The Theory of Capital
At the end of the academic year, Samuelson’s second article was published, not on consumer theory but on “Some Aspects of the Pure Theory of Capital.”52 The theory of capital was a widely discussed topic in the 1930s, mainly because of its use by Friedrich Hayek to provide an explanation of the Great Depression.53 Hayek, a prominent opponent of Keynes in 1930, blamed the business cycle on over-expansionary monetary policy, but he used a theory about capital and production to explain why a downturn would trigger dislocation and unemployment, rather than simply a fall in prices.
His idea was that low interest rates during the boom would induce businesses to invest in excessively capital-intensive methods of production; when interest rates eventually rose and the downturn took place, business would find itself saddled with production processes that were no longer profitable and would shut them down. Depression and unemployment would persist because it would take time to organize new, less capital-intensive production processes that could be profitable at higher interest rates.While Hayek was the main proponent of such views, taking a hard line on measures to alleviate the slump, this view was held by many others as well; traces of it can be found, to varying degrees, in both Hansen’s and, as has already been seen, Schumpeter’s analyses of the cycle. Significantly for Samuelson, the theory of capital was one of the subjects on which his Chicago idol, Frank Knight, had written extensively, challenging Hayek’s claim that the capital stock could be represented by a single magnitude, the “period of production”—the average time between investing in a project and obtaining a return.u The theory of capital was also central to the theory of the rate of interest, about which Knight and Schumpeter took opposing positions.
February 1937, implying that it had probably been written before the exchange with Haberler took place, given that the pure theory of trade was covered at the end of the course.
u. An example of a “short” period of production would be using workers’ shovels to build a canal. A longer process of production would involve first making mechanical diggers and then using these to dig the canal. An even longer process of production might involve designing and building machine tools that are used to make mechanical diggers, Given that two of his most important teachers were arguing about the topic, Samuelson could hardly avoid becoming involved.
However, Samuelson did not get into the larger literature on the theory of capital, despite alluding to its existence. Instead, he tackled a more isolated problem in pure theory: the objectives that should be pursued by a single company undertaking investment. His starting point was not Hayek, or any of those who were using capital theory to argue about the business cycle, but an article by a relatively unknown economist just five years older than himself, Kenneth Boulding (1910—1993). Boulding was British, graduating from Oxford in 1931. After a year of graduate work in Oxford, he went to Chicago for two years on a Commonwealth Fellowship, spending the fall of 1933 at Harvard working with Schumpeter.54 He met and engaged with Knight. Samuelson was there, but there is no reason to think they met.
Boulding's aim in “The Theory of a Single Investment” (1935) was to extend the theory of the company to decisions taking place over time. He pointed out that the theory of profit maximization could be applied to any activity defined by a single income account. This could be an entire company or an activity within a company; if there was a single account (even if a notional one) through which all receipts and payments passed, then this account could be treated as a single investment, to which the theory of profit maximization could be applied.
Boulding abstracted from uncertainty and argued that the rational, farsighted investor should invest so as to maximize the internal rate of return on the investment. The internal rate of return was the rate of discount at which the present value of the inputs equals the present value of the outputs. Using this result, he derived dynamic equivalents of the static condition that marginal cost equals marginal revenue.[21] [22]Samuelson took up Boulding's device of the single investment account, but worked out the mathematics for more general assumptions. He assumed that the time path of income and expenditure flows might have any pattern rather than the simple case assumed by Boulding, that interest might be compounded continuously or at the end of each period, and that the rate of interest might vary over time. One result of this was that the internal rate of return might not exist or it might not be unique (there might be multiple rates of interest at which the net present value of the investment was zero). Samuelson then introduced the market rate of interest to argue that Boulding's conclusion, that the firm should maximize the internal rate of return, was incorrect. Instead,
Given an interest rate at which all can lend or borrow... each entrepreneur will select that value of the variable under control which maximizes the present value of the investment account, the present value being computed by capitalization of the income stream at the market rate of interest.55
This was, as he pointed out, a well-known result. Boulding, he claimed, had assumed rather than demonstrated his result.
What Samuelson was doing in this paper formed part of an emerging pattern. He was employing more advanced mathematics than was currently being used—mathematics he had learned from Wilson (he cited both Wilson's Advanced Calculus and the textbook by Whittaker and Robinson that Wilson had recommended)—and as a result he was able to analyze a more general case, thereby reducing what he believed to be confusion in the literature.56 In other words, he was saying that Boulding had a good idea, but that it needed to be tackled using more advanced mathematical techniques.
In taking on Boulding, he was tackling someone whose views had been criticized by Knight, and Samuelson may have had Knight in mind when noting that the internal rate of return might not be unique, even if it existed.57 Moreover, though the paper focused on Boulding, Samuelson also took aim at a bigger target, John Maynard Keynes. The General Theory included a chapter on “own rates of interest.” These were rates of interest calculated in terms of different commodities. In an appendix to his paper, Samuelson argued that Keynes's statements about own rates of interest were completely misconceived, for it made no difference which of these many rates were used; the investment policy that maximized the value of an investment in terms of money would maximize its value in terms of any other commodity. This was another example of Samuelson's removing confusion from the literature by raising the level of mathematical analysis being used. It also provides evidence of Samuelson's sympathy with Knight's ideas and his taking a critical stance toward Keynes.
More on the topic The Theory of Capital:
- Schooling Investments and Returns to Education
- In this chapter, we will discuss human capital investments and the role of human capital in economic growth and in cross-country income differences.
- Conclusion
- THE THEORY AND PRACTICE OF EMPIRE-BUILDING
- The New Stylized Facts of Economic Growth
- Conflict Face Negotiation Theory
- MichalKalecki
- Human Capital Externalities
- Convergence with a Cobb-Douglas Production Function
- CHAPTER SUMMARY