Lecture Five

1. Lecture Five Neoclassicism Critiques of Neoclassicism The Rise of Keynes

2. Recap • Neoclassical theory as developed by Jevons, Walras, Marshall effectively the same as taught in Microeconomics • 2 strands • Analysis of individual consumers & producers, integrated into analysis of individual markets (“Marshallian” partial equilibrium) • Analysis of overall coordination of multiple markets (“Walrasian” general equilibrium) • Many components common to both—e.g., analysis of individual consumer, individual firm, aggregation of individual demands into market demand, individual firm supplies into market supply

3. Z X Biscuits B D Y W C A Bananas The First Zenith of Neoclassicism: Demand • Individual demand based on • utility maximisation • subject to budget constraint:

4. Demand • Individual demand curve derived by varying price ratio Z “Compensated” demand curves (discussed in Micro II?) needed to guarantee downward sloping individual demand curve X Biscuits B Y q1 q2 q3 W III II I Bananas Price Market demand derived by adding up individual demand curves (but see later!) p1 p2 p3 q3 q2 q1 Bananas

5. Labor cost B Wheat Output C A Wheat Output B A C Labor Input The First Zenith of Neoclassicism: Supply • Individual firm supply curve derived from • production function combining • (at least) one fixed input with (at least) one variable input • result: diminishing marginal productivity • productivity may rise as initial variable inputs added • but eventually diminishing productivity sets in Diminishing marginal productivity sole basis for rising marginal cost (variable input cost assumed constant) Flip axes & multiply by wage rate:

6. Supply • Firm maximises profit by maximising distance between total revenue (straight line function for PC firm) and total cost: Total Cost B Maximum Profit Total Cost & Revenue C Marginal Cost A Fixed Costs Total Revenue Wheat Output Q Hence equating marginal revenue to marginal cost maximises profits:

7. B Maximum Profit Total Cost & Revenue C Marginal Cost A Revenue Fixed Costs Q Wheat Output Average Cost Average Cost & Revenue Marginal Cost Marginal Revenue Maximum Profit Wheat Output Supply • Relationship between • total cost and marginal cost, • total revenue & marginal revenue Height of this line Equals area of this box Supply curve for individual firm equals marginal cost curve:

8. Supply • Marginal cost curve is not supply curve for monopoly because of downward sloping marginal revenue curve: PerfectCompetition Monopoly MarginalCost MarginalCost Price Price S1 S1 S2 S2 D2 D1 D2 Supply Curve D1 MR2 MR1 Quantity Quantity Diminishing marginal productivity and horizontal marginal revenue curve therefore crucial to model of perfect competition

9. Price/ bushel Supply Equilibrium Price Demand Equilibrium Quantity Wheat First Zenith of Neoclassicism: Supply & Demand • Diminishing marginal productivity generates rising marginal cost • Horizontal marginal revenue ensures that marginal cost curve is the individual firm supply curve • Sum of all firm marginal cost curves is market supply curve • Price set by intersection of downward sloping market demand curve and upward sloping market supply curve: Analysis of single market integrated into analysis of all markets: General Equilibrium

10. General Equilibrium • Walras (1870s) showed that general equilibrium feasible • Number of equations equals number of unknowns • Income and Expenditure equations consistent (see last year’s notes, & slides at end of this lecture) • However he assumed process: • I.e., given that general equilibrium can exist, how do we get there? • Must be able to go from initial disequilibrium prices to prices which result in equilibrium in all markets • Walras’ model proposed hypothetical way this could occur: “tatonnement”

11. General Equilibrium • Tatonnement • “Auctioneer” declares prices • Buy & Sell bids recorded • If Buy>Sell quantity for any stock, price adjusted up • If Buy<Sell quantity, price adjusted down • No trades allowed until all markets in equilibrium • “Tatonnement”--groping for equilibrium vector of prices • Applied to model of exchange of given quantities of commodities (distribution taken as given) • Extended to model of production from given resources

12. Problems I: Does “tatonnement” work? • Walras’ fiction of auctioneer and tatonnement • auctioneer suggests initial prices, adjusts prices according to algorithm, & forbids trades until all markets in equilibrium • needed to outlaw “out of equilibrium” exchanges • if disequilibrium trades allowed, income effects distort market outcome (those selling at above equilibrium prices have windfall gain, others windfall loss) • clearly a fiction: disequilibrium trades occur in real world. • But does the fiction itself work?: can Walras’ market “grope” its way to equilibrium price vector from random initial prices? • Walras believed so:

13. Groping towards general equilibrium? • “Once the prices … have been cried at random in terms of one of them selected as numeraire, 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…. [T]he 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)

14. Groping towards general equilibrium? • Initial stab at prices won’t clear all markets • Walras assumes process of adjustment will eventually get there • but direct effect of reducing price of one commodity where supply exceeds demand could destabilise other markets (indirect effect) • Walras assumed that direct effects would outweigh indirect effects: • If demand for B < supply of B, reduce price of B • change directly reduces oversupply of B • indirectly alters demand for all other commodities • increases demand for some, decreases demand for others • Walras assumed some cancellation, so direct effect > indirect effect, process gradually converged:

15. Groping towards general equilibrium? • “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]: 171-172)

16. P Wheat P P Beds Q Cars P Holidays Q Q Q P Cameras P Fridges Q Q Groping towards general equilibrium?  P Reducing wheat price directly pushes wheat market towards equilibrium: Wheat Q But what does it do to all other markets? ? ? ? ? ?

17. Groping towards general equilibrium? • Mathematics of proof of this beyond Walras • In 20th century, mathematical economists (see references at end) established: • Two stability conditions on input-output matrix • For stable growth, matrix must have key value (“eigenvalue”) less than one • For stable prices, inverse of matrix must have key value less than one • Both conditions can’t be fulfilled (there is no number bigger and smaller than one), so “groping” won’t work • In Walras’ terms, indirect effects outweigh direct effects • Groping will never locate equilibrium vector • If no trade till equilibrium found, trade will never occur

18. P Wheat  P Wheat Q P P Beds Q Cars   Q Q P P Cameras P Holidays  Fridges   Q Q Q Groping away from general equilibrium! Reducing wheat price directly pushes wheat market towards equilibrium: But indirect effect on all other markets outweighs direct effect on wheat

19. Groping towards disequilibrium? • “Tatonnement” thus ineffective device to avoid out of equilibrium trades • Price model therefore cannot avoid disequilibrium analysis • Intersection of supply and demand curves for all markets at once cannot be found by market processes • even if “no trades occur until equilibrium”, because equilibrium won’t be attained • If system diverges from equilibrium, it will never return there • if trades occur out of equilibrium, won’t converge because trades will alter equilibrium • simple techniques for one market (“ceteris paribus”) don’t generalise to all markets • So why do economists still use equilibrium models of prices?

20. Groping towards disequilibrium? • Most don’t know literature (see references at end of lecture) • Some who do know it believe result doesn’t apply to model with flexible production functions • They are wrong, it does • Those who do, and know it applies in general, have given up on modelling process of reaching equilibrium • process of reaching equilibrium ignored in favour of simply showing existence of equilibrium • time (and therefore process of achieving equilibrium) completely abstracted from: • Gerard Debreu’s Nobel Prize-winning Theory of Value (see OREF III)

21. Modern “Arrow-Debreu” General Equilibrium • “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 quantitities 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.”

22. More problems with neoclassical economics • “Partial equilibrium” building blocks of general equilibrium have also come in for criticism • Derivation of downward sloping market demand curve invalid • Logical basis of upward sloping supply curve unsound • Demand “critique” discovered by neoclassical economists (Gorman, Sonnenshein, Mantel, Debreu) • Supply critique made by Piero Sraffa (and others)

23. Smooth individual & “jagged” market demand • Remember “Engels curves”? • Show how consumption on different commodities change as income rises • Four possibilities • Luxury: consumption rises proportionately as income rises • Necessities: consumption falls proportionately as income rises • “Giffen”: consumption falls absolutely as income rises • Neutral: consumption proportion remains constant

24. Feasible Engels curves • All goods likely to fit 1st 3 cases: few if any likely to fit 4th a. Necessity b. Inferior All other goods Bananas Bananas c. Luxury d. Neutral Bananas Bananas

25. a. Banana hater b. Banana lover Bananas Engels curves for different individuals • Engels curves will differ between individuals because indifference curves differ between individuals • Engels curves could only be identical if people were all clones of each other All other goods Bananas Sounds obvious?…

26. Z X Biscuits B Y q1 q2 q3 W III II I Bananas Price of Bananas p1 p2 p3 Bananas q3 q2 q1 The “Sonnenshein-Mantel-Debreu conditions” • Downward-sloping individual demand curve derived from individual indifference curves which are by definition smooth • Can market demand curves be similarly derived? • If and only if: • All Engels curves are straight lines • Slope of indifference curves the same for all individuals along Engels “curves”

27. The “Sonnenshein-Mantel-Debreu conditions” • Indifference curves represent lines of constant “subjective utility” • like contour lines on map, different indifference curves represent different levels of utility • Two different individuals will get vastly different levels of utility from same combination of goods • Effect is like adding two different smooth hills together: • composite “hill” has abrupt jumps where two sets of contours intersect; resulting “social indifference curve” has kinks, intersections • “Community indifference and utility possibility loci are among the most useful concepts of welfare economics. Their great disadvantage is that they may intersect... Thus the analysis ... frequently becomes inconclusive.” (Gorman 1953)

28. The “Sonnenshein-Mantel-Debreu conditions” • Changing price at kink & intersection points has unpredictable effect on demand • Resulting market demand curve has flat bits, kinks, inversions: Biscuits Bananas • Unless changing prices doesn’t change distribution of income • no swap in total demand between banana lovers and banana haters • increasing income doesn’t alter consumption • no change in demand as incomes rise MarketDemandCurve… Price p1 p2 p3 Bananas q3 q1 q2

29. The “Sonnenshein-Mantel-Debreu conditions” • Smoothly downward sloping demand curves only possible if • All commodities are the same • hence all Engels curves are straight lines • All consumers are identical • hence changing income distribution has no effect on demand • Absurd conditions? • Not too absurd for some economists!: • “Suppose that all individual consumers’ indirect utility functions take the Gorman form... [where] ... the marginal propensity to consume good j is independent of the level of income of any consumer and also constant across consumers... This demand function can in fact be rationalized by a representative consumer…” (Varian 1984)

30. The “Sonnenshein-Mantel-Debreu conditions” • “The necessary and sufficient condition quoted above is intuitively reasonable. It says, in effect, that an extra unit of purchasing power should be spent in the same way no matter to whom it is given.” (Gorman 1953) • “Two criteria will be considered which lead to the possibility of aggregation: (1) identical preferences (hence identical demand functions), and (2) proportional incomes... These results have a number of interesting applications in the pure theory of international trade.” (Chipman 1974) • “There are several ways of ‘rehabilitating’ the Slutsky symmetry conditions... If consumers are grouped ... However, both of the above ‘grouping’ conditions come very close to simply assuming that the consumers in the aggregate have identical tastes and income.” (Diewert 1977)

31. “General”? Equilibrium • “Sonnenshein-Mantel-Debreu conditions” needed even for Debreu’s general equilibrium model • Assumptions clearly unrealistic & more restrictive than those used in partial equilibrium analysis (where Engels curves can take any shape, differ between consumers) • Normally defended on methodological grounds—discussed in a few weeks time • Explanation for upward-sloping supply curve has similar problems…

32. “Fixed factor in the short run…” • Essential foundation for upward sloping firm supply curve is diminishing marginal productivity • Essential foundation for diminishing marginal productivity is fixed factor in the short run • Sraffa (1926) challenged validity of this on 3 grounds • Broad definition and interdependence of supply and demand • Narrow definition and availability of “marginal doses” of fixed resource • Actual behaviour of businesses • 2 ways to define a factor of production or industry • Broad—e.g., “Labour”, “Agriculture” • Narrow —e.g., “Spanners”, “Barley”

33. Sraffa’s Broad critique • If broadly define factor/industry, then can regard factor as fixed since attracting additional units difficult • But increasing output of industry will affect incomes of all other industries/factors: • “[I]f 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)

34. Sraffa’s Broad critique PF (a) (c) Wheat Fertiliser PW SW MPF (b) (d) P2 D2 P1 D1 Wheat Fertiliser

35. Sraffa’s Broad critique • Sraffa 1926: • No input can feasibly regarded as fixed • If define industry broadly (e.g., agriculture), increased usage of fixed resource (land) will increase price of land and change income distribution • not all land used by agriculture (e.g., fallow, housing) • increased demand for agriculture partly met by switching resources from fallow/housing • prices of land, fertiliser will rise • Supply and demand curves therefore not independent • If not independent, can have indeterminate outcome • No unique “equilibrium” price because demand and supply interdependent:

36. Dq2 Dq3 Price/bushel Supply Dq1 ? ? ? Demand Price? (a) Agriculture q3 q2 q1 Wheat Quantity? MPF (b) F Sraffa’s Broad critique Income effects with Broad Definition of Industry Different “demand curve” for every point on supply curve since change in supply changes incomes PL PF PF, PL (c)

37. Sraffa’s Narrow critique • Constant cost with narrow definition • If use sensible definition (e.g., wheat industry), • Increased demand for wheat will mean conversion of land from (e.g.) barley to wheat • Negligible change in cost of land • Fertiliser to land ratio remains constant • Marginal product & thus marginal cost remains constant • Conditions of supply thus determine cost independent of demand • Conditions of demand determine quantity produced rather than price • Contradicts neoclassical analysis

38. Sraffa’s Narrow critique • “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)

39. Sraffa’s Narrow critique Constant cost with narrow definition Price of fertiliser unaffected by increased use in wheat production PF (a) (c) Wheat Fertiliser/land ratio held constant at ideal ratio F Horizontal wheat supply curve with constant MPF Supply sets price, demand sets quantity: position of classical school MPF PW (b) (d) D1 D2 Marginal productivity of fertiliser therefore constant P SW Wheat F

40. Sraffa’s critique & time • Many neoclassicals reject Sraffa critique because it ignores neoclassical treatment of time • Short run: when one factor fixed • Long run: when all factors variable • Sraffa correct: neoclassical treatment of time inadequate. Consider “short run profit maximisation” argument: • Profit maximised when dP/dQ=0, or MR=MC. • But what about maximisation over time? • In dynamic (real world) setting, what matters is maximising profit over time

41. Sraffa’s critique & time • Profit a function both of quantity and time • Maximum change in profit thus depends on change in quantity and change over time • must consider total differential w.r.t. quantity and time rather than just differential w.r.t. quantity Part due to change in quantity Total change in profit Part due to changein time

42. Sraffa’s critique & time • This reduces down to (dropping (t) terms): For maximum profit growth over time, this should be as big as possible • Setting MR=MC • maximises static profit; but • maximises dynamic profit (profit over time) only if quantity produced does not change over time (if first term is zero) • A paradox: static profit maximisation advice wrong in dynamic setting • What’s going on?

43. Sraffa’s critique & time • Static profit maximisation ignores time • If we ignore time, can only maximise profit by varying quantity produced • But time exists • must consider both time and quantity when trying to maximise profit • An analogy • consider trying to conserve fuel while driving • find most economical speed at which to drive • if ignore time, simple: drive at zero kph • if consider time, want to minimise petrol use while kph>0

44. Sraffa’s critique & time • Have to work out how to minimise • If do directly, get “travel at zero kph” answer • instead, break down into 2 stages: consider • Find minimum for this where both halves > zero • By analogy, neoclassical profit maximisation ignores this: like advising that “best way to conserve fuel is to travel at zero kilometres per hour” • Since Dynamic profit maximisation requires MR > MC

45. Sraffa’s critique & time • Interpretation? • Maximising profit w.r.t quantity now leaves no “energy” to devote to growth • hence get maximum possible returns today, but have no resources left to invest, so no growth • Time can’t be neatly compartmentalised into short, medium, long run • Time is continuous • If theories ignore time, they are static, and cannot make observations about change over time • Economic system is dynamic, necessarily changes over time, so static analysis of little or no relevance to economics • And there are more problems with theory of the firm… • check Debunking Economics Ch. 4 and website

46. Sraffa’s “real world” critique • Robbins definition sees economy as “resource-constrained” • Robbins’ definition: resources the key constraint on output • Sraffa instead argues that economy is demand constrained • “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 of their firm, which do not permit the production of a greater quantity without an increase in cost” (Sraffa 1926: 543). • Instead limits to sales set by “the absence of indifference on the part of the buyers of goods as between the different producers” (Sraffa 1926: 544).

47. Sraffa’s “real world” critique • Numerous reasons why resources do not in general restrain output of capitalist firms: • Excess productive capacity the norm • investment plans anticipate growth, so plants built to cope • excess capacity enables firm to take advantage of problems of competitors • Macroeconomic: pressure to keep wages low suppresses aggregate demand; normality of involuntary unemployment; insufficient aggregate demand (as per later Keynes) the norm.

48. Sraffa’s “real world” critique • Both a vice and a virtue: • Demand constrained firm must innovate to remain competitive: high level of innovation • Resource constrained firm does not need to innovate • Demand constrained economy (capitalist) will have higher degree of innovation than resource constrained (socialist) thus higher rate of growth. • Thus according to Sraffa (and today Kornai), Robbins definition thus fails to emphasise one of key virtues as well as vices of the market economy.

49. Sraffa’s “real world” critique • Empirical research supports Sraffa: • Numerous studies (Meade, Tucker, Andrews, Eiteman, Guthrie) find firms • “Administer” prices (set prior to marketing) • Endeavour to sell as much as possible at set price • Perceive costs constant or falling with increased output • E.g., Guthrie showed firms graphs of cost/quantity relation • only 1 in 20 chose graphs showing rising marginal cost:

50. Sraffa’s “real world” critique • According to Eiteman (1947), engineers design 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)