Roy Forbes Harrod (1900-1978)

Harrod was born in Norfolk on the 13 February 1900 to Henry Dawes Harrod, businessman, and his wife Frances (nee Forbes-Robertson), novelist. Following the ruin of his father’s business, Harrod won a scholarship to go up to St Paul’s, leaving two years later to enter Westminster as a King’s Scholar.

In 1919, he began studies in philosophy and modern history at Oxford, which led him in 1922 to take up a Tutorial Fellowship at Christ Church. In order to learn more about economics, Harrod was allowed to spend his first term at Cambridge where he took weekly essays on money and international trade to John Maynard Keynes. Once back at Oxford, he attended Francis Y. Edgeworth’s lectures on microeconomics. In the early 1930s Harrod came to grips with the theories of imperfect competition developed by Edward Chamberlin and Joan Robinson (Harrod 1934). Meanwhile, drawn into the Circus - a group of young economists involved in the elaboration of Keynes’s General Theory - he got deep insight into Keynesian economics (Eltis 2008). In 1936, drawing on both his microeconomic and macroeconomic backgrounds, he published his first book, The Trade Cycle (1936), in which he laid out for the first time the analytical foundations for the multiplier-accelerator model. This book, as well as “An essay in dynamic theory” (1939), marks an important step in the history of macroeconomics. Here, Harrod set the research agenda of the post-war work on economic dynamics.

His work on the theory of the firm occupied a good deal of his attention in the postwar decades. As part of the Oxford Economists’ Research Group, Harrod took a great interest in how firms set their prices by adding a margin they consider satisfactory to their average or “full” cost of production. In addition, throughout his academic career he published extensively on international monetary theory and economic policies.

Meanwhile, he had also published major works on philosophy. In his Foundations of Inductive Logic (1956) - which he regarded as his greatest achievement - he claimed that inductive arguments could be given a rational basis.

Imperfect Competition, Income Distribution and the Trade Cycle

Harrod’s argument for resorting to imperfect competition had two strands. The first was an explanation why, under increasing returns, the equilibrium approach was well suited for explaining fluctuations. Under decreasing marginal costs, there exists a multiplicity of long period equilibriums. Because any equilibrium is determined by correct producer’s expectations, any sudden revision of expectations will lead the economy to a new equilibrium position. Waves of optimism and pessimism may thus explain how the economy moves from low to high equilibrium outputs and vice versa. The second was an explanation of the behaviour of costs relative to prices during business cycles. Harrod’s point of departure was Keynes’s advocacy for public spending. Keynes made two important assumptions. First, he assumed imperfect competition in the product markets, admitting that the degree of competition in the economy can be taken as given. Second, he supposed that there was a decreasing short-run marginal product of labour. Along these lines, Keynes concluded that there existed an inverse relation between real wages and output. For that reason, Harrod thought that Keynes’s policies could cause inflationary conditions by generating demands for money-wage rises to offset falling real wages, which were likely to justify reversing the policy before much headway had been made in reducing unemployment. If, however, increasing return prevails, as long as the degree of competition remains unchanged, Keynesian policies could be implemented without bearing the risk of rising inflation and being interrupted prematurely.

Despite the effect of decreasing costs, Harrod was convinced that there existed an inverse relation between the real wage and output.

His argument relies on what he called the “law of diminishing elasticity of demand”, implying that the degree of monopoly increases in the upswing and falls in the downswing. He thought that in the upswing, the rise in the mark-up will dominate the fall in real cost, entailing what he called a “shift to profit”, that is to say a change in income distribution in favour of profit earners. Since profit earners save a greater proportion of their income than workers, this results in an increased propensity to save by the whole community. Jointly with other factors, such an evolution was likely to play a critical role in dynamics.

Instability, Cycles and Growth

Harrod’s works on dynamics are based on the concepts of natural growth, warranted growth and actual growth. The natural growth is the rate required to maintain full employment. The warranted rate of growth is

the rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount. Or, to state the matter otherwise, it will put them into a frame of mind which will cause them to give such additional orders as will maintain the same rate of growth. (Harrod 1939: 16)

This results from the interaction of the multiplier and the accelerator. The multiplier determines by how much income increases as a consequence of an increase in investment, depending on the proportion of income saved s; the accelerator, or “the relation” as he called it, determines how many units of capital, C, are needed to produce an extra unit of output, given the state of technology and the rate of interest. Each of these relations feeds on the other: if actual demand exceeds anticipated demand, firms would have underinvested and would respond by increasing investment. This would itself cause actual growth rate to rise, requiring even further investment.

Harrod explored the consequences of a divergence both between the warranted and natural rates and the actual and warranted rates.

The problem, in accordance with the “principle of instability”, was that anything that would make the warranted rate move towards the natural rate would also drag along with it a fall in the actual rate. Suppose the warranted rate rises towards the natural rate. If entrepreneurs continue to expect the same rate of growth (equal to the previous and smaller value of the warranted rate), the actual rate of growth will actually be smaller, so that the actual and warranted rates of growth will move in opposite directions. It is only because the parameters determining the warranted rate will change that this cumulative movement will be reversed. Harrod’s point was that a falling actual growth rate resulting from variations in income distribution, the saving rate or in the capital coefficient, will ultimately reduce the warranted rate to the point of making it lower than the actual rate of growth. A process of cumulative expansion will then start and a phase of expansion will take place. However, as soon as the actual rate reaches its natural limit the warranted rate will eventually grow larger. Once this happens, a reverse cumulative movement is set in motion. In this respect, Harrod’s dynamics strongly differ from Solow’s (1956) or Kaldor’s (1957) growth models. While the former focused exclusively on the adjustments of the warranted (assumed equal to the actual rate) and natural rate, Harrod was equally concerned with the adjustment between the actual and warranted rates. This explains partly why, in Harrod’s theory, the non-linear character of the investment and saving functions resulting from changes in the saving rate and the capital coefficients are supposed to produce both cycles and growth (Besomi 2001: 82). Unfortunately, although noticed by most of his contemporaries (Sember 2010), this important aspect of Harrod’s theory remained largely ignored in subsequent interpretations.

Michael Assous

Roy Forbes Harrod (1900-1978)

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