Macroeconomics II

Production and prices October 2013 - January 2014

Contents of lectures, and examples of possible exam questions   

Contents of lectures

Problems of modern general equilibrium: ch. 1 of GECM (Petri, General Equilibrium, Capital and Macroeconomics). Impossibility of comparative statics owing to impermanence problem. Difficulty with study of stability, unsatisfactory study of the ‘invisible hand’. Origin of these problems: the specification of the capital endowment as a given vector. This explains assumption of the auctioneer. The theory became dominant in a different version, aiming at determining a general equilibrium endowed with persistence, independent of accidents of disequilibrium: a long-period general equilibrium. This was made possible by conception of capital as a single factor of variable ‘form’. Supply-side and demand-side role of this conception of capital. Basic structure of the theory: labour land and one output; labour land and two outputs; corn-capital similar to land; importance of sufficiently elastic factor demand curves; practically indeterminate equilibria. GECM ch 1; MCM ch. 3 (Petri, Microeconomics for the Critical Mind, my web page) except for sections on Pareto efficiency and appendices.

Prices that long-period equilibrium tries to determine: Marshall gives the idea but insufficient, his partial-equilibrium method assumes given input costs, illegitimate if the costs of capital goods inputs include the price of the good under study. Need for simultaneous determination of all output prices (except non-basics). Equations of long-period prices with two goods, corn and iron, both circulating capital. Usual specification of costs does not make the presence of interest clear but it is there. Perron-Frobenius theorem proves uniqueness of solution. MCM ch. 2 (Petri, Microeconomics for the Critical Mind, my web page).

Proof that w decreases in any numéraire if r increases, based on reduction to dated quantities of labour. Choice of technique: proof of convergence to outer envelope of w(r) curves, based on Abraham-Frois and Berrebi. Implication: Marx wrong on tendency of rate of profit to fall.

Long-period product prices are common to classical authors and to neoclassical traditional ones. Given the needed data (technology and either real w or r) the two approaches determine the same product prices. The difference is in the theory of income distribution (which also implies differences on determination of aggregate output and employment). Adam Smith: a conflictual view of wages (Smith was a Marxist?!). Absence in classical authors of idea of factor substitution and of factor demand curves implies social-political forces are indispensable to determine wages, and not an impediment to reaching a full-employment wage like in neoclassical approach; the market is not a self-sufficient sphere, differently from neoclassical views. Classical method: strictly deductive sphere restricted to the ‘core’, non-core forces require more inductive procedures attentive to historical specificities and institutional-political elements; a given real wage does not imply a necessary level of labour employment. Exploitation? MCM ch 1, 3; Garegnani in Bharadwaj-Schefold.

Endowment of capital the single factor of variable ‘form’, if it were acceptable, would be as persistent as endowment of labour. It must be measured as an amount of value: proof with analogy to A and B two different amounts of land of the same quality. Problem: Wicksell: given value of capital before prices are determined is nonsense. Confirmation from w(r) curve, that shows, if net output is numéraire, that value of capital per unit of labour changes with income distribution even if physically nothing changes. (MCM ch. 7)

Reswitching: definition and graphical illustration. Sraffa further confirms with reswitching that no way exists of attributing to techniques for the production of any final product a capital-labour proportion independent of income distribution, that would allow an ordering of techniques in terms of capital intensity. Samuelson’s example of champagne and whiskey. Implication: changes of income distribution can cause changes of technique opposite of what neoclassical theory would expect, e.g. w decreases and the labour-output ratio decreases. Reverse capital deepening shows that also value capital per unit of labour may change anti-neoclassically. Implication: neoclassical investment function undermined. (MCM ch. 7, part on Samuelson in MCM ch. 2)

Further deficiency (Petri, “Neglected Implications ...”, my web page): capital is necessarily putty-clay, in older plants labour-output ratio is nearly fixed, and there is output flexibility owing to generally ample margins of unused capacity relative to technically maximum level (inventories allow rapid increases of production and are reconstituted by the increase itself of production); then even accepting the neoclassical conception of r determining desired K/L, it can only determine it in new plants, but without continuous full employment of labour a given K/L ratio in new plants leaves investment indeterminate, and if desired new capacity depends on demand – so in the aggregate the economy moves along a given isoquant of Y=F(K.L) –, then a decrease of wages induces a lower K/L ratio i.e. reduces investment so employment decreases, we have instability and the theory is implausible.   

Constructive implications: The flexibility of output implies no incompatibility between increases both of consumption and of investment, or between increases of real wage and of employment. The flexibility of production of capital goods industries will allow supplying new plants with whatever technology is best with respect to the given wage; so it is capital goods (‘factor supply’, a neoclassical would say) in new plants that adapt to income distribution and employment, rather than determining them. Employment and growth will depend on aggregate demand, i.e., over longer runs, on the evolution of its autonomous components (state expenditure, exports, innovation-induced investment).(Numerical example of Petri, “Should the theory of endogenous growth...”)

Back to neoclassical theory: currently there is great difficulty with understanding its need for capital the single factor of variable ‘form’; frequent mistaken belief that capital the single factor is only needed if one assumes an aggregate production function. Three different presentations of long-period general equilibrium to show that it needs that conception of capital in spite of complete disaggregation:

- A B C D model of exchange and production (MCM ch 5), then transformed with addition of equations AK, BK, etc. to admit capital goods (MCM ch 7); assumption of stationary state so no savings function;

- Petri 2003 model with price equations similar to Sraffa’s, and a savings function (no stationary state but need for something determining composition of investment)

- Australian Ec. Pap. 1978 article with Wicksellian model, again stationary.

Read in MCM ch. 3 discussion of justification of stationary assumption, which means static and not secular stationary state (in the latter the total capital stock is endogenously determined too).

In 1930s Lindahl, Hayek, Hicks admit Wicksell’s misgivings with given value capital and turn to Walrasian specification of capital endowment as a given vector. But they do not abandon faith in demand-side role of capital the single factor. GECM ch. 5 (or paper on Blaug on my web page).

This allows reinterpretation of A B C D model as intertemporal equilibrium (Arrow-Debreu-McKenzie), then the model can include capital goods without any formal modification via vertically integrated firms; reinterpreting commodities as dated and prices as discounted, and a finite horizon, it requires no formal modification..

Temporary equilibrium (without perfect foresight) is not formally identical to exchange-and-production noncapitalistic equilibrium because has expectation functions, but encounters enormous problems of formalization and existence and has been abandoned.

Implausibility of finite horizon stimulates incredible assumption of equilibrium over the infinite future. Non-existence in reality of complete futures markets ‘surmounted’ via incredible assumption of perfect foresight. (see below on what makes these assumptions accepted)

But new difficulties of ‘method’ (Garegnani):

- price-change problem: dilemma between absurdity of perfect foresight (logically impossible: what about advances of knowledge?) needed for intertemporal equilibria, and indefiniteness of expectation functions (and of their evolution from one ‘week’ to the next) needed for temporary equilibrium

- impermanence problem: vector of capital endowments (and, in temporary equilibria, expectation functions) has no persistence, disequilibrium alters the data themselves of equilibrium; this is why assumption of auctioneer (this takes us back to GECM ch. 1, read also ch. 2)

- substitutability problem: no substitutability between the same capital goods, and between the same capital goods and labour, it causes insufficient elasticity of labour demand curve, implausible equilibrium wage

Conception of capital as a single factor of variable ‘form’ avoided these problems.

A fourth problem is investment, which is treated as if the old conception of capital were valid in spite of its abandonment (which comes out therefore to be only apparent): so assumption of equilibration of savings-investment market in modern general equilibrium models is unjustified.

Other attempts to argue investment a decreasing function of the rate of interest are indefensible (Ackley 1978 ch. 18; GECM ch. 7; Neglected Implications).

So neoclassical approach indefensible in all its versions, as implicitly admitted by Hicks who had seen the problems of ‘method’ (Petri 1991, “Hicks’s recantation...”) although not the ones undermining the demand-side role of capital the single factor, a demand-side role that he still accepts (GECM ch. 5; also paper on Blaug).

Continuing faith in neoclassical theory among macroeconomists rests, not on general equilibrium microfoundations, but rather on dogmatic faith in old time-consuming adjustments, where demand-side role of capital the single factor is still accepted: it is faith in old arguments that justifies belief that assumption of continuous equilibrium does not do excessive violence to behaviour of actual economy (Neglected Implications Part I). But old adjustments are indefensible. After Keynes, the main one is formulated by the Neoclassical Synthesis: ‘Keynes effect’ used against Keynes: if money wages decrease then prices decrease, demand for money decreases, rate of interest decreases, investment increases. Undermined by reverse capital deepening, plus by my argument in “Neglected Implications” Part III.

So to what can we turn? For relative prices, return to normal prices (method of long-period positions). Even without perfect competition, prices are broadly determined by production costs, and rates of profit do tend to rough uniformity owing to entry (excepting natural monopolies, e.g. network externalities, where entry has problems) when compared with how much they might differ. Two big issues left: income distribution; employment and growth.

Kalecki Political Aspects of Full Employment: conflictual view, governments controlled by business world, unemployment will be recreated if it decreases too much. End of Golden Age appears well explained by such a view. Why downward wage rigidity: easy to understand if decreasing labour demand curve is dropped (Neglected Implications fn 47).

Heinz Kurz on accumulation takes up again the view already mentioned on growth, based on the great flexibility of output adapting to demand. Reasons for spare capacity. (Open issue: Harrod’s instability, does it really exist? wait for lectures in Macro 2)

 

Examples of questions

1 Explain why the Marshallian determination of the long-period product price of an industry, as equal to minimum average cost on the basis of given input prices, is generally illegitimate, and how this difficulty can be surmounted.

2 In the neoclassical economy where corn is the only product, produced by labour and land according to a differentiable production function, assume that the supply of labour is backward-bending, and show that in this case there is no guarantee that the demand curve for land (assuming equilibrium on the labour market) is downward-sloping. (cf. GECM ch. 1 fn. 13)

3 Suppose that labour and land, inelastically supplied, produce corn and iron in two single-product fixed-coefficients industries.  The labour-land ratio is higher in the production of corn.  According to the marginalist/neoclassical approach, if there is a shift in tastes in favour of iron, what will be the effect on quantities produced and on income distribution?

4 Some neoclassical economists have argued that Adam Smith’s description of wage determination means only that according to classical authors labour markets are not perfectly competitive, something that a neoclassical economist may well accept, and will imply labour unemployment caused by the downward rigidity of wages. Explain why this misses the true root of the difference of the classical from the marginalist view of the wage as determined by supply and demand, and how this true root makes it easier to understand why in the classical approach involuntary unemployment does not necessarily mean that wages will tend to decrease. Also explain why the classical approach to wage determination undermines the Friedmanite notion of unemployment as voluntary if wages do not decrease. (Cf. MCM ch. 3 section 3.13; Neglected Implications fn. 47)

5 Distinguish the supply-side role from the demand-side roles of the conception of capital as a homogeneous factor in the traditional versions of marginalist general equilibrium theory. (Petri GECM ch. 1 section 1.4, also §5.4.5).  On their basis, explain why capital goods cannot be aggregated in terms of weight (Help: cf. GECM  §3.3.4 and fn. 21 there.)

6 "It is in fact in value terms that capital is reckoned in economic practice, and it is from that commonsensical idea that the concept of capital as a factor of production has been derived in traditional marginal theory.  However, the value of the capital goods does not satisfy the requirement of independence from changes in disribution....One might then think that the way out of the difficulty is to renounce a unitary conception of capital and deal with the heterogeneity of the capital goods in a way analogous to that which we saw for land or labour, that is by treating each kind of capital good as the argument of independent demand and supply functions.  However, the case of capital is different from that of labour and land" (Garegnani, Quantity of capital, p. 10-11). Explain the last sentence of the quotation. (cf. GECM §6.4.4)

7 Show how one can derive graphically the dependence of the value of capital per unit of labour on income distribution from the w(r) curves. Use the result to argue that it is illegitimate to include, among the data determining a long-period general equilibrium, a given endowment of capital measured as an amount of value. Conclude that the marginalist approach is unable to determine long-period positions.  

8 Why are results concerning long-period technical choices relevant for Keynesian economic theory, which is usually argued to be only concerned with the short period?

9 Explain the difference between a long-period neoclassical general equilibrium and a secular neoclassical general equilibrium and explain why in the latter a given endowment of value capital does not appear.

10 What is the analytical main difference between long-period and neo-Walrasian general equilibria? Also indicate other important differences deriving from that one.

11 "The inconsistency relative to the specification of the capital endowment has not disappeared with the shift from long-period to neo-Walrasian equilibria, it has only taken a different form". Explain and evaluate. (Cf. Petri, §4.2 of “Professor Hahn on the neo-Ricardian criticism...” in Mongiovi and Petri, eds., Value Distribution and Capital, 1999)

12 According to at least some critics, the Cambridge critique undermines the right to draw a decreasing demand curve for labour. Explain why (GECM, Ch. 8)

13 Explain the critique of insufficient substitutability advanced by Garegnani against neo-Walrasian general equilibria (Garegnani, “Quantity of capital”, in Eatwell Milgate Newman eds., The New Palgrave: Capital Theory, 1990, pp. 57-58; GECM p. 29-32 and 44-45).  Why didn’t the difficulty arise in traditional marginalist/neoclassical theory based on the conception of capital as a single factor of variable ‘form’?

14 Explain the difficulties arising in neo-Walrasian equilibria from the impossibility, in these versions, to neglect changes of relative prices over time (GECM p. 33-34, 42-44; Garegnani Quantity of capital, 51-54). Why didn’t the same difficulties arise in traditional marginalist/neoclassical theory based on the conception of capital as a single factor of variable ‘form’?

15 Explain why it can be argued that "neither the initial-period neo-Walrasian equilibrium nor the equilibrium path (if it can be determined) based on the initial data can tell us anything at all on the actual evolution of an actual economy" (GECM Ch. 2; also cf. Petri, “Professor Hahn ...” section 4)

16 Explain why capital was traditionally measured as an amount of value by marginalist economists and had to be so measured, and what is wrong with this.

17 Why can it be argued that the reasons, why the traditional method of long-period positions has been abandoned in mainstream work on value and distribution, have nothing to do with weaknesses of that method?  (GECM ch. 9)

18 Explain why the impermanence, substitutability and indefiniteness problems did not arise for the traditional long-period equilibria. (GECM §2.2.2 p. 51)

19 Explain why reverse capital deepening undermines the belief in a negative elasticity of investment with respect to the interest rate (cf. GECM ch. 6 and ch. 4 section 4.3). Also explain why the recourse to the short period cannot save that belief. (Cf. GECM §4.3.5 and fn. 20, also p. 284, and p. 267-8; also cf. Garegnani, "Notes on consumption, investment and effective demand", in Eatwell and Milgate, Keynes's economics and the theory of value and distribution, pp. 35-37)

20 Explain how Keynes's acceptance of a negative elasticity of investment vis-à-vis the rate of interest could be used by the ‘neoclassical synthesis’ to argue that his own theory implied that persistent unemployment was due to the downward rigidity of (money) wages. (Petri GECM ch. 7 fn.1; Petri Neglected Implications Part I)

21 Point out the reason why the classical approach may support the claim that wage labour is exploited in a capitalist system, while a marginalist/neoclassical approach to value and distribution supplies arguments to dispute it. (MCM ch 3)

22 Explain why, contrary to the case in neoclassical theory, in a modernized classical approach that takes full account of the flexibility of production and of its capacity to accommodate vast variations of demand, it is not true that full employment requires a definite real wage (GECM p. 320; Neglected Implications §7).

23 Explain why modern general equilibrium theory (intertemporal or temporary) needs Say’s Law and is unable to justify it.   

24. Indicate two demand-side reasons why traditional neoclassical authors found it analytically indispensable to conceive capital as a single factor of variable form.

25. “The Sraffian picture of neoclassical theory is this. At any moment of time we can observe something physical called the stock of capital (K) as well as the amount of labour (L).  There is a concave production function Y=F(K,L) where Y is output.  In a neoclassical equilibrium all inputs are used and must be paid their marginal products.”  (Hahn, 1982, p. 370).  Is this a correct description of the “Sraffian picture of [traditional] neoclassical theory” as presented to you in our course? Do the ‘Sraffian’ critics really aim at criticising only the aggregate-production-function versions of the neoclassical approach? (Cf. GECM ch. 6 section 6.4)

24. Explain the difficulties arising in neo-Walrasian equilibria from the impossibility, in these versions, to neglect changes of relative prices over time (GECM p. 33-34, 42-44; Garegnani Quantity of capital, 51-54). Why didn’t the same difficulties arise in traditional marginalist/neoclassical theory based on the conception of capital as a single factor of variable ‘form’?

25. List Kalecki’s reasons for being skeptical about governments’ willingness persistently to pursue policies of economic intervention in favour of full labour employment.

26. Why has it been argued (Kalecki) that “unemployment is an integral part of the normal capitalist system”?

27. How does Kalecki explain the fact that Germany’s government alone was pursuing expansionary economic policies?

28. What in the Perron-Frobenius theorem allows proving the uniqueness of the solution for the rate of profit?

29. Write the equations determining long-period prices for corn and iron produced in separate single-product industries by corn, iron and labour with fixed coefficients. Corn is numéraire. Now assume that the wage can be different in the two industries. Find a proof that if r is given, if one wage increases the other one decreases.

30.  J. B. Clark, Hicks, Robertson admitted that the determination of a plausible marginal product of labour requires the ‘form’, of the quantity of capital with which labour is combined, to change so as to become adapted to the increased quantity of labour. Explain why, and why it implies that a short-period demand curve for labour would not be able to determine a plausible equilibrium real wage.

31. Why do the criticisms of the marginalist conception of capital also undermine the downward-sloping labour demand curve? And why does this make it easier to explain the downward stickiness of wages?

32. Indicate the relevance of reverse capital deepening for the theory of aggregate investment.

33. In what sense can productive capacity be overutilized?

34. Explain why a higher growth rate of state expenditure may raise the growth rate of the economy.

35. Explain why neoclassical investment theory becomes indeterminate if the continuous full employment of labour is not assumed.

36. By reference to the problems of the theory of intertemporal general equilibrium, explain why the argument of Petri ‘Neglected implications....(Investment depends on output extended version)’ is also a criticism of DSGE models.

37. Summarize what is wrong with the adjustment-costs approach to the negative interest-elasticity of aggregate investment. (Neglected Implications Part II)

38. Explain how the non-capitalistic production general equilibrium model can make room for production with capital through an intertemporal reinterpretation.