Why economics must abandon

1
Why economics must abandon

• its theory of the firm

2
Not a new call

• Clapham 1922, Sraffa 1926, 1930
• I am trying to find what are the assumptions
  implicit in Marshall's theory if Mr Robertson
  regards them as extremely unreal, I sympathise
  with him. We seem to be agreed that the theory
  cannot be interpreted in a way which makes it
  logically self-consistent and, at the same time,
  reconciles it with the facts it sets out to
  explain. Mr Robertson's remedy is to discard
  mathematics, and he suggests that my remedy is to
  discard the facts perhaps I ought to have
  explained that, in the circumstances, I think it
  is Marshall's theory that should be discarded.
  (Sraffa 1930 93)

3
Sraffas argument

• Two key assumptions of short run theory of the
  firm
• Independent supply and demand curves
• Diminishing marginal productivity
• in practice are mutually inconsistent
• Independent supply and demand curves realistic
  when define industry narrowly (e.g., wheat)
• but then increased production will result from
  industry drawing marginal doses of allegedly
  fixed resource from other industries, inputs
  lying fallow
• Constant returns, constant costs

4
Sraffas argument

• If we next take an industry which employs only a
  small part of the 'constant factor' (which
  appears more appropriate for the study of the
  particular equilibrium of a single industry), we
  find that a (small) increase in its production is
  generally met much more by drawing 'marginal
  doses' of the constant factor from other
  industries than by intensifying its own
  utilisation of it thus the increase in cost will
  be practically negligible (Sraffa 1926)

5
Sraffas argument

• Diminishing marginal productivity realistic when
  industry defined widely (e.g., Agriculture)
• Input of fixed resource can be increased only
  with difficulty
• But then change in output of this industry will
  affect income distribution
• change in income distribution will affect demand
• impossible to ignore feedback effects between
  supply and demand

6
Sraffas argument

• If in the production of a particular commodity a
  considerable part of a factor is employed, the
  total amount of which is fixed or can be
  increased only at a more than proportional cost,
  a small increase in the production of the
  commodity will necessitate a more intense
  utilisation of that factor, and this will affect
  in the same manner the cost of the commodity in
  question and the cost of the other commodities
  into the production of which that factor enters
  and since commodities into the production of
  which a common special factor enters are
  frequently, to a certain extent, substitutes for
  one another ... the modification in their price
  will not be without appreciable effects upon
  demand in the industry concerned. (Sraffa 1926)

7
Sraffas argument

• Implication of Sraffas argument constant
  marginal costs in the short run
• In normal cases the cost of production of
  commodities produced competitively ... must be
  regarded as constant in respect of small
  variation in the quantity produced. And so, as a
  simple way of approaching the problem of
  competitive value, the old and now obsolete
  theory which makes it dependent on the cost of
  production alone appears to hold its ground as
  the best available. (Sraffa 1926)
• Sraffas argument largely ignored by profession
• replies focused on his critique of concept of
  diminishing returns in long run rather than short
  run

8
Sraffas argument

• Subsequent papers (Pigou 1922, 1927, 1928
  Robertson 1924, 1930 Robbins 1932, Harrod 1934
  etc.) accept that
• diminishing marginal productivity in the short
  run as unarguable
• theory of perfect competition watertight
• Ditto any introductory to advanced micro text
  today
• Even advanced non-PC theory implicitly treats PC
  as ideal
• Why? The apparently conclusive mathematics
• It is not conclusive
• Recap argument, firstly w.r.t. perfect
  competition

9
Conventional explanation of PMC

• Unique attributes of PC industry are
• Supply curve exists (sum of MC curves)
• Price set by supply and demand
• MRP for individual firm

Sm point of supply for this D curve
Sum MarginalCost PCSupply Curve PC
Price
MarginalCost Monopoly(not Supply Curve)
Pm
Ppc
D
Marginal Revenue
Qm
Qpc

• Monopoly/Monopolistic competition
• No supply curve
• PgtMC,MR for individual firm and market

Quantity

• How are unique attributes of PC established?

10
Conventional explanation of PMC

• Start with market supply and demand curves

• Determine equilibrium quantity and price by
  intersection of two curves

Price
Supply
Pe

• Assume this is the price taken as given by PC
  firms

Demand
Quantity
Qe

• Show that the MC curve of the PC firm is its
  supply curve, assuming demand horizontal

Price
Marginal Cost
Pe

• Aggregate firm supply curves to determine market
  supply curve

qe
quantity
11
Conventional explanation of PMC

• But potentially circular logic here

Start with market supply curve
Each step depends on the other
Derive individual firm supply curve

• Argument that PC firms profit maximise by setting
  PMC should be provable at level of individual
  firm alone.
• If theory correct, should be provable that any
  change in output from qe reduces profit

Over to Mathematica
Skip summary of results
12
So Mathematica tell us

• Given linear demand and supply (for simplicity
  w.l.o.g.)

• And standard definitions of Total Revenue,
  Profit, alleged profit maximising levels of
  output

• Test alleged monopoly equilibrium

• Enigmatic concise confirmation

• Perfect competition equilibrium

• Is true if and only if

13
So Mathematica tell us

• Consider impact of perturbation of dq from
  monopoly profit maximisation point on profit

• Profit changes by clearly negative amount,
  whatever sign of dq

• Consider impact of perturbation of dq from
  perfect competition profit maximisation point on
  profit

• Profit changes by

14
Conventional explanation of PMC

• Theory intact if and only if dP/dq0
• but given assumption of atomism, dP/dqdP/dQ

• Therefore

• And
• Profit falls if output rises past where PMC
• Profit rises if output falls below where PMC
• PMC is not a (profit maximising) equilibrium

15
Logical errors in conventional theory

• Neoclassical micro assumes no feedback from
  individual firm to market price
• But feedback necessary if market demand curve
  downward sloping
• Feedback affects all firms
• aggregate effect sums to same behaviour as single
  firm given valid identical cost curves
• why should large number of rational agents reach
  different conclusion to single rational agent,
  given same data?
• Consider the Friedman argument

16
Profit maximising firms?

• Excellent predictions would be yielded by the
  hypothesis that the billiard player made his
  shots as if he knew the complicated mathematical
  formulas , could make lightning calculations
  from the formulas, and could then make the balls
  travel in the direction indicated by the
  formulas. Our confidence in this hypothesis is
  not based on the belief that billiard players,
  even expert ones, can or do go through the
  process described it derives rather from the
  belief that, unless in some way or other they
  were capable of reaching essentially the same
  result, they would not in fact be expert billiard
  players. (Friedman The methodology of positive
  economics)

Miltons Pool Hall
Skip summary of results
17
Miltons Pool Hall

• Simulation of an industry with
• Fixed linear demand curve
• Constant marginal cost (see later for rising MC)
• Given number of firms
• Each firm starts with randomly determined output
  level
• Each firm varies own output by randomly
  determined amount (ive or -ive)
• If new level of profit higher, keeps changing
  output in same direction
• Otherwise, changes in opposite direction

18
Miltons Pool Hall

• Model 1 simple mechanism
• Firm always changes output by same amount
• Model 2 (slightly more) sophisticated mechanism
• Firm tries randomly determined amount, with range
  of random variable falling each iteration
• In both cases, output and price converge to
  monopoly level (MCMR), not perfect
  competition level (PMC), regardless of number
  of firms

• Market definitions monopoly price 80, PC
  price 50

19
Miltons Pool Hall the program

• Random initial amounts

No. of firms
Calculate profits
Random adjustments
Calculate new profits
Work out direction of change
For 50 iterations
Make directed random adjustments of diminishing
size
20
Miltons Pool Hall the outcome
Market converges to monopoly price regardless of
number of firms
21
Simulation Results

• With constant marginal cost
• Number of firms makes no difference
• output converges to monopoly level, not perfect
  competition
• With rising marginal cost?

• Market definitions monopoly price 90, PC
  price 80

22
Miltons Pool Hall the outcome (2)

• Price appears to converge to PC level for gt 1 firm

• But
• Are cost functions the same?

23
Miltons Pool Hall the outcome (2)

• Apparent difference in behaviour illusory
• Difference in output level price due to
  difference in cost functions

• An aggregation problem

24
Supply aggregation

• Number of firms does make a difference, but
• cause is difference in total cost functions, not
  MRMC for monopoly, PMC for PC
• Supply aggregation (so that MC for monopoly
  identical to sum of MC for PC) only possible with
  horizontal marginal cost

25
Supply aggregation

• Monopoly/PC welfare comparison requires identical
  MC curves, otherwise

Price
Ppc
Pm
Demand/Price
Marginal Revenue
Qpc
Qm
Quantity
26
Supply aggregation

• WLOG, consider n PC firms employing x workers
• MC derived from MP
• identity of MC requires identity of MP
• TP can only differ by a constant
• constant zero if variable factor is labour
• So we have

• n competitive firms
• f PC production function
• g monopoly production function

Euler's equation
27
Supply aggregation

• Differentiate w.r.t. n

Consider ratio
Substitute
28
Supply aggregation

• Integrate w.r.t. u

• Take exponentials

• So g a staight line
• Consider f

• f same straight line

• Differentiate marginal product a constant,
  therefore marginal cost a constant

29
Supply aggregation

• Only supply curve for which sum of marginal cost
  curves of small firms identical to marginal cost
  curve of single firm is constant identical
  marginal cost
• Static profit maximisation (with identical MC
  curves) occurs where PgtMC, MCMR for both
  monopoly and competitive industries
• Neoclassical theory of the firm thus
• logically flawed
• devoid of content
• Contradictions self-evident once you know to look

30
There for all to see

• Conventional welfare comparison of monopoly to PC
  has monopoly producing to maximum profit, but PC
  producing past that point in the aggregate
• PC output past point where market MC market MR
  must be produced at a loss, yet no loss shown at
  firm level

?
?
31
There for all to see

• Producer surplus shows the fallacy
• Collective gain in producer surplus from reducing
  output from PMCgtMR to PgtMRMC obvious

P
S
Loss
PgtMC
Gain
PMC
D
Qe
Qe-DQ
Q
P
Loss
P where MRgtMC
MC
Gain
P where MRMC

• Producer surplus maximised at MRMC level

• PMC only possible with individually and
  collectively irrational behaviour

D
MR
Qe
Qe-DQ
Q
32
Root of the fallacy

• Models of PC and monopoly identical at firm level
• Sole difference is presence of market marginal
  revenue curve in monopoly, absence in PC

Perfect competition
P
S
P gt MRMC
PMC
D
MR

• But market MR curve exists independent of number
  of firms in industry

Qe
Qe
P
Monopoly
MC

• Only way to get MRP at firm level is for it to
  apply at industry level (horizontal market demand
  curve)

P gt MRMC
D

• PC theory based on equating infinitesimals to zero

MR
Qe
33
Theoretical consequences

• Supply and demand analysis not viable
• supply curve cant be constructed
• can only show point of supply for given
  (aggregate) MC and given demand
• increase in demand could lower market price

Monopoly, etc.
Perfect Competition

• Minimum of 3 curves needed to determine
  price/quantity

MarginalCost
marginalcost
S1
s2
s1
S2
d2
d1
supplycurve
D2
D1
MR2
MR1
34
Theoretical consequences

• Welfare ideals unachievable
• equality of marginal benefits to marginal costs
  impossible even under perfect competition
• all market structures will have marginal benefits
  gt marginal costs in profit maximising equilibrium
• market outcomes will not maximise social benefits
• How to interpret price-taking behaviour?
• Firms may take market price as given, but
• price does not equate price and marginal cost
• instead reflects markup in that industry
• For viable firms, price will exceed marginal cost

• LongConclusion

• ShortConclusion

• But at least MCMR rule maximises profit, right?
• Wrong

35
Dynamics of profit maximisation

• Profit maximisation rule invalid in dynamic
  setting
• MCMR rule tells how to maximise profit w.r.t.
  quantity
• Real firms more interested in maximising profits
  w.r.t. time
• Time-based rule requires MR gt MC.
• Time-based analysis shows that profit
  maximisation rules too complex to be a guide to
  determining output, even if diminishing marginal
  returns applies

36
Profit maximising firms?

• Neoclassical logic
• Profit a function of quantity

• Price decreasing and cost increasing functions of
  quantity

• Maximise profit by setting marginal revenue equal
  to marginal cost

• Mathematical logic
• Profit at least a function of quantity and time
• quantity also a function of time

• Dynamic goal maximisation of rate of growth of
  profit

37
Profit maximising firms?

• Rate of growth of profit is

• This is MR-MC

• Substituting

• Under what circumstances will setting MRMC
  maximise the rate of growth of profit?

• Is this condition relevant to a dynamic economy?
• No, it is the definition of a static one

No way!

• Are the values of MR and MC relevant to the
  conditions for maximising the rate of growth of
  the rate of profit?

38
Dynamics of profit maximisation

• Assuming, for the sake of argument, that the rate
  of growth of profit has a single maximum, set its
  differential to zero

• Assuming, for the sake of argument, that the rate
  of growth of the rate of profit is monotonic, the
  rate of change of the rate of growth of profit is
  zero where (courtesy of Mathematica)

39
Profit maximising firms?

• No mathematician in her right mind would advise a
  firm to manage this function!
• Pulling MC and MR out of this, we derive

40
Dynamics of profit maximisation

• For profit maximisation

Mathematica

• Useful rule?
• Of course not too complex, and firm cant know
  dq/dt anyway but regardless, neoclassical rule
• invalid if dq/dtgt0
• would cause lower rate of growth of profits if
  followed in practice.
• Supports Sraffas 1926 argument MC MR
  irrelevant to firms output decisions

41
Dynamics of profit maximisation

• Founders of neoclassical analysis realised that
  concepts of statics and short run inadequate
  proper analysis should be dynamic.
• Only reason to imagine a static economy was to
  make analysis tractable
• Marshall ...dynamics includes statics... But
  the statical solution is simpler... it may
  afford useful preparation and training for the
  more difficult dynamical solution and it may be
  the first step towards a provisional and partial
  solution in problems so complex that a complete
  dynamical solution is beyond our attainment.
  (1907, in Groenewegen 1996 432)

42
Dynamics of profit maximisation

• Jevons If we wished to have a complete solution
  ... we should have to treat it as a problem of
  dynamics. But it would surely be absurd to
  attempt the more difficult question when the more
  easy one is yet so imperfectly within our power.
  (1871 1911 93)
• J.B. Clark on the future of economics A point
  on which opinions differ is the capacity of the
  pure theory of Political Economy for progress.
  There seems to be growing impression that, as a
  mere statement of principles, this science will
  fairly soon be complete It is with this view
  that I take issue. The great coming development
  of economic theory is to take place, I venture to
  assert, through the statement and solution of
  dynamic problems (Clark 1898)

43
Dynamics of profit maximisation

• Statics has clearly led to misleading and
  irrelevant advice re profit maximisation
• Dynamic answer different to static one
• This is a common result in mathematics
• Static and dynamic results only coincide when
  relevant system is stable
• Stable in this context means a no-growth
  economy
• Unstable means growing economy, and MCMR
  irrelevant
• So if economists cant provide guidance for firms
  from a priori theory of cost and revenue
  functions, what can it do?

44
What can economics do?

• Become an empirical discipline ask firms what
  they actually do
• Dominant tendency in economics is a priori
  analysis work out what must be from prior
  axioms
• A pre-Galilean approach to science
• Why not experiment/survey?
• Numerous researchers have done so, and found that
  MC/MR analysis irrelevant to real firms
• Andrews, Bishop, Downie, Eiteman, Eiteman and
  Guthrie, Haines, Hall Hitch, Lee, Means,
  Tucker, the Oxford Economic Research Group,
  (see Lee 1998 for full details), Blinder et al
  1998

45
Actual firms behaviour

• Empirical researchers found
• average costs of production declined as output
  rose
• marginal costs were always well below their
  average costs, and substantially smaller than
  marginal revenue, and
• concept of a demand curve (and therefore its
  derivative marginal revenue) was simply
  irrelevant.

46
Actual firms behaviour

• Eiteman Guthrie (1952) showed factory managers
  graphs indicating possible different cost curve
  relations
• Outcome was

• Businessmen viewed the economists concepts of
  perfect competition and monopoly as virtual
  nonsense and the product of the itching
  imaginations of uninformed and inexperienced
  armchair theorizers. (Lee 1998, citing Tucker)

47
Actual firms behaviour

• Major reason why economic a priori did not apply?
• Engineers designed factories so as to cause the
  variable factor to be used most efficiently when
  the plant is operated close to capacity. Under
  such conditions an average variable cost curve
  declines steadily until the point of capacity
  output is reached. A marginal cost curve derived
  from such an average cost curve lies below the
  average cost curve at all scales of operation
  short of capacity, a fact that makes it
  physically impossible for an enterprise to
  determine a scale of operations by equating
  marginal cost and marginal revenues. (Eiteman
  1947)
• As Sraffa put it

48
Actual firms behaviour

• Business men, who regard themselves as being
  subject to competitive conditions, would consider
  absurd the assertion that the limit to their
  production is to be found in the internal
  conditions of production in their firm, which do
  not permit of the production of a greater
  quantity without an increase in cost. The chief
  obstacle against which they have to contend when
  they want gradually to increase their production
  does not lie in the cost of production-which,
  indeed, generally favours them in that
  direction-but in the difficulty of selling the
  larger quantity of goods without reducing the
  price, or without having to face increased
  marketing expenses. (Sraffa 1926)
• See also Kalecki 1937 Principle of increasing
  risk

49
Profit maximising firms?

• Most recent survey work by Blinder et al 1998
• Over 89 per cent of respondents indicated that
  marginal costs either declined or stayed
  constant with changes in output (sometimes
  involving discrete jumps). Finally, only four of
  200 enterprises had both elastic demand curves
  and increasing marginal costs. (Downward Lee
  2001, reviewing Blinder)
• Fixed costs appear to be more important in the
  real world than in economic theory. (Blinder)
• Economists no longer have an excuse to ignore
  this research

50
Conclusion

• Neoclassical economics has at its core a theory
  of firm behaviour which is
• mathematically erroneous
• misleading guide to profit maximisation in a
  dynamic economy
• contradicted by empirical research
• Economics needs a theory of firm behaviour which
  is
• Empirically grounded
• Dynamic, and cognisant of uncertainty
• Best existing alternative is Post-Keynesian
  theory of the firm (Lee 1998)
• much more remains to be done
• but to start, we must abandon erroneous beliefs

51
Conclusion

• As Samuelson said in summarising the Capital
  Controversies of the 1960s
• If all this causes headaches for those nostalgic
  for the old time parables of neoclassical
  writing, we must remind ourselves that scholars
  are not born to live an easy existence. We must
  respect, and appraise, the facts of life.
  (Samuelson 1966)

52
Acknowledgements

• Geoff Fishburn
• conjectural variation argument
• John Legge
• perturbation analysis proof of non-profit-maximisi
  ng conjecture
• producer surplus analysis

53
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