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 homepage – 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]
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.
The Saturday Quiz will be back again tomorrow. It will be of an appropriate order of difficulty (-:
That is enough for today!
(c) Copyright 2013 Bill Mitchell. All Rights Reserved.