Political Economy: Critique of Neoclassical Economics

Political Economy: Critique of Neoclassical Economics Wrong answers to the wrong questions: Equilibrium

Last week, Supply • Theory of the firm a shambles • Profit maximisation formula wrong. When amended: • PC “Price=Marginal Cost” impossible • P>MR=MC for profit maximisers • Competition & monopoly produce same results • If costs lower, monopoly better than PC • “Welfare loss” due to profit-maximising behavior, not monopoly • Theory irrelevant to real world anyway • This week • “General Equilibrium” can’t be in equilibrium • “General Dynamics” needed, not “general equilibrium”

From one to many • Previous lectures: flaws in (Marshallian) model of single industry • This lecture: Ignoring flaws in Marshallian model(!), flaws in (Walrasian) model of entire economy • The dilemma • Equilibrium in one market can be disturbed by disequilibrium in another • What are conditions that will give equilibrium—equality of demand & supply—in all markets? • First person to consider this: Leon Walras (1874) • Real-world equilibrium involved use of some commodities to make others, dynamic price & output setting, product innovation…

Walras’ General Equilibrium • Walras abstracted from all this • Pure exchange model (all quantities of all goods already given and pre-allocated) • Traders simply wish to exchange surplus commodities for desired ones • Even so, out of equilibrium trade would disturb income/wealth distribution • “Above equilibrium” sellers gain income, “below equilibrium” lose • Non-equilibrium system might never converge • Invented fiction to avoid problem: • No trades allowed in any market until all markets in equilibrium • Prices set by impartial & costless “Auctioneer”

Walras’ General Equilibrium • “First, let us imagine a market in which only consumer goods and services are bought and sold… Once the prices … of all these goods and services have been cried at random …, each party to the exchange will offer at these prices those goods or services of which he thinks he has relatively too much, and he will demand those articles of which he thinks he has relatively too little for his consumption during a certain period of time. The quantities of each thing effectively demanded and offered having been determined in this way, the prices of those things for which the demand exceeds the offer will rise, and the prices of those things of which the offer exceeds the demand will fall. New prices now having been cried, each party to the exchange will offer and demand new quantities. And again prices will rise or fall until the demand and the offer of each good and each service are equal. Then the prices will be current equilibrium prices and exchange will effectively take place.” (Walras 1874) • A dynamic but “out of time” process of price adjustment to equilibrium…

Walras’ General Equilibrium: the Process • “Auctioneer” makes initial guess at Prices • Prices determine agents • Wealth (Prices * quantities held) • Supplies (Stocks held – desired for consumption) • Demands (Quantities desired – stocks held) • Each agent balanced (Prices * Supplies = Prices * Demands) • If all markets in equilibrium, trade occurs • If not • Auctioneer increases price for commodities where Demand > Supply, decreases where Supply > Demand • Agents recalculate Demands & Supplies • Process continues until equilibrium in all markets • Then trade allowed to occur…

Walras’ General Equilibrium: the Problem • Will process actually converge to equilibrium Prices? • Walras thought so: • “Then the prices will be current equilibrium prices and exchange will effectively take place.” • But the problem is • Change in price in one market affects all others • Feedback from other markets back to first one • Feedback effects could overwhelm direct effects • Walras surmised that • Direct effects all in correct direction (price up where demand>supply, down where supply>demand) • Indirect effects in any direction, but could “cancel each other out”:

Walras’ General Equilibrium: the Problem • “This will appear probable if we remember that the change from p’b to p’’b, which reduced the above inequality to an equality, exerted a direct influence that was invariably in the direction of equality at least so far as the demand for (B) was concerned; while the [consequent] changes from p’c to p’’c, p’d to p’’d, …, which moved the foregoing inequality farther away from equality, exerted indirect influences, some in the direction of equality and some in the opposite direction, at least so far as the demand for (B) was concerned, so that up to a certain point they cancelled each other out. Hence, the new system of prices (p’’b, p’’c, p’’d, …) is closer to equilibrium than the old system of prices (p’b, p’c, p’d, …); and it is only necessary to continue this process along the same lines for the system to move closer and closer to equilibrium.” (Walras 1874 [1954]:; my emphasis)

Walras’ General Equilibrium: the Promise • (1) Establish correctness of surmise of convergence to equilibrium; • (2) Generalise to system with • (a) Production • (b) Out of equilibrium exchange • Unfortunately, didn’t even get to 1st base… • “From static analysis (going back to Walras and Marshall), it is known that, even under very plausible circumstances, [Walrasian tatonnement] systems … have multiple equilibria … Hence it is not to be expected that, in a reasonably broad class of economic environments … every equilibrium point of a Walrasian tatonnement process will be stable.” (Hurwicz 1986: 46-47)

Walras’ General Equilibrium: the Failure • How should neoclassicals have reacted? • “From a normative and computational point of view it is natural to conclude that the possible absence of global stability calls for … • … a non-equilibrium model of exchange”? • How did they react? (Hurwicz 1986: 47-48) • … replacing the Walrasian tatonnement by another dynamic process”! • Proposed adjusting individual demand functions! • “Clearly the informational burden of this system is greater than that of [Walras]”, but … • “one must, in general, be prepared to require a bigger message space when stability is demanded.”

Walras’ General Equilibrium: the Failure • Walras’ model already fictional • Abstracts from real-world phenomena of • Production • Non-equilibrium exchange • If it can’t necessarily reach equilibrium, what hope is there that real-world can? • But neoclassicals take succour in even more unreal assumptions to make model “work”—even if can’t be applied to real world • Pinnacle of this the “Arrow-Debreu model of general equilibrium”

Walras’ General Equilibrium: the Failure • Debreu (1959) establishes necessary conditions for general equilibrium to exist • Instantaneous “market” where all producers & consumers • Know the future • Decide all purchases for all time • “Generalised” to “uncertain” future by effectively making past mistakes reversible via insurance markets for all possible future events • Insure against buying an umbrella on days when it doesn’t rain… • Only have to pay for umbrella if it does rain (& you need it), not if it doesn’t

Walras’ General Equilibrium: the Failure • “For any economic agent a complete action plan (made now for the whole future), or more briefly an action, is a specification for each commodity of the quantity that he will make available or that will be made available to him, i.e., a complete listing of the quantities of his inputs and of his outputs… • For a producer, say the jth one, a production plan (made now for the whole future) is a specification of the quantities of all his inputs and all his outputs … The certainty assumption implies that he knows now what input-output combinations will be possible in the future (although he may not know the details of technical processes which will make them possible)… • As in the case of a producer, the role of a consumer is to choose a complete consumption plan… His role is to choose (and carry out) a consumption plan made now for the whole future, i.e., a specification of the quantities of all his inputs and all his outputs. “ (Debreu 1959)

Walras’ General Equilibrium: the Failure • “The analysis is extended in this chapter to the case where uncertain events determine the consumption sets, the production sets, and the resources of the economy. A contract for the transfer of a commodity now specifies, in addition to its physical properties, its location and its date, an event on the occurrence of which the transfer is conditional. This new definition of a commodity allows one to obtain a theory of uncertainty free from any probability concept and formally identical with the theory of certainty developed in the preceding chapters.” (Debreu 1959; my emphases) and get serious! Let's cut the...

Walras’ General Equilibrium: the Failure • A physicist’s take on this “model”: • “Here is an example: at time t=0 you plan your entire future, ordering a car on one future date, committing to pay for your children’s education on another datse, buying your vacation house,… placing all future orders for daily groceries, drugs… All demands for your lifetime are planned and ordered in preference. In other words, your and your family’s entire future is decided completely at time zero. These assumptions were seen as necessary in order to construct a theory where one could prove rigorous mathematical theorems. Theorem proving about totally unrealistic markets became more important than the empirics of real markets in this picture.” (McCauley 2004: 15)

Walras’ General Equilibrium: the Failure • Why such unrealistic assumptions? • Because any even slightly more realistic model is provably unstable Warning! Warning! • Serious maths zone approaching! • Intuition main thing that matters: • Stability of outputs & stability of prices in conflict

Can General Equilibrium be in equilibrium? • Simplest possible “real world” model • n markets • Commodities produced using input-output system • Spot markets for sale of output (“supply=demand”) • All output in year t becomes input in year t+1 • Consumption “internalised” • Economy growing over time • For equilibrium, • Outputs in year 0 must be sufficient for production in year 1 • Prices must enable producers to buy all inputs • Conditions expressed in matrix equations:

Can General Equilibrium be in equilibrium? • Outputs in year t+1 “output input” transformation of inputs in previous period t: Outputs in 2004 areinputs for 2005 Production process derived from “productive” input-output matrix Output in 2005(vector of outputs) • For stable growth, each sector must grow at the same rate (a % p.a.) 2005’s output of socks,DVD players, etc., is a%greater than 2004’s

Can General Equilibrium be in equilibrium? • Two conditions on production can be combined using matrix maths… The production relation… Has to equal growth condition… Equating them… Rearrange using matrix rules… I is matrix equivalent of 1… So this bit has to be somehow equivalent to zero for this equation to be feasible

Can General Equilibrium be in equilibrium? is equivalent to zero if • The expression its “determinant” is equal to zero; more on that soon • Price condition also expressed in matrix equation • Prices must enable producers to purchase necessary inputs • For equilibrium, relative prices must be constant (p) • Cost of inputs is p (list of prices) times A (table of outputs produced from inputs) times equilibrium rate of profit p: Table of outputsproduced frominputs List of prices Uniform profit rate

Can General Equilibrium be in equilibrium? • Rearrange using matrix rules • Order of multiplication important: • (1) Multiply both sides by inverse of A • (2) A times its inverse equals I (matrix with 1’s on diagonal & 0’s elsewhere) • (3) Move to LHS: • (4) Group on p:

Can General Equilibrium be in equilibrium? is equivalent to zero if • The expression its “determinant” is equal to zero… • Matrices have a property called “eigenvalues” • Basically, roots (zeroes) of polynomial—where it crosses x-axis • (1 root for y=a+bx, 2 for y=a+bx+cx2, etc.) • For stability, biggest root must be less than 1 • Problem: A & A-1 have inverse roots… • If ½ biggest “eigenvalue” of A, then 2 is biggest eigenvalue of A-1. • Not a problem if all eigenvalues of A < 0 • -½ and -2 both less than zero • Unfortunately…

Can General Equilibrium be in equilibrium? • Matrix A derived from table of inputs needed to produce outputs • Input-output table has all non-negative entries • Can’t use negative quantities of commodity as input • Advanced maths theorems (“Perron-Frobenius”) show that A’s biggest eigenvalue must be > 0 • So either A or A-1 (or both) must have root > 1 • If A has root of ½ then A-1 has root of 2 • Results: • Either prices or quantities must be unstable • If system diverges a fraction from stability, it will never return… • “General Equilibrium” will never be in equilibrium…

Can General Equilibrium be in equilibrium? • Intuition: • Walras hoped “direct effects” of price changes • Banana supply exceeds demand  banana price falls  closer to equilibrium • would outweigh “indirect effects” • Banana price fall  fall in income for banana producers  fall in demand for biscuits  feedback on banana industry… • Maths shows not the case: plausible model of growing production economy unstable; feedback effects outweigh direct

Can General Equilibrium be in equilibrium? • Neoclassical reactions? • (1) “It’s just an artefact of matrices” • (2) “Let’s find ways to make it stable!” • (3) “Let’s ignore stability” • (1) “It’s just an artefact of matrices” • Input-output table strictly linear: has rigid proportions between inputs (commodities) & outputs • Neoclassical production functions nonlinear: variable proportions, input substitution (labor for capital…) • Therefore neoclassical model will be stable while IO/matrix/Leontief systems will not… Wrong!

“It’s just an artefact of matrices” • Matrix is linear • like b in y(x)=a+bx only with many variables • Neoclassical production functions are nonlinear • like y(x)=a+bx+cx2+dx3+… • But • Any nonlinear function can be approximated by polynomial • E.g., sin(x): • “Linear bit” of sin(x) is x • Best guess for sin(x) near x=0 is x • “Linear bit” of production function is IO matrix • Stability near equilibrium determined by linear bit only

“It’s just an artefact of matrices” • Linear part “rules the roost” the closer you get to equilibrium • Linear bit of any nonlinear production function is IO matrix • Its stability determines system stability near equilibrium: nonlinear bits irrelevant

“It’s just an artefact of matrices” • Nonlinear “production function” might stop prices/quantities becoming crazy • Negative prices or quantities… • But won’t make equilibrium stable • Multiple “supply & demand” markets can’t all be in equilibrium • unless started out there and never disturbed… • which takes us to (2) “Let’s find ways to make it stable!” • First neoclassical to realise instability problem was Jorgenson (1960)…

(2) “Let’s find ways to make it stable!” • “If the output system is relatively stable, the price system cannot be, and vice versa… ” (Jorgenson 1960: 895) • “The conclusion is that excess capacity (or positive profit levels or both) is necessary … for the interpretation of the dynamic input-output system … as a model of an actual economy…” (Jorgenson 1960: 893) • So far so good; but then in 1961… • “To avoid dual instability, a number of re-interpretations of the basic model have been proposed… In this paper, a third re-interpretation … is suggested…” (Jorgenson 1961: 106)

(2) “Let’s find ways to make it stable!” • “First, the behavior of the system depends not only on the technological characteristics of the system, but also on the behavior of economic decision-makers in each of the sectors of the economy. Secondly, the complete system surmounts the difficulties associated with dual instability; by suitable restrictions on the initial values of the disequilibrium variables, the non-negativity of all economic variables is preserved…” • Introduced stocks & Reserve Bank interest rate to try to stabilise model; • Got maths wrong! (See Blatt 1983: 134, Jorgenson 1961: 112, 115) System still unstable… • Other equally flawed attempts (turnpike theorems etc.); so…

(3) “Let’s ignore stability” • Dominant model of general equilibrium “Arrow-Debreu” • “Model” designed to remove dynamics entirely • “For any economic agent a complete action plan (made now for the whole future)…” • No time process: • “Market” occurs once only in history of planet • All transactions for all time take place at once • Uncertainty re “future” abolished: • “A contract for the transfer of a commodity now specifies, … an event on the occurrence of which the transfer is conditional. This new definition of a commodity allows one to obtain a theory of uncertainty … formally identical with the theory of certainty developed in the preceding chapters.”

It’s equilibrium, but is it economics? • “For Walras, general equilibrium theory was an abstract but nevertheless realistic description of the functioning of a capitalist economy. He was therefore more concerned to show that markets will clear automatically via price adjustments … than to prove that a unique set of prices and quantities is capable of clearing all markets simultaneously. By the time we got to Arrow and Debreu, however, general equilibrium theory had ceased to make any descriptive claim about actual economic systems… It had become a perfect example of what Ronald Coase has called “blackboard economics”, a model that can be written down on blackboards using economic terms like “prices”, “quantities”, “factors of production”, and so on, but that nevertheless is clearly and even scandalously unrepresentative of any recognizable economic system.” (Blaug 1998)

Is equilibrium economics? • Obvious conclusions from general equilibrium failures: • If model can’t be in equilibrium, then • economy itself certainly can’t be • economics should model “out of equilibrium” behaviour • equilibrium analysis can’t be economics • Economics can only develop using dynamics • “Out of equilibrium” modeling commonplace in true sciences • Example from meteorology: Lorenz model of “2-dimensional” weather system (foundation of modern weather prediction)

Non-equilibrium modeling • Non-equilibrium models use • Differential rather than simultaneous equations • “Rate of change of x a function of x” • Computer simulations rather than drawings… • Lorenz’s weather model simplified version of empirically derived fluid flow equations: x displacement y displacement temperature gradient • Thinking like a (neoclassical) economist, let’s work out equilibrium…

Lorenz’s weather model • First step, set all rates of change to zero: y=x part of equilibrium (also x=y=0)… b-z=1 part of equilibrium (& z=0 if y=0) x2=c.z part of equilibrium… • Oh Oh… there are 3 equilibria!: & the other root of x2: Nope! • Surely 1 is stable & the other 2 aren’t?

Lorenz’s weather model • All 3 equilibria are unstable! • If system starts at (1), (2) or (3), it stays there; • But if disturbed even a fraction, it flies away • So the system must break down? Nope! • Wild dynamic behaviour • But never “nonsense” values for x,y, z: • The tiniest push and “equilibrium” is out the window… • But the system cycles rather than breaking down

Lorenz’s weather model • And behind the apparent “chaos” • A complex pattern of feedbacks between x, y & z • Inspiration for modern science of complexity

Meanwhile, back in the economy • Economy just as cyclical as the weather… • Need models of cyclical behaviour, not “equilibrium” • Plenty exist, but not developed by neoclassicals • Neoclassicals almost afraid to think in cyclical terms… Can’t think outside equilibrium “square” • Instead Post-Keynesians (Kaldor, Goodwin), some Marxists (Foley, Levy…), evolutionary economists (Schumpeter), chaos/complexity theorists (Goodwin, Chiarella) econophysicists (Ponzi)… • An example: Goodwin’s 1967 cyclical growth model • Based on Marx’s verbal model in Capital I:

The Cyclical economy • “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, because the stimulus of gain is blunted. 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 mechanism of the process of capitalist production removes the very obstacles that it temporarily creates. 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: Chapter 25 Section 1)

The Cyclical economy • Marx’s model • High wages  low investment  low growth  rising unemployment  falling wage demands  increased profit share  rising investment  high growth  high employment  High wages: cycle continues • Goodwin’s mathematical rendition • % Change employment rate =growth rate minus productivity & population growth • % change workers’ income share = Real wage growth minus productivity

The Cyclical economy • Neoclassical equilibrium hangup a hindrance on real progress in economics… • Cyclical nature of economy can be modelled • & advanced computer tools exist to do it! Not to mention advanced thinkers...

Political Economy… Old and New… • “Political Economy” traditionally included • Post Keynesians • Believe Keynes misinterpreted by Samuelson, Hicks et al. in “Keynesian-neoclassical synthesis” • Reject IS-LM, AS-AD interpretations • Marxists • Continue “Classical” tradition • Most still believe “labour theory of value”, some don’t • New entrants • Ecological & feminist economists • Focus on issues ignored by neoclassicals (& to some extent other schools) • “Econophysicists”…

Econophysicists • Physicists applying tools from physics to analyse economy • Reject neoclassical economics as based on false analogy to outdated 19th century physics • E.g. “Anyone who has taken both physics & economics classes knows that these subjects are completely different in nature, notwithstanding the economists’ failed attempt to make economics look like an exercise in calculus…” (McCauley 2004: 3) • See economics as necessarily non-equilibrium • “There is no empirical evidence for stable equilibrium, for a stabilizing hand to provide self-regulation in unregulated markets.” (McCauley 2004: 4)

Econophysicists (& mathematicians…) • Emphasise reality & empiricism over theory: • “Our emphasis is on understanding how markets really behave, not how they hypothetically ‘should’ behave as predicted by completely unrealistic models.” (McCauley 2004: xi) • Reject neoclassical economics: • “An aim of this book is to make it clear to the reader that neo-classical theory, beloved of pure mathematicians, is a bad place to start in order to make new models of economic behavior. This includes the neoclassical idea of Nash equilbria in game theory.” (McCauley 2004: 6)

And the last word… • Goes to Australian econophysics pioneer John Blatt: • “The competitive system must not be treated as if it should be in, or near, the balanced growth state (or, even less realistically, a state of static equilibrium). The system, instead, has a natural tendency to depart from this state and undergo oscillations… This conclusion, arrived at theoretically, is confirmed by some two centuries of empirical observation. It is about time we recognize the obvious facts about the system in which we live.” (Blatt 1983: 148)

Welcome to Political economy! • Here ends the demolition job on neoclassicism… • Next week, Neil Hart on Post Keynesian economics • Ideas in my lectures further developed in • History of Economic Thought (if you haven’t already done it); • Financial Economics; • Honours courses in Nonlinear Finance, Advanced Political Economy; • Possibly next year Managerial Economics

References • Blatt, J.M., 1983. Dynamic Economic Systems, ME Sharpe, Armonk. • Blaug, M., 1998. 'Disturbing currents in modern economics', Challenge!, 41(3): 11-34. • Debreu, G., 1959. Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Yale University Press, New Haven. • Hurwicz,L.,1986. “On the stability of the tatonnement approach to competitive equilibrium”, in Sonnenshein, H.F.(Ed.), Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin. • Jorgenson , D.W., 1960. “A dual stability theorem”, Econometrica 28(4), pp. 892-899. • Jorgenson, D.W., 1961. 'Stability of a dynamic input-output system', Review of Economic Studies, 28: 105-116. • Jorgenson, D.W., 1963. 'Stability of a dynamic input-output system: a reply', Review of Economic Studies, 30: 148-149. • McCauley, J.L., 2004. Dynamics of Markets: econophysics & finance, Cambridge University Press, Cambridge. • McManus, M., 1963. 'Notes on Jorgenson’s model', Review of Economic Studies, 30: 141-147. • Walras, L., 1874, 1900 [1954]. Elements of Pure economics, George Allen & Unwin, London.

Political Economy: Critique of Neoclassical Economics