, to shift his ground from the general to the particular, and to 9follw the ethods and the experience of the engineer .

This means forgetting about formlating the problem so that a solution is possible in matheasatical symbols, and instead widen-ing the limits of formlation to include whatever can be solved numerically, graphically, or by any other means, for particular ocases This approach usually requires a large numbercf solutions to survey the effects of chanring various paramters and of

apply-1

,d p. 285.

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ing different disturbances, but if that can scehos be done, it can be very enlighitening.

This approach has been used with rearding results by Phillips, in his two well-knovn studies of stabilization policy 1 _{In each of} these he has postulated a simple income-flo model with particular parameters, has subjected it to arbitrary disturbances, and has tried cut varicus fomalatioms of stabilization policy, to see what has desirable effects. Co clusions are based on co mrisoms of many particular cases. Incidentally, the results of the second study strongly bear cut a point that both Tustin and Allen empha-sized: that the form of time lags is very important to the sta-bility of a feedback system-assuming a discrete delay when the

actual process involves a distributed lag, or vice versa, may lead to significantly false conclusions.

Application of this approach to a system complex enough for studying the take-off problem requires co mricon of a very large number of particular cases, in each of which the computatins would be extremely cumbersome by numerical methods. Calculation

"by hand" would be out of the question. Two alternatives are avail-able: digital computation and analog simulation. Either of these

IA. W. Phillips, "Stabilization Policy in a Closed Econom," The Economic Journal, June, 1954, and "Stabilization Policy and the Ti-For oM Reponses The Econ Journal, June, 1957.

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methods oat do the job well; each has oertain advantages that the other lacks, so that for particular applications one or the other may ba superior, but for some probless the difference in technical suitability is very small. _{Digital techniques are being applied to} the econonic dynamics of the firm and industry by a group under Forrester in the School of Industrial Management at the Msac-bu

&ettz Institute of Technology,a and to the economic dynamics of tke UoSo e con o my by another group under Orcutt of Harvard University.

Both are using the IBM 701 machine of the Compton Cosputatice Cen-ter at the Masachusetts Institute of Technology.

For this study of the take-off problem, analog similation was chosen because of its flexibility and convenience for feeling out unexplored areas and for fitting a progran by cut-snd-try methods to a set of goals. The idea of a sinalat or Is explained by Tustin as follows:

A siualat or is a physical system, analogous to the model to be studied, in which there is a more or less complete part-by-part correspondence, the variables that are significant in the model appearing as analogous

var-iables-s-mchanioal, electrical or hydraulic or other quantities-between which corres nding relationships are

set up by suitable construction.

'So Jay W. Forrester, "Systems Technology and Industrial Dynaics," an article in Adventure in Thougt and Action, School of Zrcustrial a t, ausett Institute of Technology, June, 1957' (proceedings of the Fifth Anniversary Convocation). Also pub-lished in The Technology Review, June, 1957.

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With the simulator that will be used here, the operator sees the results of each run in the form of graphs, and can make changes for the succeeding run by turning knobs that directly correspond to parameters of the program or policy he wishes to alter.

Analog Simlation

The 1957 study by Phillips has probably been the most fruit-ful use thus far of analog simulation of an economic system. Earlier studies siaulated a simple Inventory-fluctuation model, the Ooodwin model,3 and the Ealecki model.4 Unlike Phillips' study, these were

primarily experiments in applying the technique to problems for which solutions had already been found by other means (except the effect of paramter variations in the Goodwin model). They were interesting deastrations of the technique, but did not create awareness of its potential utility for problem that are otherwise i.tratable. Still earlier analogs-hydraulic rather than electrical--were invented by

1_Phillip, _{"Stabilisation Policy and the Tie-Forms of lagged}

Responses, "f Op. cit .

N. _{F. Morehouse, R. H. Strots, and S. J. Horita, "An} Electro-Analog Method for Investigating Problems in Economic Dynamics:

In-ventory Oscillations," Ecnoutrica October, 1950, also R. H. Strotz, J. F. Calvert, and N. F. Morehouse, "Analog Computing T

plied to Economics," Transations of American Institute of Electrical Engneers, Vol. 70, Part I, 1951.

3R. H. Strots, J. C. McAnlty, and J. B. Haines, "Goodwin's

Non-Linear Theory of the Business Cycle: An Electro-Analog Solution," Econometrica, July, 1953. Reprinted as Cowles Commission Paper, N. 8. 74.

O. J. Smith and H. F. Erdley, "An Electronic Analogue for an Economic System," Electrical Engineering, April, 1952.

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Phillips and by Abba Lerner.2 These were useful for illustrating the interdependences in the systems they represented, but not for investigation beyond the limits of algebraic solution. Using the same principles as all of the analogs mentioned above but on a larger scale and with more diversity, the equipment available at the Masachusetts Institute of Technology makes it possible to

simlate a mch more complex model, such as Chapter 1 has indicated inecessary %or a tuidy of take-off problems.

The technique of simlation is based on interconnecting vari-ous kinds of electronic and electro-mechanical units, each of which receives and produces signals which can vary continuously through time. The signal a unit produces is functionally related to the signals it receives from one or more other units. Different kinds of units embody different relationships, some depending on the past history of inputs, some on their derivatives, some just on current values . The simplest type of unit receives several varying signals and produces their sun continuously. Another type, a "lagT unit, responds to a single input about the way the speod of an automobile

responds to changes in the accelerator position. An abrupt change

IA. W. Phillips, "Mechanical Models in Economic Dynamics," Economica, 1950.

2

Abba larner' model, of about 1951, is known to this author only by hearsay. It was evidently similar to Phillips'.

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in incoming signal causes the outgoing signal to start immediately changing toward the level of the incoming signal, but to change

less rapidly as it approaches. (The function is an exponential lag.) Graphically, the response is as follows:

Input

Voltage

Output Time

-Other units can select one of two incoming signals depending on the magnitude of a third, or impose a ceiling on a signal, or multiply two magnitudes, or integrate a varying signal (so that, if the incoming signal repreated a fluctuating rate of flcw of liquid into a tank, the signal produced would tell the level in the tank). These and a number of other kAnds of units can be

inter-ncaoected to simulato auch more complex relationships.

To illustrate the principle, there follows a simple example translating a dynamic income-mltiplier relationship into a diagram

of analog units and connections:

Example: Assume that consumption, C, tends toward a con-stant proportion, a, of income, Y. In equilibrium, C = cY, but

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adjustment to changes in Y involves a time-lag of the kind de-scribed above. This my be expressed explaitly in terms of the rate of change of C as

a g (cY - C)

dt

where g is a constant. Combining this with the accounting identity, Y a C + I, makes a system relating income, Y, dy-nmsically to investmeut, 1.

The analog of this system uses three units, one to add C and I, one to multiply Y by the coefficient c, and one to produce C as a lagging counterpart of OY. The time constant of the lag unit is chosen to give a convenient timo-scale in the analog. For instance, one second of analog time might represent one year of real time. The arrows in the diagram below show what information comes into sad comes out of eaoh relationship; in the analog they are actually wires,

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When this is set up in analog components, the voltage repre-senting I could be varied in any arbitrary way and the correspond-ing variations in Y recorded. More important, the incoming signal, I, can be produced by other analog units representing an investment decision function, which in turn responds to market prices, costs, and financial conditions. Likewise, the signal produced, Y, can be connected as one of the inputs to a demand function, and so on. Thus a large number of separate dynamic relationships can be

inter-connected so that they interact continuously.

It is important to an understanding of the more complex dia-gram in later chapters to visualize the arrows as representing transmission of information or signals. They may happen to coin-cide with flows of goods or payments in sows cases, but in others the direction may be reversed. For example, if business savings,

are determined by some decision function outside of the simple loop shown above and have to be deducted from income to find dis-posable incoms, to which the consumption relation applies, the modification to the diagram is as follows:

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It is to be noted also that the saw information can be used for any nuber of different purposes. The signal, Y, in the above diagrams, is represented as going down to the consumption function, and going also to some unspecified location off to the right, where it perhaps might be used with other variables in making Investment decisicns, and where it might also enter business saving decisions. Since the informtion, in the analog, is a voltage signal and not a current flow, It is a simple matter to make mitiple connections

from one relationship's cutput to the inputs of several others. After appropriate analog units have been set up and intercon-nected to correspond to the model, as well as units corresponding

to the programs or disturbances to which it is to be subjected, the system is activated and acts out a run. Voltage signals previously selected wherever desired In the system are recorded on tima-gphs by moving pens. The run is switched off either when it is consider-ed to have coverconsider-ed enough time or when some variable has exceconsider-edconsider-ed its allowed range. Voltages to be recorded in this study represent time histories of such information as output and prices In various

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E-2PATION# O? TUi, EL PART li

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Chapter 3

GENERAL DESCRIPrION OF THE SYSTEM

This chapter begins the specification of the model which is to be si.lated. It discusses concepts and describes the model in

out-line to give the picture of the over-all system and the relatione between its various major parts. Chapters 4 through 8 fill in the

d

l ,diing each relation specifically, in words and q

asc.h of thos chapters is followed by an

sppendix

in which the same sets of relations are presente4 in the form of blocik diagisws, which are the basis for setting up the analog circuits.

To be useful, of course, the model must have some reasonable relation to the thousands of different activities that compose the econories of real countries. Obviously it canot represent then all in detail, but rat omit meih of what is real, including only what seems most important. Wandreds of different kinds of activity must be lumped together in each of the various aggregate quantities

that are the variables of the model. How the grouping is done

de-pends on the purposes of the model and on some notion of the char-actaristics of particular countries which the model is intended to resemble .

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The theoretical aspects of grouping production activities into aggregates are explained by athilda Holman in her chapter of the Leontief group's study. It is justifiable to combine goods which

are close substitutes and have similar production functions, and to

combine goods without regard to production function if they arc com-plemnts. Also, althwgh Miss Holzman does not have occasion to discuss it, sequential activities may be combinod, as if the sectov were a vertically intograted monopoly.

These considerations apply conceptually to this model, although on a rather loose basis, since the sectors are ew and very btroad. Each productica sector is ecaceived of as producing a large variety

of goods which could be groped into sets of complementary goods on the basis of stability of the ratio in which they are purchased. Each such set , as a set, has about the same production functico and the nets are fairly close substitutes . ubstituticn also ob-tains within the seta. Vertical integration is assumed complete in each sector, except to the extent that som intermediate goods are imported o transferecd from one sector to another.

Distinctions between the sectors are on the basis of diff2rent production functions or different kinds of demand. Tbus, hndicrafts

1_{W. W. Loontief and others, Studies in} _{the Structure of tho}

Amrican_ Econoy, New York: Orford University Presa, 1953; Chapter 0: § oblems of Classification and Aggretion" by Mathida HolaN=.

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and industrially

mafactured

consumer goods are close substitutes,

but differ in capital-output and labor-cutput ratios, while indus-trially maufactured consumer goods and capital goods have similar production functions, but one is amued only by consuers, the other only by maufacturers, and productive capacity is not con-vertible from one of these uses to the other .

Goods

for export are combined with industrial casumer goods an the basis that their production functions are similar and capacitio are transferable between these two outputs. Imports are distinguished by their use as either consumer goods, Intermadiate goods, or capital goods.

Consumer tastes, including saving habits, are assumed to be the same for all groups, except that profit-earners tend to save more. Their extra savings awe accounted for as if they were re-tained in businesses; their consumption preferences otherrise are like all others. Consumption and production are assumed equal;

there are no unintended or speculative inventory changes, and the

changes conneoted with expansion are included in capital formtio.

The degree of integration in each sector is presumed to go from exploitation of natural resources to delivery and servicing of finished products. The breadth of each sector is so great that the high-capital-output-ratio sector, for example, includes all of the services that distinguish modern urban living from the tradi-tional rural variety. All of this, of

course,

goes beyond the rig-orous limits of

mam

Holmzan' prescriptions and leads to serious

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questions about product mix and indez number validity. These will not be discussed further, hwever. Either these gross and questicn-able aggregates must be used, or macro-economica must be abandoned.

The output of each sector is treated in the model as a flew of

a homogenous quantity. Its flw rate may vary cctinuously. bike-wise, payments and informtion signals may vary continuously. This

formlation is prerred to period analysis partly because it in the way analoeg work , It is also a good representatin of processes that my well Vary from Meek to week When the time span with which

the problem is concerned is twenty to fifty years. Certainly it io superior to analysis by quarters or one-year periods with all delaya assumed equal to one period-an assumption sometimes made, which is certain to yield very special results.

Payments are coeived of as flosw of signals which have effects like ordinary transfers of cash, but include also soae accruals and

putationsa. For exaMplo a ordit sale is construed to include a payment because it has the saw effect as a cash sale on the manu-facturer's production decisions. The essential feature of paymnts, under this concept, is their effect on decisin-decisicn to

produce, to invest, and to consume. Thus the money associated with a payment my be imaginary or my be newly created in the process of paymnt. Rosever, the quantity o2 money in the system is niot an explicit variable in this analysia and does not have to tie accouted for.

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The Model

The model represents an imaginary underdeveloped coutry, whose rural population is eccessive for its food-producing capacity. Thus

a shortage of people is never a bottleneck in production. In the industrial sectors, where relocation and training of people are re-quired, these activities are considered part of the process of capi-tal formation.

C mers' expenditure flass at ny mont are distriuted be-tweon four categories of goods, according to disposable income and the four prices, interacting with a consumrs' preference function. Demnd for food is relatively inelastic with respect to both income and price. The other three hinds of goods are strong but not per-feet substitutes for each other. ThEy are high-eapital-cutput-ratio mnufactured goods, lsw-capital-output-ratio goods including mm-factures and handicrafts, and cosmers' imports. To avoid repeti-tion of the cumbersome descriprepeti-tions of the first two of these, they

are called high-cor and 1o-cor goods, respectively. The price of each hind of consumer good is determined at any tim by interna&.tia of the joint demaad function with four supply functions, one for each of the four categories of ccnsmrs' goods. (See the

inter-actions shown in

FIgure 1.)

For

, there is

a ftsd world price, subject to a tariff which may be changed by the governmnt. The other supply functions are more complex 4

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33

Figure 1

SUPPLY ATM DEMATD I'JTERACTTONS (Consumers' and intermediate goods)

)isposable Income CI, SUPPLY OF IMPORTS Price Purchases

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involving effects of capacity changes and (for all except food) coest

road output i limited by the area of land that has been cleared and by the extent of irrigation facilities. Increases in aggregate output capacity require large-scale projects which are beyond the scope of individual proprietors to organise. Such private projects as are done are coleentary to govewnment prograns. Hence,

invest-ment in deternined by governinvest-ment decisions labor is redundant and cannot be laid off, but does not receive fixed wages, being largely made up of proprietors, their dependent relatives, and people who work for a share of the output Under these conditions no losses

can be avoided by deciding not to produce, and therefore output always equals capacity, regardless of price.

The low-cor sector (handicraft and manufactures)

has

a low capital-output ratio and static technology, with capacity limited by the stock of critical tools. Changes in capacity camn (after a short wait) from investing in making more tools at a rate above or below the rate at which they wear out. In this sector there is a minimum supply price determined by wages and imported-aterial prices. Hence, at low levels of demand, output may be less than capacity. High demand raises prices, yields profits, and hence

stimulates private investmant. Also, wages tend to rise when profits are made. Governsment action may add to or limit investmento

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35 Industrially manufactured goods (from tho hil -cor sector) are sold to both domestic ccnsuers and foreign customers. Output at any time is limited by plant capacity--but may be less than capacity it demand is low relative to the supply-price function. Initially, this sector has little or no capacity. Investments to increase capacity are motivatod by expected profits, but may be limitod or

augmnted by governmnt action. Invstment in this sector increasoa labor productivity as well as expanding capacity. labor is hired or laid off to mtch output. The wage rate index in negotiated up-ward when business is profitabl, but nevo goes do=. Increases

in capacity, be ides requiring expenditure for elastically-uppied factors, involve waiting through a significant gestaion time and

purchasing

scarce capital goods. These

my

be imported (if foreign echange pormits) or purchased from a doamstic industry (if domestic capacity permits).

The domestic cml.od sector has character-istics Identical, except for numerical magnitudes, to the anufactured consur-goods~ sector. Its capacity is initially asall or meroe In addition to the four doestic sectora described above, there is a gtbgIc cvr~haad sector, of which the product is not separately identified, being an

internadiate good. Expansion of this sector reduces costs of pro-duction in the other sectors.

Investants and current production in the varicus domestic sec-tors are reflected in the gross national product, from which tames

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and business savings are subtracted to ascertain disposable perstmal income. This information enters the deM function to determine personal savings and the expenditure an each kind of consumer good, as described initially. The principal interdependences for the wholt system are indicated in Figure 2, at the end of this chapter.

Within each domestic sector, and not evident in Figure 2, are capacity-creatiea processes. In agriculture and public overhead those are directly controlled by goverment. In the other sectors they rvev motivated by profit meeking, Wut entrepreers' decisions

may be modiufieda ,,y governMent controls. 1The controlls are Introduced iu the model as direct upper and lower limitations on construction. Whther they would actually take the form of credit expansien and restriction, subsidies, license requirements, allocation of scarce building mterials, or any other form is outside the scope of the model. So too are the problem of manipulating finance. Taxes and savings are accunted for, but do not influence the sectoral investment pattern or, in a direct way, the total ependiture, which thus my imply deficit iwncing. The mechanisms of inflation work, nevertheless, even though budgets are not =do explicit .

The

controls on capacity creation will be time-programme to represent development plans. The programmd values my be

auto-watically modified, hewevar, in respnse to inflatien or balance-of-paytents deficits. Other tools of governnt policy lor which the model provides are ohangos in interest rates, import tariffs,

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?7

and the foreign exchange rate. Investors' expectations may later be associated with government actions or with current economic

con-ditions, but for the present are left as fixed paramters. Com-pletely independent or exogencus quantities are the supply prices of imported goodsat two paramters that define the demand function for exports, and the time profile of long-term capital inflow from abroad.

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Figure 2

GENERAL OITLPTE OF INTERDEPENDENCES

(Not including government controls and policies)

Disposable Income

KEY:

Prices

-Purchases

Other signals

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39

Chapter 4

CONSUMERS JOINT DEMAND FUNCTION

General

The consmers' demd function is a set of relations allocat-ing disposable incom awong savallocat-ings and the four kinds of consumer goods according to their prices,, Prices, of course, are determinod at any timo by the interaction between this function and the four supply functions in a short-run general equilibrium. It is a mat-ter of convenience, with no restrictive effect, to formulate the demand function with income and prices as independent and the values of purchases as dependent variables, end to formulate the supply functions with purchases independent, prices dependent. In the analog the appropriate interactions will occur so that prices and purchases will be mutually determined.

The consumers' allocation of disposable income nay be thought of as occurring in two stages. First, incom is divided between food, all other consimer goods, and voluntary savings. This divi-sion depends on disposable income and the price of food, and is in-dependent of other prices and of the interest rate. Then, the ex-penditure for "other consumer goods" is allocated amng the three kinds according to their prices, with a relatively high degree of substitutibility. Each of the two allocation functions is a special

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case of a joint demand function developed ar i used by Richard Stone.1 This function way be expressed in the following general form for the

expenditure flow on the L-th good in a set on n goods:

D

0 YI 2 0

C.

p. Q, + + b, ( - p ) (4.1)

Where Y disposable income, megabucks per year.

C. ' expenditure rate for L-th good, megabucks per year. pr price of i -th goodS, $/quant .

Q a parameter for the L-th good, in mega-quants per year, b, w another parameter for the 1-th good, dimnsionless, and

4.

subject to the condition

b,

I

Summation of these expenditures, with the stipulated condition on the b constants, confirms that

C, YD

(.

As Stone points out in his discussion, the relationship is not meaningful unless

> Q4 0

In the model formulated here, failure to meet this condition will be equivalent to a state of fanine and hence fai lure of the program being tried.

1_J. _{R. N. Stone, "Linear Expenditure Systems and Demnd}

Anal-ysis: An Application to the Pattern of British Demand," The Eco-nomic Journal, September, 1954

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41

Choice 1: Food, *Other Goods, and Savings

For the set of relations like Equation 4.1, Stone offers the follaEring common-sense interpretation:

. . . on the asoumption that Ip ' Q> , it entails that consumers first use up a certain amout of their

in-ooue. . . .

in acquiring the consumption vector [Q ,...,

Q%] at current prices, whatever these may be, and then distribfute their remaining incoe over the set of available coycdities

in certain fixed proportions given by [b, .. , b ]

One of the special assumption in the present model in that only

0

the demand for food includes the initial inelastic coaponent, Q The other two categories, "other goods" and "savings," have Q-w%. Using the subscript 2 for food and c for other consumer goods, and with S for savings and a" the warginal propensity to save out of

disposable incom, the relations are simplified as follows: C2 2 + b2 2

Qi]

C

a b

[Y

p

2 Qo] (4.2) C

SyD

.. Q0

a,

_P

cQ

b2 + be + er= ElUticit Relations

Expressed in quantity rather than money terms, Equation 4.1

becomas:

Q Ql + L ( -D PQ ) (4.3)

P

1

Ibi., p. 512. Notation changed to suit this foranlation. stone 's is in vector terms, with different symbols.

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Differentiating this, the varginal propensity to SpeOd incoMe on a particular kind of goods is found to be:

a pt

while the fraction of incone spent thereon is:

QQ b. b.

Q

- - + s -

--The ratio of these two quantities gives the incoe-elasticity of e

d for theSi goa

Q

="

-(4.A)

With the assumptins of Equations 4.2, for food,

0

p

Q

_p

2

Gy,

<

I

for other consumer-goods, or for saving, p Q * 0

PjQ

j

p

2

Q2

>0

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43

other goods and savings are relatively income-elastic. With respect to price, the demand-curve slope to

&Q-

b.

Pap2

ji,

j

P. L and: 00

Q(

Q

b.

bo

Q-- + - p Q

The ratio of these quantities gives the price-elasticity of

demand:

EpL

1+

(4.5)

bj

00

For positive values of b7 and Q0.

or dond is relatively inelastic. This is the cane for food deand

For Q a 0,

Ep;

I,

or dessand is unit-elastic. This

is

the case f or other consumr

goeds as a group.

Mathematically it could be said that this, applies

to savings, but there is little economic

meaning to

the Idea of a

variable

price

of savings.

It can generally be taken to be one

doi-ler

per'dollar. (Interest is not the price of money, but its rental

.rte;

savings are assumed insensitive to interest in this mxel.)

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Choice 2: Lw-cor, High-cor, and Iported Consumer Goods

For the first stage of choice, formulated above, these income and price elasticities are appropriate. For the second stage, higher price elasticity is necessary. In this second stage, the total e-penditure for nonfood conaumer goods (already determined) is to be divided among goods from three sources: two categories of domestic production and the import mrket. The goods produced by these three sources are not all the saen. _{Nevertheless enough of them are fully} or nearly equivalent so that strong substitutability exists among the three groups. Hence their demnd curves should be relatively price elastic no that an increased price would reduce the total expenditure on the corresponding goods.

This _{elasticity is achieved by using negative values of the}

Q parameters in a second demand function of the Stone type. With negative values, these paramters can no longer be interpreted in the common-sense terms of the quotation from Stone's article, given above. They reduce to a strategen for obtaining certain desired mathematical properties. The demand equation for each good--In terms of absolute values of Q

's,

and with the total nonfood ex-penditure represented by C -- is:

C. -

Q

0 +

b.

[C

+

p

Q|.

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(NMTE: The three categories are identified by the following sub-scripts: 1 for high-cor goods, 4 for low-cor goods, and 6 for imports.)

This relation requires restriction, for at some price ratios it will indicate negative expenditure on one of the goods. In such on event this indication must be re-interpreted to mean zero

ex-pdrand the demand functions for the other two gxds must be chnged to act as if the third were not available. For exaMle,

if the price p4 Is o high that Equation 4,6 indicates C ( 0,

the following relations are substituted:

Cg

= 0

C4

C W -P + n( + P I +3 (4.7)

1b 1 b 6 I

C6 6% =_6. 1 b1 + m+ob [Cc + P1. Q, + P6* 66

If two of the functions indicate negative expenditures, say C4

<

0

and C

<

0, the re-interpretation it quite simple:

C

₌

_C4

₀

(4.8)

C6

C

Growth ad DvelopingTastes

For two reasons the desad function should not be statico First, even if individual tastes were otatic, the miniuna food requirements,

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Q , should grow proportionally to population growth. Secondly, as Stone points out in his discussion, I the Q quantities reflect "con-sumers' notions of their standard of living" which change with ex-perience. In the first stage of choice, these are crudely accounted for in the minims food requiremnt by aking Qj increase with time at an arbitrary rate, higher than the assumed population growth rate:

S Q+Qt (4.9)

The savings and total nonfood cocusuption are not modified (xcept by the food Cross-effect). In the second-stage choice among dif-forent nonfood goods, the population effect would make the negative Q values more negative, wereas the habit effect would work the

other vay. The not effect is probably not important to this study, and is neglected.

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47

APPENDIX TO CHAPrE 4

In this appendix, the demand function that has been formulated in Chapter 4 is presented again in terms of block diagram. This will be done for each _{chapter concerned with details}_of_{the model.} The language of these diagrams was briefly introduced in the last

section of Chapter 2. Additional symbols will be explained as need-ed . Each block, it _{will be remembered, represents an operation}

per-formed on the Independent variables (represented by arrows coming to the _{block) to determine a single dependent variable (shomn by a} line l.eaving the block, i.c., with an arrhead on the far end). A small circle,

0

, _{is sometimes used to represent summtion of} vari-ables _{(algebraically, with}signs as indicated). The basic scheme is like that of Phillips,1 _{with some}

additional symbols.

In the demand function diagrams in this appendix, each block also _{corresponds to a specific piece of analog hardware which} em-bodies the relationship, and each line corresponds to a ire. In some diagrams following later chapters, some blocks correspond to simple combinations of several analog components. They are not

shown in complete detail because the diagrams would then be too cluttered to be easily read. When necessary, their details are given separately.