Eckhard Hein DISTRIBUTION AND GROWTH AFTER KEYNES A Post Keynesian Guide (Edward Elgar 2014)

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1 Eckhard Hein DISTRIBUTION AND GROWTH AFTER KEYNES A Post Keynesian Guide (Edward Elgar 2014) Chapter 2 FROM KEYNES TO DOMAR AND HARROD: CONSIDERING THE CAPACITY EFFECT OF INVESTMENT AND AN ATTEMPT AT DYNAMIC THEORY

2 Content 2.1 Introduction: the transition from Keynes s short period macroeconomics to the post Keynesian distribution and growth theory 2.2 Domar: the conditions for a constant rate of utilization of growing production capacities 2.3 Harrod s formulation of a dynamic theory 2.4 Assessing Harrod s approach 2.5 The textbook version ofthe post Keynesian Harrod Domar growth model assuming away Harrod s and Domar s central problems 1

3 2.1 INTRODUCTION: THE TRANSITION FROM KEYNES S SHORT PERIOD MACROECONOMICS TO THE POST KEYNESIAN DISTRIBUTION AND GROWTH THEORY 2

4 A. Distribution theory Keynes s General Theory (1936): No fundamental critique of marginalist theory of distribution but rather an inclination to accept them if full employment is given But also: [t]he outstanding faults of the economic society in which we live are its failure to provide for full employment and its arbitrary and inequitable distribution of wealth and incomes (Keynes 1936, p. 372) Keynes s Treatise on Money (1930): fundamental equations, widow s cruse: I > S means quasi rent (profits), increase in investment therefore increase in profits 3

5 Thus profits, as a source of capital increment for entrepreneurs, are a widow s cruse which remains undepleted however much of them may be devoted to riotous living. When, on the other hand, entrepreneurs are making losses, and seek to recoup these losses by curtailing their normal expenditure on consumption, i.e. by saving more, the cruse becomes a Danaid jar which can never be filled up; for the effect of this reduced expenditure is to inflict on the producers of consumption goods a loss of an equal amount. (Keynes 1930a, p. 139) 4

6 Post Keynesian distribution theory Kaldor Keynesian theory of income distribution, draws on Keynes s Treatise on Money Kalecki mark up determines distribution 5

7 B. Accumulation and Growth Keynes General Theory (1936): capital stock is given income and employment theory, but no growth theory Economic possibilities of our grandchildren (1930) The long term problem of full employment (1943) Post Keynesian growth theory Harrod,Domar,Kaldor,Robinson,Kalecki,Steindl, Unifying theme: Investment is independent of saving also in the long run! 6

8 The Keynesian models (including our own) are designed to project into the long period the central thesis of the General Theory,thatfirms are free, within wide limits, to accumulate as they please, and that the rate of saving of the economy as a whole accommodates itself to the rate of investment that they decree. (Robinson 1962, pp ) 7

9 2.2 DOMAR: THE CONDITIONS FOR A CONSTANT RATE OF UTILIZATION OF GROWING PRODUCTION CAPACITIES 8

10 Because investment in the Keynesian system is merely an instrument for generating income, the system does not take into account the extremely essential, elementary, and well known fact that investment also increases productive capacity. (Domar 1946, p. 139) 9

11 Domar Capital expansion, rate of growth and employment (1946) Assumptions: Closed private economy Constant price level No lags in behavioural equations Saving and investment net of depreciation Productive capacity can be measured Initially the economy is in full employment equilibrium (however no further consideration of labour supply) 10

12 Capacity effect of investment: (2.1) dy p dk I Y P : productive capacity/potential output given by the capital stock, I: investment, K: capital stock, κ: capital productivity Income/demand effect of investment: (2.2) dy 1 s di s: propensity to save 11

13 Equality of capacity and income effects: (2.3) dy P dy Inserting equations (2.1) and (2.2) into (2.3): (2.4) (2.5) I 1 s di Î di I s Investment has to grow at a certain rate to make sure that additional productive capacities will be utilized 12

14 (2.6) Ŷ dy Y s Constant capital productivity requires capital stock to grow at the same rate as output/income: (2.7) ˆK dk K s Capital productivity and propensity to save determine the rate at which I, Y and K have to grow in order to allow for dynamic equality of demand and capacity/supply No investment function, no disequilibrium analysis in Domar 13

15 2.3 HARROD S FORMULATION OF A DYNAMIC THEORY 14

16 Harrod An essay in dynamic theory (1939) The following pages constitute a tentative and preliminary attempt to give the outline of a dynamic theory. (Harrod 1939, p.14, emphasis in the original) Assumptions: constant prices closed economy 15

17 Conditions for dynamic goods market equilibrium (I=S) (2.8) S = sy S: aggregate saving, s: average propensity to save, Y: domestic product (2.9) S K S Y Y Y P Y P K su v σ:savingrate,y P : potential output, K: capital stock, u: rate of capacity utilization, v: capital potential output ratio 16

18 (2.10) g* I K S K su v Constant v implies: (2.11) g* Kˆ Yˆ su v The line of output traced by the warranted rate of growth is a moving equilibrium, in the sense that it represents the one level of output at which producers will feel in the upshot that they have done the right thing, and which will induce them to continue in the same line of advance. (Harrod 1939, p. 22) 17

19 (2.12) g w su v n g w : warranted rate of growth, u n : normal or target rate of capacity utilization Since s, u n and v are each fixed, g w is invariant, too. warranted rate becomes a benchmark for actual rate of accumulation/growth (2.13) g ( u u n ),, 0 (2.14) d ( u u n ), 0 cumulative deviations 18

20 Figure 2.1 The unstable warranted rate of growth 19

21 The dynamic theory so far stated may be summed up in two propositions. (i) A unique warranted line of growth is determined jointly by the propensity to save and the quantity of capital required by technological and other considerations per unit increment of total output. Only if producers keep to this line will they find that on balance their production in each period has been neither excessive nor deficient. (ii) On either side of this line is a field in which centrifugal forces operate, the magnitude of which varies directly as the distance of any point in it from the warranted line. Departure from the warranted line sets up an inducement to depart farther from it. The moving equilibrium of advance is thus a highly unstable one. (Harrod 1939, p. 23) 20

22 (2.15) g n ˆL ŷ L: labour force, y: labour productivity Figure 2.2 The warranted rate of growth below the natural rate of growth 21

23 Figure 2.3 The warranted rate of growth above the natural rate of growth 22

24 2.4 ASSESSING HARROD S APPROACH 23

25 The distribution of income was not a topic that received much attention in Harrod s writings on dynamic economics. The equilibrium distribution was taken as given, rather than explained by Harrod s model, and he admitted that he had not gone deeply into the question of income distribution. (Asimakopulos 1991, p. 153) Harrod has provided a much needed methodological approach and a valuable start towards placing the General Theory in a dynamic context. The idea that the warranted and the natural rate are not necessarily the same or equal and the complications that arise when they are not ranks as a basic contribution to growth. The general approach, however, lacks the necessary variables to answer other important problems in growth. (Kregel 1971, p. 118) 24

26 What is important in Harrod s procedure is that he not only determined the warranted rate of growth at a given moment in time, but that he examined the stability of the warranted rate at a moment in time as well, assuming the determinants of the warranted rate to remain constant if the system is out of equilibrium. This is, of course, problematic, because it excludes the possibility that the determinants of the warranted rate, the average propensity to save and firms target capital output ratio (and thus the normal rate of utilisation) might change, whenever there is a deviation from the warranted rate. Shifts in equilibria generated by disequilibria and hence potential path dependence of the growth equilibrium get out of the pictures. 25

27 Figure 2.4 The normal rate of capacity utilization as a range, preventing Harrod s instability problem 26

28 Figure 2.5 The endogenous average propensity to save as a remedy for Harrod s instability problem 27

29 While I hold that the instability theorem is safe, in the sense that the warranted rate of growth is surrounded by centrifugal forces and that a chance divergence will be accentuated, I do not claim to have made any thorough going analysis of the regions lying farther afield of the warranted rate. (Harrod 1959, p. 460) 28

30 Figure 2.6 Interaction of the actual and warranted rates of growth in the course of the trade cycle 29

31 Upper turning point Full employment or limitations to labour mobility or bottlenecks in the production of capital goods Price inflation, re distribution towards profits and a higher average propensity to save Firms expectations change Warranted rate rises above actual rate Lower turning point Autonomous investment Replacements Autonomous consumption (fall in propensity to save) Warranted rate falls below actual rate 30

32 2.5 THE TEXTBOOK VERSION OF THE POST KEYNESIAN HARROD DOMAR GROWTH MODEL ASSUMING AWAY HARROD S AND DOMAR S CENTRAL PROBLEMS 31

33 In Harrod s terms the critical question of balance boils down to a comparison between the natural rate of growth which depends, in the absence of technological change, on the increase of the labor force, and the warranted rate of growth which depends on the saving and investment habits of households and firms. But this fundamental opposition of warranted and natural rates turns out in the end to flow from the crucial assumption that production takes place under the conditions of fixed proportions. There is no possibility of substituting labor for capital in production. If this assumption is abandoned, the knife edge notion of unstable balance seems to go with it. (Solow 1956, p. 56, italics in the original) 32

34 Fixed coefficients (Leontief) production function (2.16) Y min K v, L a v: capital output ratio, a: labour capital ratio (2.17) K v L a K L v a Investment is identical to saving (2.18) I S sy 33

35 If the capital stock is fully utilized, or utilized at the target or normal rate, we obtain from the production function in equation (2.16): (2.18) Y K v Accumulation rate at which the goods market equilibrium output and full capacity output are equal: (2.19) g I K s v 34

36 From the assumption of a technologically given and fixed capital output ratio, it follows that capital stock and output grow at the same rate: (2.21) g I K dk K dy Y s v g w warranted rate of growth 35

37 Rate of growth of output which is associated with full employment: (2.22) Y L a (2.23) Ŷ ˆL (2.24) Ŷ ˆL ŷ g n 36

38 Only by a fluke will warranted and natural rate be equal so that (2.25) s v ˆL ŷ g w g n s/v ˆL ŷ : the economy will be facing increasing unemployment s/v ˆL ŷ : utilization of the capital stock will decrease continuously knife edge properties Solow s (1956) solution: replace limitational by substitutional production function. 37

39 I think that the attempt to hybridise Harrod and neo classicism can only produce a freak. Harrod wanted to show the relevance of effective demand to long run growth, and his equation makes sense only in this context. In contrast to this neo classicism is interested in an optimum, an equilibrium implying full employment, a concept which is difficult to adapt to growth and development in conditions of rapid change. Economists should rather not try to unite what logic has parted. (Steindl 1981, p. 130) 38

Eckhard Hein DISTRIBUTION AND GROWTH AFTER KEYNES A Post Keynesian Guide (Edward Elgar 2014) Chapter 1 Introduction

Eckhard Hein DISTRIBUTION AND GROWTH AFTER KEYNES A Post Keynesian Guide (Edward Elgar 2014) Chapter 1 Introduction 1.1 DISTRIBUTION IS BACK ON THE RESEARCH AGENDA ON THE SUBJECT OF THE BOOK 1 OECD (2008;