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					The sorry history of Macroeconomics

                        Steve Keen
In the beginning…
• Were the Physiocrats!
   – First school of thought with clear macro-economic
      • Circular flow of income
      • Production & distribution of surplus
      • ―Multiplier‖ effects from change in investment…
• With Smith, a ―great leap backward‖
   – Macro issues almost completely disappeared
      • Belief market system would not suffer from
        ―permanent glut‖
          – ―Invisible hand‖ comment misinterpreted, but
            gist correct as statement of belief
• Ricardo‘s framework admitted macro issues, but
Was Jean Baptiste Say…
• Accepted Say‘s macro vision (―no general glut‖) even
  though value systems fundamentally different
   – Ricardo heir to Smith in classical scheme
      • Value reflects effort, not utility:
         – ―everything rises or falls in value, in
           proportion to the facility or difficulty of
           producing it, or, in other words, in proportion
           to the quantity of labour employed on its
           production. ‖ (Ricardo, Principles)
      • Utility a pre-requisite for exchange, but plays
        no role in setting value:
Was Say…
• ―Utility then is not the measure of exchangeable
  value, although it is absolutely essential to it.‖
  Ricardo, Principles.
   – Caveat that ―If a commodity were in no way useful
     … it would be destitute of exchangeable value,
     however scarce it might be, or whatever quantity
     of labour might be necessary to procure it.‖
      • Changes in perceived utility/demand may change
        temporary market price, but ultimately when
        equilibrium restored, value determines price
• Despite this very non-neoclassical microfoundation,
  Ricardo accepted Say‘s microeconomic argument that
  there could not be macroeconomic problems:
Was Say…
• ―M. Say has, however, most satisfactorily shewn,
  that there is no amount of capital which may not be
  employed in a country, because demand is only limited
  by production. No man produces, but with a view to
  consume or sell, and he never sells, but with an
  intention to purchase some other commodity, which
  may be immediately useful to him, or which may
  contribute to future production. By producing, then,
  he necessarily becomes either the consumer of his
  own goods, or the purchaser and consumer of the
  goods of some other person…‖ (Ricardo Principles;
  emphasis added)
Was Say…
• ―Productions are always bought by productions, or by
  services; money is only the medium by which the
  exchange is effected. Too much of a particular
  commodity may be produced, of which there may be
  such a glut in the market, as not to repay the capital
  expended on it; but this cannot be the case with
  respect to all commodities; the demand for corn is
  limited by the mouths which are to eat it, for shoes
  and coats by the persons who are to wear them; but
  though a community, or a part of a community, may
  have as much corn, and as many hats and shoes, as it
  is able or may wish to consume, the same cannot be
  said of every commodity produced by nature or by
• So according to Ricardo, following Say, there cannot
  be insufficient aggregate demand…
―Say‘s Law‖
• Say (writing 1821-34)
   – ―Utility‖ theory of value (contra. Smith & Ricardo):
      • ―Give to a thing, to a material which has no
        value, utility, and you give it a value; that is,…
        you create wealth.‖ (Catechism of Political
   – Utility subjective:
      • ―you call only useful that which is so to the eye
        of reason, but you ought to understand by that
        word whatever is capable of satisfying the wants
        and desires of man such as he is... He is the
        sole judge of the importance that things are of
        to him,... We cannot judge of it but by the
        price he puts on them.‖
―Say‘s Law‖
• Crises caused by ―disproportionality‖ only
   – Excess supply in one market, excess demand in
• ―General gluts‖ or ―general slumps‖ impossible
• Argument
   – Money only an intermediary in barter
   – People sell only to buy again (increase in utility the
      • Each person‘s supply is matched to his/her
   – Sum of all supply thus cannot exceed sum of all demand
     (no ―general gluts‖); but
―Say‘s Law‖
• Slumps in one market can occur if supply of X exceeds
  demand for X at price producers of X want; however
   – Unless government regulations, monopolies intervene
   – Price of X falls, demand for X rises: equilibrium…
• Basic logic ―micro‖ in nature
   – Hypothesis about behaviour of each individual in
     market system (micro)
   – Aggregate hypothesis to overall economy
   – Argument also essential ―real‖ rather than
―Say‘s Law‖
• ―Every producer asks for money in exchange for his
  products, only for the purpose of employing that
  money again immediately in the purchase of another
  product; for we do not consume money, and it is not
  sought after in ordinary cases to conceal it: … . It is
  thus that the producers, though they have all of
  them the air of demanding money for their goods, do
  in reality demand merchandise for their merchandise.‖
   – So micro balance of each consumer/producer
     ensures overall macro balance
      • Some markets may have over-supply; others will
        be under-supplied; changes in prices will
      • All markets in aggregate balanced
 Marx and the ―Circuits of Capitalism‖
• Marx provides best rejection of Say:
   – Not true that ―Every producer asks for money in
     exchange for his products, only for the purpose of
     employing that money again immediately in the purchase
     of another product‖
   – Some ―producers‖ motivated not by consumption but by
     accumulation: capitalists
      • Capitalist objective not commodities but money/wealth
      • Will withdraw from market if fear can‘t turn produced
        commodities into money profits
          – They do seek ―in ordinary cases to conceal
          – Demand not ―merchandise for their merchandise‖
            but ―more money for their money‖
• ―Say‘s Law‖ fits economy of simple commodity producers—
  but not capitalism
Marx and the ―Circuits of Capitalism‖
• Marx worked out flaw while writing ―Rough Draft‖ of
  Capital in 1857:
   – The commodity is exchanged for money; money is
     exchanged for the commodity. In this way, commodity
     is exchanged for commodity, except that this exchange
     is a mediated one. The purchaser becomes a seller
     again and the seller becomes purchaser again. In this
     way, each is posited in the double and the antithetical
     aspect, and hence in the living unity of both aspects.
     (Marx 1857: 197)
• Circulation of commodity A to money to commodity B
   – ―One moment of circulation is that the commodity
     exchanges itself through money for another
     commodity.‖ (204)
• But there is a second, vital, unbalanced capitalist circuit:
Marx and the ―Circuits of Capitalism‖
• ―But there is, equally, the other moment, not only that
  commodity exchanges for money and money for commodity, but
  equally that money exchanges for commodity and commodity for
  money; hence that money is mediated with itself by the
  commodity, and appears as the unity which joins itself with itself
  in its circular course.
• Then it appears no longer as the medium, but as the aim of
  circulation (as e.g. with the merchant estate) (in commerce
  generally). If circulation is looked at not as a constant
  alternation, but as a series of circular motions which it
  describes within itself, then this circular path appears as a
  double one: Commodity-Money-Money-Commodity and in the
  other direction Money-Commodity-Commodity-Money; i.e. if I
  sell in order to buy, then I can also buy in order to sell.
• In the former case money only as a means to obtain the
  commodity, and the commodity the aim; in the second case the
  commodity only a means to obtain money, and money the aim.‖
  (Marx 1857: 201; emphases added).
Marx and the ―Circuits of Capitalism‖
• Balance of value makes sense in 1st circuit
   – Exchange one commodity for another
   – Equivalents exchanged: $ value of commodity A
     equals $ value of commodity B
   – Differences in qualitative utility the result
      • Seller of A/Buyer of B prefers B to A
      • Ditto in reverse
• But balance doesn‘t make sense in 2nd circuit
   – Exchange of money for money only sensible if
    second quantity exceeds the first:
Marx and the ―Circuits of Capitalism‖
• ―Now one can say: to exchange commodity for commodity
  makes sense, since commodities, although they are
  equivalent as prices, are qualitatively different, and their
  exchange ultimately satisfies qualitatively different needs.
• By contrast, exchanging money for money makes no sense,
  unless, that is, a quantitative difference arises, less
  money is exchanged for more, sold at a higher price than
• In the real process of buying in order to sell, admittedly,
  the motive is the profit made thereby, and the ultimate
  aim is to exchange less money, by way of the commodity,
  for more money, since there is no qualitative difference
  between money and money.
• All that given, it cannot be denied that the operation may
  come to grief and that hence the exchange of money for
  money without quantitative difference frequently takes
  place in reality.‖ (Marx 1857: 201–02; emphases added)
Marx and the ―Circuits of Capitalism‖
• Money incidental to barter; merely makes it easier
• But money essential to understanding capitalism:
   – ―money functions neither only as measure, nor only as medium
     of exchange, nor only as both; but has yet a third quality. It
     appears here firstly as a end in itself, whose sole realization
     is served by commodity trade and exchange.
   – Secondly, since the cycle concludes with it at that point, it
     steps outside it, just as the commodity, having been
     exchanged for its equivalent through money, is thrown out of
     circulation. It is very true that money, in so far as it serves
     only as an agent of circulation, constantly remains enclosed in
     its cycle.
   – But it appears here, also, that it is still something more than
     this instrument of circulation, that it also has an independent
     existence outside circulation, and that in this new character
     it can be withdrawn from circulation just as the commodity
     must definitely be withdrawn. We must therefore observe
     money in its third quality.‖ (Marx 1857: 202-03)
Marx and the ―Circuits of Capitalism‖
• So one component of exchange is balanced:
   – ―Of the part of the revenue in one branch of
     production (which produces consumable commodities)
     which is consumed in the revenue of another branch
     of production, it can be said that the demand is
     equal to its own supply (in so far as production is
     kept in the right proportion).
   – It is the same as if each branch itself consumed
     that part of its revenue. Here there is only a
     formal metamorphosis of the commodity: C-M-C'
     Linen-money-wheat.‖ (Marx 1861: 233)
• Second is necessarily not balanced:
Marx and the ―Circuits of Capitalism‖
• ―The circuit C-M-C starts with one commodity, and
  finishes with another, which falls out of circulation and
  into consumption. Consumption, the satisfaction of wants,
  in one word, use-value, is the end and aim.
• The circuit M-C-M+, on the contrary, commences with
  money and end with money. Its leading motive, and the
  goal that attracts it, is therefore mere exchange-value.‖
  (Marx 1867:148)
• ―Say‘s Law‖ is thus wrong from first principles:
   – Capitalism is more complex than simple commodity
     production & exchange
   – One vital class of agent in capitalism is motivated not
     by consumption but accumulation
   – Sum of demands of two circuits is aggregate demand
       • CAN be deficient if capitalist expectations of profit
Marx and the ―Circuits of Capitalism‖
• Possibility of aggregate, macroeconomic deficiencies/
  excesses in demand come from M-C-M+ circuit
  neglected by Say (and subsequent neoclassicals)
• Complexities of capitalist system arise from this
  second essentially capitalist circuit
• Neoclassical failure to understand
   – cyclical nature of capitalism
   – Possibility of financial crises etc.
• Arises from failure to appreciate existence of M-
  C-M+ circuit & its fundamentally different nature
  to C-M-C:
Marx and the ―Circuits of Capitalism‖
• ―It must never be forgotten, that in capitalist
  production what matters is not the immediate use-
  value but the exchange-value, and, in particular, the
  expansion of surplus-value. This is the driving motive
  of capitalist production, and it is a pretty conception
  that—in order to reason away the contradictions of
  capitalist production—abstracts from its very basis
  and depicts it as a production aiming at the direct
  satisfaction of the consumption of the producers.‖
  (Marx 1861: 495).
• Marx puts motive of capitalist well (if verbosely):
Marx and the ―Circuits of Capitalism‖
• ―The expansion of value, which is the objective basis or main-
  spring of the circulation M-C-M, becomes his subjective aim,
  and it is only is so far as the appropriation of ever more and
  more wealth in the abstract becomes the sole motive of his
  operations, that he functions as a capitalist …
• Use-values must therefore never be looked upon as the real aim
  of the capitalist. Neither must the profit on any single
  transaction. The restless never-ending process of profit making
  alone is what he aims at.
• This boundless greed after riches, this passionate chase after
  exchange-value, is common to the capitalist and the miser; but
  while the miser is merely a capitalist gone mad, the capitalist is
  a rational miser.
• The never ending augmentation of exchange value, which the
  miser strives after, by seeking to save his money from
  circulation, is attained by the more acute capitalist, by
  constantly throwing it afresh into circulation.‖ (Marx 1867: 151;
  emphases added)
Critique of Say‘s Law
• A capitalist economy is therefore the sum of two
  processes: C-M-C and M-C-M+:
   – Commodity—Money—Commodity (C—M—C)
      • Objective to increase utility
      • Monetary value constant, utility (qualitative)
      • Say‘s Law applies
   – Money—Commodity—Money+ (M—C—M+)
      • Objective to increase monetary-value
      • Utility irrelevant, monetary value increased,
        surplus produced
      • Say‘s Law invalid in economy with accumulation
• ―Aggregate Balance‖ explicit in Say‘s Law & Walras‘
  Law does not apply in capitalism:
Critique of Say‘s Law
• ―The capitalist throws less value in the form of money
  into the circulation than he draws out of it … Since he
  functions … as an industrial capitalist, his supply of
  commodity-value is always greater than his demand
  for it. If his supply and demand in this respect
  covered each other it would mean that his capital had
  not produced any surplus-value … His aim is not to
  equalise his supply and demand, but to make the
  inequality between them … as great as possible.‖
  (Marx 1885: 120-121)
• So if it is true that
   – There are capitalists in the capitalist system
• Then
   – Modelling capitalism as if there aren‘t any
     capitalists won‘t work…
Critique of Say‘s Law
• In particular:
   – Demand for labour a derived demand
      • Only hired if capitalists expect profit
   – Demand derived from
      • Demand from C—M—C circuit plus
      • Demand from M—C—M+ circuit
   – Former relatively stable; latter very volatile
   – Only if sum of two equals supply of labour do we
     get ―full employment‖
• Unemployment/underutilised capacity/cycles
  predictable features of capitalist economy
• Interestingly, Keynes agreed with Marx on this issue:
Critique of Say‘s Law
• ―One of the rare occasions in which Keynes praised
  Marx occurred in a 1933 draft of the General
  Theory. Here Keynes credits Marx with the
   – ―… pregnant observation … that the nature of
     production in the actual world is not C—M—C',
     i.e.. of exchanging commodity (or effort) for
     money in order to obtain another commodity (or
     effort). That may be the standpoint of the private
     consumer. But it is not the attitude of business,
     which is a case of M—C—M' , i.e.. of parting with
     money for commodity (or effort) in order to obtain
     more money‖ (1971, Vol. 29, p. 81, Keynes's
       • Dillard 1984 ―Keynes and Marx: a centennial
         appraisal‖ Journal of Post Keynesian Economics
         p. 424
Critique of Say‘s Law
• ―In the immediately following paragraphs, Keynes
  emphasized that business firms subordinate making
  goods to making money:
   – ―An entrepreneur is interested, not in the amount
     of product, but in the amount of money which will
     fall to his share. … The firm is dealing throughout
     in terms of money. It has no object in the world
     except to end up with more money than it started
     with. That is the essential character of an
     entrepreneur [capitalist] economy.‖ (1971, Vol. 29,
     pp. 82, 89. Keynes's emphasis)
• Favourable comments on Marx did not make it into
  General Theory as published (political reasons?); but
   – Keynes gave very similar but far more obscure
     analysis as basis for rejection of Say‘s Law:
Critique of Say‘s Law
• “This theory can be summed up in the following propositions:
• (1) In a given situation of technique, resources and costs, income
  (both money-income and real income) depends on the volume of
  employment N.
• (2) The relationship between the community's income and what it
  can be expected to spend on consumption, designated by D1, will
  depend on the psychological characteristic of the community, which
  we shall call its propensity to consume. That is to say, consumption
  will depend on the level of aggregate income and, therefore, on the
  level of employment N, except when there is some change in the
  propensity to consume.
• (3) The amount of labour N which the entrepreneurs decide to
  employ depends on the sum (D) of two quantities, namely D1, the
  amount which the community is expected to spend on consumption,
  and D2, the amount which it is expected to devote to new
  investment. D is what we have called above the effective demand.
Critique of Say‘s Law
• (4) Since D1 + D2 = D = f(N), where f is the aggregate
  supply function, and since, as we have seen in (2) above,
  D1 is a function of N, which we may write c(N),
  depending on the propensity to consume, it follows that
  f(N) - c(N) = D2.
• (5) Hence the volume of employment in equilibrium
  depends on (i) the aggregate supply function, , (ii) the
  propensity to consume, and (iii) the volume of
  investment, D2.
• This is the essence of the General Theory of
  Employment.” (Keynes 1936 pp. 28-29; bold emphases
• Reiterated in key 1937 paper ―The general theory of
Critique of Say‘s Law
• ―The theory can be summed up by saying that, given the
  psychology of the public, the level of output and employment as
  a whole depends on the amount of investment.
• I put it in this way, not because this is the only factor on which
  aggregate output depends, but because it is usual in a complex
  system to regard as the causa causans that factor which is most
  prone to sudden and wide fluctuation.
• More comprehensively, aggregate output depends on the
  propensity to hoard, on the policy of the monetary authority as
  it affects the quantity of money, on the state of confidence
  concerning the prospective yield of capital-assets, on the
  propensity to spend and on the social factors which influence the
  level of the money-wage.
• But of these several factors it is those which determine the
  rate of investment which are most unreliable, since it is they
  which are influenced by our views of the future about which we
  know so little.‖ (Keynes 1937, p. 221; emphases added)
Critique of Say‘s Law
• Micro fact that production is not solely motivated by
  consumption means that
   – Total employment depends on consumption demand
     and investment
   – Investment depends on volatile expectations of
     profit in an uncertain world
   – Involuntary unemployment can arise if low
     expectations of profit depress investment
• Monetary nature of capitalism vs commodity nature of
  simple commodity production the key reason why
  unemployment exists…
   – Not ―money is the problem‖ but ―money is the
     object‖ and employment incidental to making money…
   – Expectations crucial here too…
Expectations & uncertainty
• Previous (neo)classical theory ignored expectations,
  asserted Keynes:
   – ―at any given time facts and expectations were
     assumed to be given in a definite and calculable
   – The calculus of probability, tho mention of it was
     kept in the background, was supposed to be
     capable of reducing uncertainty to the same
     calculable status as that of certainty itself…‖
     (1937: 212-213)
   – ―I accuse the classical economic theory of being
     itself one of these pretty, polite techniques which
     tries to deal with the present by abstracting from
     the fact that we know very little about the
     future.‖ (1937: 215)
In Marshall (& Walras) We Trust…
• So what was ―classical economic theory‖?
• Prior to Great Depression, neoclassicals simply
  assumed macro was ―scaled up micro‖
   – Aggregate balance assured by Say‘s Law
      • Individual market could have excess supply; but
         – Had to be balanced by other market(s) with
           excess demand
         – Solution was for price of good in excess
           supply to fall
         – If there were unemployed workers, it was
           because wages were too high…
         – Cut wages:
             • demand for labour would rise; and
             • supply of labour would fall
             • Equilibrium restored…
Neoclassical Macro
 • And then, a funny
   thing happened on the
   way to equilibrium…

Arguably began with
Stock Market Crash
And just one week
before, the leading
neoclassical economist
said that…
Irving Fisher…
• ―Stock prices have reached what looks like a
    permanently high plateau.
•   I do not feel that there will soon, if ever, be a fifty
    or sixty point break below present levels, such as Mr.
    Babson has predicted.
•   I expect to see the stock market a good deal higher
    than it is today within a few months.‖ (Irving Fisher,
    October 15 1929)
        • In the next few years, Irving Fisher lost12
          million dollars!
•   That‘s more than $100 million in 2000 prices
•   Crash occurred on October 23rd 1929:

               Volume Traded

      1 2 3 4 5 6 7 8 9 1
            00 00 00 00 00 00 00 00 00 E+
  /O          0 0 0 0 0 0 0 0 0 0
16 / ct 0 0 0 0 0 0 0 0 0 0 5
  /O 2
17 ct/ 9
  /O 2
18 ct/ 9
  /O 2
19 ct/ 9
  /O 29
20 ct/
  /O 2
21 ct/ 9
  /O 2
22 ct/ 9
  /O 2
23 ct/ 9
  /O 29
24 ct/
  /O 2
                                                                                                                      Point Break in just

25 ct/ 9
  /O 2
26 ct/ 9
  /O 2
27 ct/ 9
  /O 29
                                                        Crash continued for another 3 years:

28 ct/
  /O 2
29 ct/ 9
  /O 2
30 ct/ 9
  /O 2
                                                                                               The Great Crash 1929

31 ct/ 9
  /O 29


The Great Wall Street Crash
               and that’s the index
 1948 S&P had many stocks that didn’t exist in 1929                                                                                    S&P 500
   while many of 1929 firms had gone bankrupt…                                                                                         from 32 at

                                                                                                                                       its zenith
   S&P 500 Composite Index


                                                25 years to recover

                                                                                                                                        To below



                                                                                                                                         at its
                                         25/11/21     12/12/33      29/12/45     15/01/58     1/02/70      18/02/82      7/03/94
                                                4/12/27      21/12/39      7/01/52 Week24/01/64     10/02/76      27/02/88

                                                                 in less than 3
         S&P 500 Composite Index

                                                                                                                                       Not only the




                                   2/01/29                 2/04/30               1/07/31              28/09/32              27/12/33
The Great Depression

     250                                                                                                                           30%
                                                                     10 years to
                  GDP Index (1913=100)

                                                                restore output levels                                              20%

     150                                                                                                      10%

     100                                                                                                                           0%

                                                                                                               GDP Change
              30% fall in
           output in 4 years
     50                                                                                                                            -10%


      0                                                                                                                            -20%











                                 -2                                      USA Unemployment Rate (Seasonally Adjusted)

                           O        9
                           A 9
                           O 0
                           A 0
                           O 1
                           A 1
                           O 2
                           A 2
                           O 3

From effectively zero...
                           A 3
                           O 4
                                                                                                                                               The Great Depression

                           A 4
                           O 5
                                                                                                                      To 25% in 3 years

                           A 5

                                            Source: NBER data series m08292a
                           O 6
                           A 6
                           O 7
                           A 7
                           O 8
                           A 8
                           O 9
                           A 9
                           O 0
                           A 0
                           O 1
                                                                                                             WW II Brings

                           A 1
                           O 2
                                                                                                           Sustained Recovery

Pre-Keynesian Macro
• After the event, neoclassicals tried to construct a
  truly ―macro‖ rendition of their theory
• Example: Hicks‘s ―typical classical theory‖ (outlined in
  ―Mr Keynes and the Classics‖)
   – 2 industries: Investment goods X & consumption
     goods Y
   – 2 factors of production: labor (variable); capital
     (fixed in short run)
   – Given capital stock in both industries:
Hicks‘s ―typical classical theory‖
• Output a function of employment Nx & Ny
   – X=fx(Nx); Y=fy(Ny) where f has diminishing marginal
• Prices equal marginal costs = marginal product of
  labour times wage rate (since labour is only variable
   – Marginal cost is increase in labor input (dNx & dNy)
     for each increment to output (dx & dy)
   – Px=w.dNx/dx; Py=w.dNy/dy
• Income = value of output = price times quantity:
   – I = Ix + Iy = w.(dNx/dx) .x + w.(dNy/dy) .y
Hicks‘s ―typical classical theory‖
• Quantity of Money M a given, and fixed relation
  between M and income I (transactions demand for
  money only: money ―a veil over barter‖):
   – M = k.I (k constant ―velocity of money‖)
• Demand for investment goods a function of interest
   – Ix=C(i)
• Supply of savings                           Determines
  a function of interest rate:                    Nx
   – Ix=S(i)
   – Higher savings means                  Demand
     higher investment (a
     familiar argument?)      Ix (output of capital goods)
Hicks‘s ―typical classical theory‖
• Causal chain:
   – M determines I (total output)
   – i determines Ix (output of investment goods)
   – Ix determines Nx (given w)
   – I-Ix determines Iy (output of consumption goods is
     a residual…)
   – Iy determines Ny (given w)
• Lower money wage means higher employment:
   – Lower wage means lower prices
   – Unchanged money I means higher income relative to
     prices, so higher sales
   – Higher sales mean increased employment (and lower
     real wage due to diminishing marginal product)
• Against which Keynes argued that…
Expectations & uncertainty
• ―the level of output and employment as a whole
  depends on the amount of investment … because this
  .. factor … is most prone to sudden and wide
  fluctuation … since … [it is] influenced by our views of
  the future about which we know so little.‖
• Investment undertaken in order to generate profit
• Likelihood of profit depends on the future
• Need expectations of future now to decide how much
  to invest
• How do we form those expectations
   – By rational calculation?
Expectations & uncertainty
• ―we have, as a rule, only the vaguest idea of any but the most
  direct consequences of our acts.
• Sometimes we are not much concerned with their remoter
  consequences, even tho time and chance may make much of them.
• But sometimes we are intensely concerned with them, more so,
  occasionally, than with the immediate consequences.
• Now of all human activities which are affected by this remoter
  preoccupation, it happens that one of the most important is
  economic in character, namely, Wealth.
• The whole object of the accumulation of Wealth is to produce
  results, or potential results, at a comparatively distant, and
  sometimes at an indefinitely distant, date.
• Thus the fact that our knowledge of the future is fluctuating,
  vague and uncertain, renders Wealth a peculiarly unsuitable
  subject for the methods of the classical economic theory…‖ (213)
• What does ―uncertain knowledge‖ mean?
Expectations & uncertainty
• ―By ‗uncertain‘ knowledge, let me explain, I do not mean merely
  to distinguish what is known for certain from what is only
• The game of roulette is not subject, in this sense, to
  uncertainty; nor is the prospect of a Victory bond being drawn.
  Or, again, the expectation of life is only slightly uncertain. Even
  the weather is only moderately uncertain.
• The sense in which I am using the term is that in which the
  prospect of a European war is uncertain, or the price of copper
  and the rate of interest twenty years hence, or the
  obsolescence of a new invention, or the position of private
  wealth-owners in the social system in 1970.
• About these matters there is no scientific basis on which to
  form any calculable probability whatever. We simply do not
  know.‖ (214)
• What do we do then? Can we use probability anyway?
Expectations & uncertainty
 • Imagine you are very attracted to someone
 • This person has accepted invitations from 1 in 5 of
   the people who have asked him/her out
 • Does this mean you have a 20% chance of success?
 • Of course not:
    – Each experience of sexual attraction is unique
    – What someone has done in the past with other
      people is no guide to what he/she will do with you
      in the future
    – His/her response not ―risky‖ but uncertain.
 • Ditto to investments
    – success/failure of past instances give little guide
      to present ―odds‖
Expectations & uncertainty
• How to cope with ―relationship uncertainty‖?
   – We try to ―find out beforehand‖
      • ask friends—eliminate the uncertainty
   – We do nothing…
      • paralysed into inaction
   – We ask regardless…
      • compel ourselves into action
   – We follow conventions
      • ―follow the herd‖ of the social conventions of
        our society
      • ―play the game‖ & hope for the best
• So what about investors?
   – Have to form some expectations of future…
Expectations & uncertainty
• ―Nevertheless, the necessity for action and for
  decision compels us as practical men to do our best to
  overlook this awkward fact [that ―we simply do not
  know‖] and to behave exactly as we should if we had
  behind us a good Benthamite calculation of a series of
  prospective advantages and disadvantages, each
  multiplied by its appropriate probability, waiting to be
• How do we manage in such circumstances to behave in
  a manner which saves our faces as rational, economic
  men? We have devised for the purpose a variety of
  techniques, of which much the most important are the
  three following:‖
Expectations & uncertainty
• (1) We assume that the present is a much more
  serviceable guide to the future than a candid
  examination of past experience would show it to have
  been hitherto.
   – In other words we largely ignore the prospect of
     future changes about the actual character of which
     we know nothing.
• (2) We assume that the existing state of opinion as
  expressed in prices and the character of existing
  output is based on a correct summing up of future
   – so that we can accept it as such unless and until
     something new and relevant comes into the picture.
Expectations & uncertainty
• (3) Knowing that our own individual judgment is
  worthless, we endeavor to fall back on the judgment
  of the rest of the world which is perhaps better
   – That is, we endeavor to conform with the behavior
     of the majority or the average. The psychology of
     a society of individuals each of whom is
     endeavoring to copy the others leads to what we
     may strictly term a conventional judgment.‖ (214)
• As a result, expectations are:
   – ―subject to sudden and violent changes…. All these
     pretty, polite techniques, made for a well-panelled
     Board Room and a nicely regulated market, are
     liable to collapse…‖ (214-15)
Expectations & uncertainty
• As a result investment is volatile
   – ―It is not surprising that the volume of investment, thus
     determined, should fluctuate widely from time to time. For it
     depends on two sets of judgments about the future, neither
     of which rests on an adequate or secure foundation—on the
     propensity to hoard and on opinions of the future yield of
   – Nor is there any reason to suppose that the fluctuations in
     one of these factors will tend to offset the fluctuations in
     the other. When a more pessimistic view is taken about
     future yields, that is no reason why there should be a
     diminished propensity to hoard [which would reduce the rate
     of interest].
   – Indeed, the conditions which aggravate the one factor tend,
     as a rule, to aggravate the other. For the same
     circumstances which lead to pessimistic views about future
     yields are apt to increase the propensity to hoard [driving up
     the rate of interest].‖ (218)
• So investment can‘t be regulated by the rate of interest…
Expectations & uncertainty
• Key aspects of Keynes‘s arguments include
   – Uncertainty
   – Volatility of investment
   – Impossibility of regulating investment using interest
• So how on earth did we get from this to IS-LM???
   – Because Hicks‘s ―review‖ of the General Theory
     presented an entirely different model
      • ―review‖ taken as ―convenient summary‖ of Keynes
          – But omitted uncertainty entirely
          – Presumed investment & demand for money were
          stable functions of the rate of interest…
Keynes according to Hicks
• ―Mr Keynes begins with three equations,
   – M=L(i), Ix=C(i), Ix=S(I)
   – [in contrast to (neo)classical theory] ―... the
     demand for money is conceived as depending upon
     the rate of interest (Liquidity Preference).
   – On the other hand, any possible influence of the
     rate of interest on the amount saved out of a
     given income is neglected. Although it means that
     the third equation becomes the multiplier equation,
     which performs such queer tricks, nevertheless this
     second amendment is a mere simplification, and
     ultimately insignificant.‖
Keynes according to Hicks
• In this model:               Ms
   – Money demand/supply
     determines i

 • i determines Ix
 • Ix determines I via              Md
   the multiplier
 • Increase Ms-
   >increase I
 • Increase propensity
   to invest, or to
   consume-> increase I
Keynes ―special theory‖, according to Hicks
  i                   Money market        i          Investment
                   determines int. rate                interest rate
                Md (liquidity                               Ix=f(i)
                      M                                    Ix
      I (output)                          I (output)
                          employment                       Investment

                     N (employment)                            Ix
                                              The multiplier
Keynes ―special theory‖, according to Hicks
  i                   Money market        i          Investment
                   determines int. rate                interest rate
                Increasing Ms increases N:              determines
                Md (liquidity                               Ix=f(i)
                      M                                    Ix
      I (output)                          I (output)
                          employment                       Investment

                 N (employment)                                Ix
 Employment grows more than                      I=f(Ix)
 output because of diminishing                The multiplier
       marginal product
  Keynes ―special theory‖, according to Hicks
    i                   Money market        i       Investment
                     determines int. rate                interest rate
                  Reducing LP increases N:                determines
                  Md (liquidity                               Ix=f(i)
                        M                                    Ix
        I (output)                          I (output)
                            employment                       Investment

                    N (employment)                   Ix
 Employment grows more than output       I=f(Ix)
                                      The multiplier
because of diminishing marginal product
Keynes ―general theory‖, according to Hicks
• ―something appreciably more orthodox‖
• ―The dependence of the demand for money on
  interest does not ... do more than qualify the old
  dependence on income. However much stress we lay
  upon the 'speculative motive', the 'transactions
  motive' must always come in as well.‖
• Hicks‘s version of Keynes‘s ―GT‖
   – M=L(I,i), Ix=C(i), Ix=S(I).
• vs Hicks‘s version of ―typical classical theory‖
   – M=k.I, Ix=C(i), Ix=S(i)
Keynes ―general theory‖, according to Hicks
• The LL (LM) curve:
   – Fixed Ms; Md negative fn of i; positive fn of I:
      Exogenous Ms                   The LM curve
i                           i

                Md1 (I2)

                 Md1 (I1)
                                         I2    I
                     M              I1
Keynes ―general theory‖, according to Hicks

           I (income) Ix=S(I)(income)

The IS curve:
  Investment        Savings a
  demand -ive      function of
  fn of i            income
  [Ix=C(i)];                S            I (income)
  supply +ive i    Investment a i
  fn of
                    function of     The IS curve
                   interest rate
  [Ix=S(I)]          Multiplier
                   Ix (Investment)       I(output)
Keynes ―general theory‖, according to Hicks
       The product: IS-LM analysis


                                     LL (now LM)


                                      I (output)
Keynes ―general theory‖, according to Hicks
• Keynes a neoclassical marginalist, according to Hicks:
   – ―Income and the rate of interest are now
     determined together ... just as price and output
     are determined together in the modern theory of
     demand and supply.
   – Indeed, Mr Keynes's innovation is closely parallel,
     in this respect, to the innovation of the
   – Integrating ―Keynes and the Classics‖:
       • Slope of LM curve
          – almost horizontal for low levels of I
          – almost vertical for high levels of I:
Keynes ―general theory‖, according to Hicks
• In “Keynesian” region,     i
  rightward shift of IS
  curve (by fiscal policy,
  etc.) mainly boosts income                         LM
• In “Classical region”,
  rightward shift of IS
  curve (by fiscal policy,
  etc.) mainly boosts
  interest rate
• “the General Theory of                              IS
  Employment is the
                               “Keynesian region”
  Economics of Depression”,
  Classical is Economics of                       I (output)
  full employment
Nice theory, but is it Keynes?
• Whatever Happened to Uncertainty & Expectations?
  – Hicks: Ix=f(i) Investment demand a function of the
    rate of interest (and income in more general model)
  – Keynes: ―Our knowledge of the factors which will
    govern the yield of an investment some years hence
    is usually very slight and often negligible‖
  – ―It would be foolish, in forming our expectations,
    to attach great weight to matters which are very
    uncertain… therefore, [we are] guided … by the
    facts about which we feel somewhat confident, …
    the facts of the existing situation enter …
    disproportionately, into the formation of our long-
    term expectations…‖
  – Why not Ix=f(i,I,E) where E is expectations?
Nice theory, but is it Keynes?
• ―Keynesian Economics‖ as practised
   – Keynes minus uncertainty & expectations
      • ―Keynes without uncertainty is something like
        Hamlet without the Prince.‖ (Minsky, John
        Maynard Keynes, 1975, p. 57)
   – Evolved towards the ―Neoclassical synthesis‖
      • IS-LM macro grafted onto neoclassical micro
      • Key architects Hicks & Samuelson
          – Revival of neoclassical economics as Keynes
            criticised for having ―bad microfoundations‖
          – The accusation
             • Can‘t derive Keynesian results from micro
             • Therefore Keynesian macro at fault…
Nice theory, but is it Keynes?
• Versus Keynes: neoclassical microfoundations at fault
  when applied to real world:
   – ―I accuse the classical economic theory of being
     itself one of these pretty, polite techniques which
     tries to deal with the present by abstracting from
     the fact that we know very little about the
• But Hicksian version of Keynes
   – Omits uncertainty, expectations, monetary nature
     of system
   – Accepts neoclassical marginalism
   – A ―straw man‖ easily demolished in debate
• Ultimate outcome the ―rational expectations‖
Rational Expectations Macroeconomics???…
• Why rational expectations?
   – Because if you believe neoclassical economics, you
     have no choice!
      • Neoclassical vision: micro explains macro
      • Micro in balance—macro must be in balance
      • Cycles, ―unemployment‖, etc. anomalies to be
        explained from within paradigm
• Back to basic neoclassical vision
   – Demand derived from utility maximising individualS
     given budget constraint
   – Supply derived from profit maximising firmS given
     market demand
   – Equilibrium determines output AND relative prices:
                   In Marshall (& Walras) We Trust…
                              Z                                              Costs
                         X                                                     and



                                                                           P=MR1                           P = AR = MR


                                                                                   0   Q1   QMAX   Q2           Quantity
                         q1       q2 I   q3   II   III

                                                             Price Level
Price of Bananas



                         q1       q2     q3        Bananas
In Marshall (& Walras) We Trust…
• Only conditions under which this applies are:
   – When there are no aggregation issues
      • Deferred until later, but remember from
        Advanced Political Economy:
         – Sonnenschein-Mantel-Debreu conditions
         – Theory of firm aggregation errors…
   – When expectations equal predictions of model; and
   – Predictions are correct…
• Prelude: the ―Phillips curve‖
   – Focus of much of neoclassical critique of Keynes
   – So why did Phillips develop ―his‖ curve?
Phillips & Systems Engineering
• A.W. Phillips originally an engineer
   – Learnt dynamic methods of engineering
   – Applied them to economics
   – Engineers model dynamics using time-varying equations:
      • Ordinary Differential equations
          – Rate of change of variable(s) at time t functions of
            values at time t
      • Partial Differential equations
          – Rate of change of variable(s) at time t & place p
            functions of values at t/p
      • Difference equations
          – Value of variable(s) at time t functions of values at
            previous discrete time intervals
   – Engineers add ―systems‖ flavour—model interacting systems of
Phillips & Systems Engineering
• Graduate British Institute of Electrical Engineers
• Apprenticeship at NZ hydroelectric power station
• Social policy interest after being Japanese POW
   – Applied Engineering training to social dynamics
   – Key question: how to stabilise unstable economy at
     desired levels of output growth, employment etc.
      • ―The Phillips curve was not constructed by
        someone who regarded himself as a statistician,
        or an econometrician, or even an economist.
      • Phillips regarded himself (and was regarded by
        his contemporaries) as an engineer, constructing
        ingenious optimal control solutions to the
        stabilisation problem.‖ (Leeson)
Phillips & Systems Engineering
• Key observation by Phillips from engineering
   – ―The system has fairly satisfactory self-regulating
     properties when prices are moderately flexible; but
     becomes unstable when there is a high degree of
     price flexibility.‖ (1954, 313)
      • In other words, excessive flexibility
        destabilising—opposite to economics belief
          – Dynamic systems have tendency to overshoot
            equilibria if rate of adjustment too high…
      • Phillips‘s dynamic models considered parameter
        values and policies that could lead to
        stabilisation rather than explosive cycles…
―Hydraulic Keynesianism‖
• Work pre-dated availability of computers
• Built first models as analog hydraulic computer:
                   • Models
                      – Rate of
                        change of
                      – Function of
                        level of
―Hydraulic Keynesianism‖
• Derided as ―hydraulic Keynesianism‖ by many economists, but in
  reality Phillips an early critic of comparative statics in economics:
   – ―RECOMMENDATIONS for stabilising aggregate production and
     employment have usually been derived from the analysis of
     multiplier models, using the method of comparative statics.
   – This type of analysis does not provide a very firm basis for
     policy recommendations…
   – First, the time path of income, production and employment
     during the process of adjustment is not revealed.
       • It is quite possible that certain types of policy may give
         rise to undesired fluctuations, or even cause a previously
         stable system to become unstable,
           – although the final equilibrium position as shown by a
             static analysis appears to be quite satisfactory…‖
             (Phillips 1954, Stabilisation policy in a closed economy,
             Economic Journal p. 290; e.a.)
―Hydraulic Keynesianism‖
• Phillips‘s dynamic model had proposition of nonlinear
  relationship between ―factor prices‖ and output:
   – ―We may therefore postulate a relationship between
     the level of production and the rate of change of
     factor prices, which is probably of the form shown
     in Fig. 11, the fairly sharp bend in the curve where
     it passes through zero rate of change of prices
     being the result of the greater rigidity of factor
     prices in the downward than in the upward
     direction…‖ (p. 308) • After postulating existence
                             of relationship, went looking
                             for it in the data…
                           • Intended purpose lost in
                             subsequent ―debate‖
                              – Wildly at variance with
                                how applied in practice…
A systems approach to economics
• Phillips‘s ambition: to wean economists off statics
   – Built dynamic systems model of macroeconomy:
       • Time lags in adjustment of variables rather than
         ―comparative statics‖
           – Time path of system plotted and analysed
• Basic model:
   – Production (P) & Consumption (E) start in equilibrium
   – Initial change in E
   – Lagged response in P
       • ―On the supply side, … the rate of flow of
         current production … is adjusted, after a time
         lag, to the rate of flow of aggregate demand…
       • On the demand side, … aggregate demand varies
         with real income or production, without
         significant time lag.‖ (291)
A systems approach to economics
• Time lag: adjustment parameter of dynamic system to
  change in state
   – Simple time lag easily solved and given intuitive
   – Basic model: ―the rate of flow of current
     production … is adjusted, after a time lag, to the
     rate of flow of aggregate demand‖

 • Gap between P & E
 • decays exponentially over time       P     P  E   
 • by changes in P
• Solving this symbolically:
A systems approach to economics
• Take equation:         d
                            P     P  E      
• Rearrange to put P‘s & t‘s on either side:
                                     dt
                         P  E 
• Integrate LHS w.r.t. P & RHS w.r.t. t:
                          P  E  dP     dt
• LHS gives a log, RHS a constant time t
                         ln  P  E    t  C 0

• Take exponential: P t   E  e  t C   0

• Rearrange:             P t   E  C1  e  t
A systems approach to economics
• Include initial condition of equilibrium so P(0)=0
       P  0   E  C1  e  0  0
• Solve for constant of integration C1:
       C1  E
• Substitute back into equation for P(t):
        P t   E 1  e  t    Plot of closed form solution for P

• Plot the solution:
                                                               Effective Demand

• We can now interpret :
  – Tangent to P at t=0:

     • Line through 0,0

     • with slope   P t  t 0             0.8


                                                  0   0.2   0.4           0.6   0.8

A systems approach to economics
• Find differential:
     d            d
        P t      E 1  e  t 
     dt          dt
                    d  t
                E    e
                E  e  t

                E    e  t • At t=0 this is

       E    1  4  4

• Equation of tangent is thus          T t   4 t

• Graphing this with P:
A systems approach to economics
 • Tangent to P intersects E at t=0.25 or t=1/:
      Plot of closed form solution for P            • This is not an accident
                                                    • Tangent from initial

                                                      condition on function f(t)
                                Effective Demand
 0.2                            Tangent to P at t=0

                                                      intercepts ultimate value
                                                      of f [f(∞)] at t=1/
                                                       – where

                                                                   f    f
                           • Phillips‘s ―=4‖ means

                              – ―Production adjusts to
       0   0.2   0.4   0.6
                                effective demand with a

                                lag of ¼ of a year‖

• Modern systems engineers state lag explicitly
  – Use ―=¼‖ & write equation as d f   1  f
                                                  dt         
• We‘ll stick with Phillips‘s notation for now…
 A systems approach to economics
• Phillips designed systems as engineering flowcharts…

• 50 years after Phillips, systems easily simulated
    A systems approach to economics
    • As flowcharts…
                                                                       Adjustment of Production to Effective Demand
                                                                                       with a time lag
                                  P initially in equilibrium     0
           P                                                          Production(deviation from equilibrium)
                     +                               +                  Effective Demand
 -1          E       -       *             1/S       +          -.2
Fall in Effective Demand                  Integrator

   alpha           -X                                           -.4

    Production adjustment speed


                                                                  0   .2    .4    .6     .8    1     1.2       1.4   1.6   1.8   2
                                                                                          Time (years)
A systems approach to economics
• Or as equations…
  4      Given         P ( t)     ( P ( t)  E ( t) ) P ( 0)   0
                          E ( t)   0                       E ( 0)     1
                P              P              
                   Odesolve    t  1  1000
                E              E              
                                                      Production (deviation from equilibrium)
 P ( t)
                                                      Effective Demand
 E ( t)                                               Time Lag tangent
   t                                               0.25


                0                  0.2                   0.4                      0.6   0.8
                                                               t  t  t  0.25
A systems approach to economics
• Phillips built complex model by series of extentions:
   – Start with simply lagged response of P to ED
   – Add stabilisation policies
   – Expand model to multiplier-accelerator
   – Incorporate flexible prices
       • Model price level as response to income demands
          – Hence the ―Phillips curve‖…
• Discounted impact of marginal cost on prices:
   – ―if … factor prices … are absolutely rigid, product
     prices, tending to move with marginal costs, will
     vary directly with the level of production.
   – This component of the change in product prices is
     probably not very large, and will be neglected in
     the following analysis.‖ (307)
A systems approach to economics
• Then provided rationale for ―factor price‖ inflation in context of
  high demand:
   – ―Even with flexible factor prices, there will be some level of
     production and employment which … will just result in the
     average level of factor prices remaining constant, this level
     of production and employment being lower, the stronger and
     more aggressive the organisation of the factors of
   – If aggregate real demand is high enough to make a higher
     level of production than this profitable, entrepreneurs will be
     more anxious to obtain (and to retain) the services of labour
     and other factors of production and so less inclined to resist
     demands for higher wages and other factor rewards. Factor
     prices will therefore rise.
   – The level of demand being high, the rising costs will be
     passed on in the form of higher product prices…‖ (307;
     emphases added [e.a.])
A systems approach to economics
   – ―Conversely, if aggregate real demand is so low
     that production at the level which would result in
     constant factor prices is unprofitable,
     entrepreneurs will be more anxious to force down
     factor prices, while at the lower level of
     employment factors will be less able to press for
     higher rewards and more inclined to accept lower
   – Factor prices will therefore gradually move
     downwards, and the level of demand being low, the
     falling costs will be reflected in falling product
     prices.‖ (307; e.a.)
• Then drew nonlinear relationship between level of
  production & prices: the (non-empirical) Phillips Curve
A systems approach to economics
• Wrote 2 more systems papers & then published
  – ―The Relation Between Unemployment and the Rate
    of Change of Money Wage Rates in the United
    Kingdom, 1861-1957‖
  – Went from this conjecture…
                        • To this estimation:
A systems approach to economics
• How Phillips Curve was used shortly…
• How Phillips intended to use it first:
  – Control engineering background
      • Design systems to control fluctuating dynamic
         – Air conditioning systems; amplifiers;…
  – First thought: how to control fluctuations in
    dynamic changing economy
  – First additions: control systems to stabilise output
  – Later addition: nonlinear price relationship to
    increase realism of model
      • Crucially, model naturally cyclical:
A systems approach to economics

• Modern dynamics (later than Phillips) tells us
  – nonlinear dynamic models normally have endogenous
  – fluctuations often ―chaotic‖
A systems approach to economics
• Modern example of former: Goodwin‘s ―predator-prey‖
  model of cyclical growth
  – Predator-prey?
     • Fish eat seagrass (assumed unlimited supply)
     • Sharks eat fish
     • Together, a cycle:
         – Low numbers of fish, sharks die off
         – Less sharks, more fish reproduce
         – More fish available, shark numbers rise
         – More sharks, fish population declines
         – Low numbers of fish, sharks die off…
     • How to model it?
         – Use F for Fish and S for Sharks
Nonlinear Dynamic Systems
• Simplest population growth model             1 dF
                                                      a
   – (Fish) Population F grows at a% p.a.: F dt
• Formula is: F t   F  0   e a t
• Simulated as flowchart:         • Simulated as equation:
                  1                      a

    Fish growth rate
                                                             a  100%                Given            Fish ( t)   a  Fish ( t)
                             10000                                                                dt
                            Initial No. fish
                                                +            Fish ( 0)      10000                 Fish  Odesolve [ (Fish )  t  10  1000]
                       *         1/S            +
                           Fish Population                               1  10

                                                                         1  10

200000000                                                                1  10
                                                              Fish( t)
                                                                         1  10

100000000                                                                     5
                                                                         1  10
                                                                         1  10
       0                                                                          0           2        4           6         8     10
        0              2         4          6       8   10
                                 Time (Years)                                                                t
      Nonlinear Dynamic Systems
      • Similar relations apply for sharks                                                                  1            dS
                                                                                                                            b
                                                                                                            S            dt
      • Formula is: S t   S  0   e b t
      • Simulated as flowchart:         • Simulated as equation:
                      0.5                         b                                                         d
                                                                             b  50%              Given        Sharks ( t)   b  Sharks ( t)
          Shark death rate                                                                                  dt
                                                                             Sharks ( 0)       10           Sharks  Odesolve [ (Sharks )  t  10  1000]
                                      Initial Sharks
                             *             1/S          +
 1                                   Fish Population

                                                                              Sharks ( t) 5


                                                                                               0        2        4        6         8            10
10                                                                                                                   t
      0        1     2           3     4     5      6       7   8   9   10
                                        Time (Years)
Nonlinear Dynamic Systems
• Simplest way to introduce interaction between
  fish & sharks:
   – Sharks reduce fish growth rate in    1 dF
                                               a  b S
     proportion to number of sharks       F dt
   – Fish reduce shark death rate in               1       dS
                                                              c  d  F
     proportion to number of fish                  S       dt
• Now have to model populations as linked
• Nonlinear relationships arise naturally:
  – Fish numbers times shark numbers: quasi-quadratic

   dF                    dS
       a F  b S F       c  S  d  F  S
   dt                    dt
Nonlinear Dynamic Systems
 • Generates system with endogenous cycles:
          Fish                                 100      +
                         *       +
         2                                     1/S      +
                                 -                                      Sharks                             10      +
                                              IC:0;ID:1                               *         -
       Sharks                                                            1                                1/S      +
         1/10            *                                                                               IC:0;ID:0
       Fish                                                               1/200            *

                  Plot                                           Plot                                      Plot
500                                              500                                           40

400                                              400
300                                              300
200                                              200
100                                              100

  0                                                0                                            0
   0      2       4          6       8   10         0       10      20           30       40     0   2     4      6     8   10
                 Time (years)                                                                            Time (years)
  Nonlinear Dynamic Systems
   • Simulated as equation:
Given           Fish ( t)     a  Fish ( t)  b  ( Sharks ( t)  Fish ( t) )       Fish ( 0)   5000
                Sharks ( t)      c  Sharks ( t)  d  Sharks ( t)  Fish ( t)     Sharks ( 0)   10

   Fish                 Fish                   
            Odesolve           t  10  1000
   Sharks               Sharks                 

           5000                                                                          14

                                                                                                 • Similar logical chain
Fish( t)                                                                                 10 Sharks ( t)
                                                                                                        generates cyclical
                                                                                                        growth model…
                                                                                         8       • With ―Phillips curve‖ as
                                                                                                        essential component…
           3500                                                                         6
                   0             2              4              6                8      10
 A predator-prey cycle in capitalism
• Goodwin (1967) implemented model of Marx‘s:
  – ―a rise in the price of labor resulting from
    accumulation of capital implies … accumulation
    slackens in consequence of the rise in the price
    of labour… The rate of accumulation lessens; but
    with its lessening, the primary cause of that
    lessening vanishes, i.e. the disproportion
    between capital and exploitable labour power…
    The price of labor falls again to a level
    corresponding with the needs of the self-
    expansion of capital, whether the level be
    below, the same as, or above the one which was
    normal before the rise of wages took place…‖
    (Marx Capital I, Ch. 25)
A predator-prey cycle in capitalism
• To put it mathematically, the rate of accumulation is the
  independent, not the dependent variable; the rate of wages
  the dependent, not the independent variable.‖ (Marx 1867,
  1954: 580-581)
• Same passage used by Goodwin (1967) to devise a
  ―predator-prey‖ model of cycles in employment and
  income distribution
   – High wages shareLow rate of
     accumulationIncrease in unemploymentDrop in
     wagesIncrease in accumulationIncrease in
     employmentHigh wages share
      • ―Phillips curve‖ part of Marx‘s logic (wage change
        a function of the rate of unemployment)
A predator-prey cycle in capitalism
• Capital stock determines output
• Level of output determines employment
• Level of employment determines rate of change of
  wages (―Phillips curve‖)
• Integral of rate of change of wages determines wages
• Output - Wages determines profits
• Profits determine investment
• Investment determines rate of change of capital
• Capital determines output…
• The basic mechanism as a causal flowchart
   – Each stage in loop directly causes next stage
   – System ―closed‖ so causation flows back to start
A predator-prey cycle in capitalism
• Capital K determines output Y via the accelerator:
          K           1/3                  Y

• Y determines employment L via productivity a:
              Y               l
                                      /            L
    1         a               r
   Labour Productivity

• L determines employment rate l via population N:
               L          l
                                  /            l
   100       N            r

• l determines rate of change of wages w via P.C.
      l            PhillipsCurve                       dw/dt

• Integral of w determines W (given initial value)
     Initial Wage              +                       w
                                                                *      W
       dw/dt           1/S     +                       L

• Y-W determines profits P and thus Investment I…
      Y        +                                                             1
                                      Pi           I           dK/dt
      W        -
                         • Closes the loop:
                                                                           Initial Capital             +
                                                                            dK /dt             1/S     +
A predator-prey cycle in capitalism
• Turning this into a real model… • Replace ―black box‖
   – Link the bits together:        Phillips curve with a
           K     1/3
                                    functional form (even
                                    linear one will do)…
                                              /             L
        1        a                   r
       Labour Productivity                                                      l    +
                                 l                                          0 .9 5   -   *   P hillipsC urve
                                          /             l               "NAIRU"
        100       N              r
       Population                                                         10

                PhillipsCurve                     dw/dt

                                 +                 w
    Initial Wage                                                *       W
                         1/S     +                 L
        Y          +
                                     Pi             I           dK/dt

      Initial Capital               +
                            1/S     +
A predator-prey cycle in capitalism
• Model generates endogenous cycles:
                 K               1/3                     Y                                                       Endogenous Cycles
                                Accelerator                                                                  in Employment and Wages
                                                                                                        Employment Rate
                                      l                                              l                   Wage
                                               /             L                                 5
      1        a                      r
     Labour Productivity
                                  l                                                            3
                                           /             l
   360                N           r
  Population                                                                                   1

                          Phillips                 dw/dt
                          Curve                                      W   l
                                                                                 /       ws    -3
                                                                     Y   r
    .9                            +                                                            -5
                                                    w                                               0        2         4        6      8     10
  Initial Wage                    +                              *           W
                       1/S                          L                                                                 Time (Years)
                                                                                                                 Endogenous Cycles
      Y          +
                                      Pi             I           dK/dt                                       in Employment and Wages
                 -                                                                            7
    Initial Capital                 +                                                         3
                            1/S     +
                          Integrator                                                          1

                                                                                                                                                  ―Natural‖ source
                                                                                                                                                   of nonlinearity
                                                                                     ws       -3

                                                                                                   0    .5         1     1.5    2      2.5   3
                                                                                                                   Employment Rate

• So this is how Phillips wanted to use relationship
• Next lecture: how he derived it; & how it was used…

Description: Law School Flowcharts Future Interest document sample