Growth and Inequality – Part 4

I am now using Friday’s blog space to provide draft versions of the Modern Monetary Theory textbook that I am writing with my colleague and friend Randy Wray. We expect to publish the text sometime around mid-2014. Our (very incomplete) textbook home page – Modern Monetary Theory and Practice – has draft chapters and contents etc in varying states of completion. Comments are always welcome. Note also that the text I post here is not intended to be a blog-style narrative but constitutes the drafting work I am doing – that is, the material posted will not represent the complete text. Further it will change as the drafting process evolves.

Previous blogs in this series:

Chapter X Growth and Inequality

X.2 Keynesian growth theories – Harrod-Domar

[PREVIOUS MATERIAL HERE]

Required growth and the full employment of labour

In the previous example, we assumed that if actual growth was equal to the growth in potential output, then both labour and capital would be fully employed. We then defined the condition that will ensure the economy remains on this full employment growth path, given the dual nature of investment.

However, the condition we derived actually only guarantees that all new productive capital is utilised. We need to consider under what conditions this growth rate will also ensure that all workers who desire to work will find a job. What we will show is that a rate of real GDP growth that ensures all new capital is utilised in each period may not be sufficient to absorb all the new entrants to the labour force as the population grows.

British economist Roy Harrod was interested in that problem. He considered the growth process by examining whether real GDP growth was sufficient to induce enough investment in the current period to absorb the planned saving. This is a different focus to the discussion in the previous sections, which reflected the work of Evsey Domar.

We introduced the investment accelerator in Chapter 22 and learned that firms will plan investment in the current period based on expected output changes (ΔY) to ensure that the change in the capital stock (ΔK) is sufficient to facilitate that planned output growth.

Underlying the investment accelerator is the concept of the capital-output ratio, which reflects the state of technology.

Warranted rate of growth

Harrod (1948: 82) considered the rate of growth that would ratify the production decisions of the entrepreneurs and leave them “prepared to carry on a similar advance”. Recall that firms determine current production levels based on expectations of aggregate demand (that is, what they think they can sell).

For this condition to exist, planned investment should equal actual investment, which means no unintended inventory accumulation would arise.

Harrod observed that in a closed economy, with no government sector, this equilibrium would require planned investment to equal actual savings.

Harrod defined this rate of growth as the warranted rate of growth, Gw, which is the rate of growth that ensures that all available capital is fully employed.

He introduced a concept, Cr or the ‘capital requirements’ which is (Harrod, 1948: 82):

… the requirement of new capital divided by the increment of output to sustaint which the new capital is required.

In other words, Cr, and tells the firm which is operating at full capacity how much new capital it will need in the next period to ensure their planned output can be realised. Note that if there is idle productive capacity, firms can expand output in the next period with no additional capital stock.

Further, a fixed capital-output ratio, which is an indicator of the productivity of capital, is assumed. The capital requirements thus becomes:

(X.12)      Cr = ΔK/ΔY = In/ΔY

Equation (X.12) tells us that at full capacity, net Investment (In) equals the change in capital stock (ΔK) and that Cr is driven by the capital-output ratio (K/Y) and the expected change in output (ΔY).

Equation (X.12) is also equivalent to the accelerator because it tells us how much firms will have to invest to be consistent with the expected sales in the current period, which are reflected in the additional output the firms are willing to supply.

Harrod noted that the volume of saving in each period i a function of income and assumed that in the long-run the average and marginal saving propensities were identical so:

(X.13)      s = S/Y = ΔS/ΔY

Noting that Gw = ΔY/Y, Harrod introduced the following relationship:

(X.14)      GwCr = s

We can rewrite Equation (X.14) as:

(X.15)      (ΔY/Y)(In/ΔY) = S/Y

Which simplifies to:

(X.16)      In/Y = S/Y

Which means that for the economy to achieve the equilibrium path defined by the warranted rate of growth, planned investment has to equal actual saving.

Another way of thinking about this is to note that planned investment is driven by the change in output, which firms believe will be sufficient to realise the expected aggregate demand. In equilibrium, this output has to be sold and so investment has to be sufficient to absorb the planned saving. If, for example, planned saving exceeds planned investment, then unintended inventory accumulation would occur signalling to firms that they were overly optimistic. The behavioural response to that signal would be to cut back output.

The warranted growth rate allows us to appreciate that economic growth and the expansion of potential output is facilitated by adding more capital to the economy through investment. This can be accomplished through both private and public capital formation, which means that fiscal policy can be an effective growth instrument independent of the desirability of public infrastructure development.

Harrod’s approach to economic growth thus remains faithful to the fundamental principles of macroeconomics that we have developed in this textbook.

However, economic growth cannot just be a process of expanding the stock of productive capital because other inputs, in particular, labour are required. For example, the economy can only achieve the warranted rate of growth if there are no labour supply constraints.

In the next section, we introduce the concept of the natural growth rate, to determine the broader conditions which are required for the warranted rate of growth to be realised.

The Natural rate of growth

While the warranted rate of growth would maintain the full utilisation of capital for a fixed output-capital ratio over time, other conditions are required for it to be realised.

Harrod (1948: 87) defined the natural growth rate, Gn as “the rate of advance which the increase of population and technological improvements allow. It has no direct relation to Gw.”

It is the rate of growth that ensures that all workers that desire work can find employment and it is dependent on the growth of the labour force and technical progress (which influences productivity growth). If the economy is growing at the rate Gn then there is “no possibility of involuntary unemployment” (Harrod, 1948: 87).

So while Gw is the “line of advance, which, if achieved, will satisfy profit takers that they have done the right thing; in Keynesian fashion it contemplates the possibility of growing ‘involuntary’ unemployment” (Harrod, 1948: 87).

It is important to note that its determinants are different to those of the warranted rate of growth, which means that the two growth rates will not automatically coincide. An important contribution of Keynes in the General Theory was to demonstrate that even in an equilibrium that satisfied the production decisions of firms and left them with no desire to change, there could be significant (and rising) unemployment.

Harrod this considered it essential to complete his dynamic analysis by analysing divergences between Gw and Gn, for this would help us understand how mass unemployment occurs and the stimulus that might be required to eliminate involuntary unemployment.

The natural growth rate, Gn sets the limit on what actual growth can be over some long period. An economy cannot grow once it has exhausted its labour resources. In periods of low activity where there is mass unemployment and other idle resources, restoring the warranted rate of growth is unproblematic. The solution is to increase aggregate demand.

However, in lieu of idle labour resources, the labour force growth rate must match the warranted rate of growth if the expanding capital stock is to be fully employed over time.

If we think of technological progress as being of a labour-saving nature, which means that it allows the same quantity of output to be produced with less labour (enhancing the productivity of labour) then for full employment to be maintained, employment growth (ΔN/N) has to be equal to the sum of the labour force growth (ΔL/L) plus the labour-saving technological change.

That sum is equivalent to the natural rate of growth and if it is equal to the warranted rate of growth then we say that the economy is maintaining full employment growth.

A Social Model of Productivity Growth

Our brief study of the growth process has introduced the importance of productivity growth in the capacity of the economy to maintain a full employment growth equilibrium.

In Chapter 25 we consider the ageing population debate and the implications for government outlays. In that context, whether a nation can maintain an adequate supply of real goods and services as the dependency ratio rises (that is, as the number of productive workers to the total population falls), depends, crucially, on productivity growth.

The declining proportion of productive workers will have to generate more output per hour over time than their predecessors if the material needs of the ageing population are to be catered for.

In this section, we consider a social model of productivity growth that considers the issue from a broader perspective than most studies you will find in the economics literature. Typically, productivity growth is considered to be a process by which firms add more capital to the production process and introduce technological changes which allow the workers to produce more effectively. It is a mechanical vision of what is, in fact, a social process.

As an example, in the early days of the industrial revolution, the cottage industry thrived. This involved a capitalist (entrepreneur) supply spinning equipment and raw materials necessary for cotton production to households who would then work on piece-rates. At regular intervals the capitalist would return to pick up the output.

They soon found that their expectations of that output were not met for several reasons among them the fact that workers would work until they had earned enough to cover their household expenses (subsistence needs) and then they would stop and enjoy social activities. Further, some unscrupulous households would seek to sell the capital and raw materials in neighbouring towns.

The solution was to bring the cottage industry ‘under one roof’, which was the beginnings of the modern factory system. Productivity went up rapidly. Why? It was clear that the technology was unchanged. But what was different was a new function was now defined – supervision and oversight. By bringing the decentralised production units together in time and space, the capitalist could supervise the work and ensure that the workers produced a desired surplus.

The point is that the productivity growth came about through a social innovation – the creation of authority and supervision in the workplace. It had nothing to do with an increased number of spinning jennies or better technology.

A similar observation is made when considering the role of women in manufacturing during World War II.

[TO BE CONTINUED]

[NEXT WEEK TO FINISH THE GROWTH PART OF THE CHAPTER I WILL DISCUSS DETERMINANTS OF PRODUCTIVITY AND INTRODUCE THE SOCIAL MODEL OF PRODUCTIVITY WHICH CHALLENGES THE MAINSTREAM CONCEPTION OF THE DETERMINANTS OF PRODUCTIVITY]

References

Harrod, R. (1948) Towards a Dynamic Economics, London, Macmillian.

Weisskopf, T.E., Bowles, S. and Gordon, D.M. (1983) ‘Hearts and Minds: A Social Model of U.S. Productivity Growth’, Brookings Papers on Economic Activity, 2, 381-450.

Saturday Quiz

The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:

That is enough for today!

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    19 Responses to Growth and Inequality – Part 4

    1. Alan Dunn says:

      Bill, is this a typo ?

      “Which means that for the economy to achieve the equilibrium path defined by the warranted rate of growth, planned saving has to equal planned saving.”

      Planned investment has to equal actual saving ?

    2. bill says:

      Dear Alan Dunn (at 2014/02/08 at 12:21)

      Thanks for picking up the typo. The correct condition is that planned investment must equal actual saving, in a closed economy with no government.

      best wishes
      bill

    3. PZ says:

      Why do you think it is a good idea to brand your textbook as presenting views of the fringe – modern monetary theory, as opposed to being just an textbook about economy? Do you think it more likely to enhance its popularity or vise versa?

    4. Ikonoclast says:

      The elephants in the room are Limits to Growth and Climate Change. Both of these factors will lead to at least a plateauing of growth and even a possible reversal of growth. Best LTG estimates of the peak or plateau of possible economic growth on earth indicate about 2030 plus or minus 10 years. How will economics (including MMT) address steady state economies and/or shrinking economies?

      After the works of Meadows, Hall, Tainter and others in their fields, these eventualities (peak, plateau, managed decline or collapse) must be acknowledged as the near future of humanity. A peak is certain given that the economic system is a sub-system of the biosphere system where the Laws of Thermodynamics pertain as indeed they do throughout the known universe. What is not certain is the post-peak situation which could involve a steady or undulating plateau, a managed decline or uncontrollable collapse.

      The most likely outcome (IMO) will be somewhere in the range from managed decline to uncontrollable collapse due to ecological footprint overshoot. Economics cannot and should not ignore these looming, near- term realities.

    5. SteveK9 says:

      Ikonoclast: Your ‘elephants’ in the room are actually mice. You’re a typical pessimist, and you are also quite wrong, as you ‘limits to growth’ folks have been for many decades. When 2030 rolls around you will be telling us the end is coming in 2050.

      We have the technology now to deal with all of mankind’s issues (e.g. atomic fission can supply environmentally benign energy, virtually forever) and the situation is only going to continue improving (I spend my days working to make that true). There is no slowdown in technological progress. In fact, in most areas, it is accelerating.

      All of humanities problems now stem from what seems our natural inclination to treat each other like shit. The only thing we have in short supply is goodwill, charity, fairness… And, in that regard the work of Professor Mitchell and others really is crucial.

    6. Neil Wilson says:

      “and the situation is only going to continue improving (I spend my days working to make that true). ”

      And long may that continue.

      The problem with ‘limits to growth’ is that it assumes that growth uses up resources. Whereas sustainability of course requires that we recycle resources constantly – as the planet has done for a very long time with carbon and water.

      Fission energy is usable but just turns the climate change issue from a CO2 issue into a heat issue. The planet’s air-conditioning system can only handle the sun’s input plus natural nuclear decay from the planet’s core. So we really need to get inside that envelope to make energy use sustainable.

      It’s all about improving the efficiency and effectiveness of our matter transformation technology and getting that distributed widely across the world. Then we don’t have to fall back on our rabbit like in-built replication technology to ensure that humans survive.

    7. Ikonoclast says:

      In reply to SteveK9 and Neil Wilson.

      Economic growth takes two forms. The first form involves production of an increasing number of units of a given complexity. The second form involves increasing the complexity of each unit (be it an upgraded unit or a unit of a new design).

      With respect to the first form (increasing numbers of units) there must be a limit to this kind of growth on the surface of the earth. A crude form of economic growth is to simply increase the number of human units (population). Another relatively crude form of growth would be to increase numbers of manufactured units without design (complexity) improvements. Logically, this form of growth is limited by space considerations alone. In practice, it is limited by resource availability.

      Neil Wilson writes, “The problem with ‘limits to growth’ is that it assumes that growth uses up resources. Whereas sustainability of course requires that we recycle resources constantly – as the planet has done for a very long time with carbon and water.”

      Growth does use resources. Does it “use up resources”? In many very important cases it does use up resources. A resource in this case is something available and useful for economic production. An ore, like copper ore, is available and useful because it contains some level of concentration of copper which makes it energetically and economically feasible to extract and concentrate copper from that ore. When all ore bodies which contain copper above a threshold concentration, which makes it feasible to extract and concentrate copper, are depleted then no more copper can be mined. Copper can continue to be recycled for a time but no recycling is 100% effective. Small amounts of copper are lost with each cycle and join the background dispersal of copper atoms at unminable concentrations.

      Energy cannot be created or destroyed. However, humans are concerned with energy available for useful work. Oil reserves contain energy available for useful work now we have developed ways to harness that work. But burning of the earth’s oil, coal and gas reserves is a once-through process. It took many hundreds of millions of years for these reserves to be created by combined biological and geological processes from the orginal input energy which was sunlight and geological energies. However, we are burning these reserves within the span of about 150 years. This resource is being used up.

      These two examples are important because they interconnect and interrelate. To mine and concentrate copper we need a viable ore body and fossil fuel energy input. Each is ultimately a one way or once through process. When all fossil fuels are exhausted and/or all copper ore bodies are exhausted than all copper production ceases. Recycling also follows a diminishing downward spiral and in any case cannot occur without energy inputs. In each case and in the combined case, what defeats us in the end is the change in entropy towards a state of greater disorder.

      Entropy:
      1. Symbol S For a closed thermodynamic system, a quantitative measure of the amount of thermal energy not available to do work.
      2. A measure of the disorder or randomness in a closed system.
      3. The tendency for all matter and energy in the universe to devolve toward a state of inert uniformity.

      The earth technically approaches a closed system in thermodynamic terms. In a closed system energy can come in and exit but mass is not transferred. (Loss of atmosphere particles and incoming meteors are the exceptions for earth but these exceptions are not significant on the timescale of humans.)

      Not all resources are used up, given that the biosphere does recycle and renew some resources on a time scale useful to humans. Also, very significant energy comes in from outside the closed system of the biosphere via sunlight. But where resources are not used up (i.e. are renewable) they still have a maximum finite flow. So resource analysis is stocks and flows analysis; something very familiar to MMT analysts who also consider stocks and flow.

      Non-renewable stocks like oil reserves are one-use-only. Where they impinge on other finite capacities (the capacity of the biosphere to absorb CO2 without serious climate disruption) it appears we cannot use them all up without damaging our benign Holocene climate on which we rely for crops growth and thus food.

      Renewable resources come with a flow only, like sunlight, or an intital buffer stock and a flow, like fresh water (aquifers, lakes, rivers). All stocks and flows on earth are finite. Therefore even utilisation of renewables suffers from a limit which prevents perpetual growth.

      What I take issue with is any economics which assumes perpetual growth is possible. Perpetual growth is impossible on earth. The biosphere is a finite system with finite stocks and flows. What is more, the work of scientists and systems analysts consistently indicates that we are now very close to these growth limits. The year 2030, plus or minus 10 years for estimation error, for peak economic production is eminently supportable by all the relevant literarature. The empirical evidence is extensive and well beyond the scope of my short blog post here.

    8. Neil Wilson says:

      “copper can continue to be recycled for a time but no recycling is 100% effective.”

      The Carbon and Water cycles are.

    9. Ikonoclast says:

      In the context, it is clear I was referring to industrial recycling, not natural recycling. In any case, the current natural water and carbon cycles are not effective against modern industrial manufacturing processes in time frames that matter to humans and civilization. Concentrations of CO2 are rising in the atmosphere and in the oceans and this is leading to global warming. The biosphere’s water cycle and the purity of fresh water are being degraded by the current level of industrial activity. Aquifers, lakes and rivers are being exhausted.

      If you had a substantial point you would have made it. The problem you face is that the points I have made are incontrovertible. The laws of physics ultimately condition what is possible not the “laws” of economics. The economy is a sub-system of the biosphere which in turn is a sub-system of larger physical systems. In this universe, the Laws of Thermodynamics hold sway. The economy cannot escape the limitations imposed by these natural laws. The key intellectual problem in this arena is to integrate economics with the known laws science or at least recognise that physical laws impose natural limits.

      The time is past when economics could be theorised or practised without regard to these laws. When the limits to growth were distant they could be temporarily and provisionally ignored (though it is a pity we did not pay attention to them sooner). Now the limits to growth are close, these limits, or the laws they represent, become immediate conditioning factors with a massive impact on economic possibilities.

    10. Neil Wilson says:

      “The laws of physics ultimately condition what is possible not the “laws” of economics.”

      They do, but they are still subject to narrow interpretation by zealots that have made up their mind a-priori just like the ‘laws’ of economics.

      A more open mind sees more possibilities.

    11. Ikonoclast says:

      What is physically impossible is economically impossible. That is all I have said. Since it is physically impossible for any sub-system to grow indefinitely within a finite system then it is impossible for the economy (a sub-system of the biosphere) to grow indefinitely. The simple proof comes from the natural exponential function.

      Arguments for indefinite qualitative growth (as opposed to indefinite quantitative growth) fail when it is realised that such indefinite qualitative growth must;

      1. Involve an increase in complexity.
      2. Involve an increase in energy use to organise greater complexity and preserve it against entropic processes.

      Thus endless qualitiative growth would presuppose endless growth in energy use. Again, this is an impossibility.

    12. Neil Wilson says:

      “What is physically impossible is economically impossible.”

      What is physically impossible isn’t the same as what you believe is physically impossible.

      As I said a more open mind sees more possibilities.

    13. Ikonoclast says:

      I am making precise assertions based on science (particularly the Laws of Thermodynamics). I do not merely believe the Laws of Thermodynamics in the way that a person believes asserted and undemonstrated dogma. I accept these Laws as operatively true and highly dependable statements derived from a large body of experimentation, empirical evidence and integrated theory with said theory being of demonstrable predictive power.

      You want to derail the discussion by misdirecting the debate into issues of epistemology (questions of knowledge and the uncertainty of knowledge). It’s a cheap debating trick. This is why I referred to “operatively true and highly dependable statements derived from a large body of experimentation, empirical evidence and integrated theory with said theory being of demonstrable predictive power” rather than talking simplistially about knowledge and belief. I leave the simplistic conflation of knowledge and belief to others.

      So let us get down to tin tacks. Are you saying you believe endless growth is possible in a finite system?

    14. Some Guy says:

      Ikonoclast, the problem is that you are identifying something essentially immaterial, dependent on human preferences – economic growth – with something material. Nobody thinks that the earth’s human population or resource usage can grow indefinitely. But how much economic growth per material usage? The argument with 1 & 2 above is basically hand-waving. It is not at all clear that “endless qualitative growth would presuppose endless growth in energy use”. And increasing energy use for quite some time, perhaps at a somewhat slower rate of increase than the last few centuries, may very well not be all that hard or unGreen.

      In any case, precisely because modern economies are so inefficient macroeconomically, so spectacularly wasteful, it would be easy to do more with less, if we just improved social technology by not doing things the insanity of which is obvious to a child. By demonstrating enormous current macroeconomic inefficiency, MMT shows there is more room than analyses informed by neoclassical quackery. As I’ve posted before here, John Bellamy Foster’s The Planetary Emergency is worth reading and should be congenial to your viewpoint. MMT – particularly the JG -is intrinsically Green and against waste, and propagating its understanding is one of the very biggest things we can do to confront such emergencies.

    15. Ikonoclast says:

      Some Guy, I take your points and agree with some but not all.

      “Nobody thinks that the earth’s human population or resource usage can grow indefinitely.” This should be re-worded as “Nobody sensible thinks that the earth’s human population or resource usage can grow indefinitely.” There are indeed many people, probably the majority of both economists and people, who act, in practice, as if they believe earth’s human population and resource usage can grow indefinitely. Indeed, that is the way our entire system works. I would argue that acting in an operative way in this manner either constitutes the belief or renders contrary belief moot.

      In terms of waste (of both human potential and natural resources) yes the wastefulness of the current capitalist system is immense. MMT prescriptions would greatly assist. I think we need to go further and realise capitalism is the problem. Capitalism IS the crisis! The faults of this system, the unemployment, the waste, the environmental destruction are all inherent in capitalism, they are capitalism. The problems cannot be removed without removing capitalism itself.

    16. Neil Wilson says:

      “Are you saying you believe endless growth is possible in a finite system?”

      Are you saying you’d rather rely upon the logical fallacy of excluded middle arguments, than actually confront the fact that you have a belief problem?

    17. Jeff Everitt says:

      Ikonoclast,

      I can’t figure out if you’re more on the side of Technocrats or Primitivists. I get what you’re saying, I really do, but you have to realise that things like ending capitalism can’t work until we devise a non-coercive method of distributing scarce resources, because as much as I hate to admit it, the market system is still the least destructive for the corner of economics where “products” are still inherently or otherwise severely limited in quantity.

      It IT stupid, however, that most of the market-driven world DELIBERATELY creates artificial scarcity and severe waste just to keep “the system” going. Without causing all-out unrest, how do we rapidly transition? How do we get past the largest obstacle, that is, people’s unwillingness to embrace change (even if it will benefit them and everyone they know)?

    18. Ikonoclast says:

      “Side? I am on nobody’s side. Because nobody is on my side…” – Treebeard.

      I am merely on the side of objectivity: materialism and empiricism. The scientists of various fields, who have studied climate change, species extinctions, environmental destruction, natural cycles, global footprint analysis and limits to growth all concur, at least implicitly. The results of their work all point to one fact. We are approaching the end-point of growth of the industrial-economic system. This is a near point now (within one generation) not some distant point in the far future where science denialists wish and believe it to be.

      I would be on the side of a steady-state, clean technology economy if it could be achieved. I simply doubt that it can be achieved now because of;

      1. the damage we have already done to the biosphere;
      2. our advanced stage of overshoot;
      3. the entrenched nature of the capitalist system;
      4. the nexus between “offensive realism” and industrial capitalism.

      Point 4 has to do with militarism, geostrategy and economic systems. It would take me too far away from “mere” economics to discuss it.

      Your implicit characterisation of capitalism as “a non-coercive method of distributing scarce resources” is completely flawed. Capitalism is coercive and exploitative at all levels. The money or finance system, along with the ownership system constitute a powerful overall control system. Where this system alone does not suffice, the monopoly power of the capitalist state (police, criminal justice system and army) is deployed to control the citizen.

      The main problem now with capitalism, with respect to the climate emergency and limits to growth emergency, is that capitalism is predicated on endless growth. It is also predicated on ignoring negative externalities, that is ignoring and not costing the damage it does to the environment. Is it not ironic that at the very moment when we should be conserving resources and seeking renewable paths, capitalism is promoting more consumerism, more built-in obsolesence, the throw away culture, yearly fashion changes in everything from clothes to cars and so on? Capitalism is also funding the propaganda campaigns of denialism; denying climate change and denying the limits to growth. Capitalism is clearly grossly maladaptive at this stage in our history.

      The best ideas for transitioning from capitalism at this stage probably come from David Harvey and Richard Wolff. Both of these intellectuals are Marxists. (Although, I am not sure that either of them realise just how critical and near are our approaching crises of climate change and limits to growth.) Rather than try to summarise their ideas I would point you to searching for them, their essay and their videos on the net.

    19. Robert says:

      How would profit be made in a steady-state economy?

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