Editing Interest (section)

===<span id=classicalinterest>The classical theory of the interest rate</span>===
The classical theory was the work of a number of authors, including Turgot, [[David Ricardo|Ricardo]],{{refn|group=note|Isolated remarks in the chapters "Effects of accumulation on profits and interest" and "On currency and banks" in "Principles of political economy and taxation"}} [[Mountifort Longfield]],<ref>"Lectures on political economy", IX.</ref> [[John Stuart Mill|J. S. Mill]], and [[Irving Fisher]].<ref>"The rate of interest", 1907.</ref> It was strongly criticised by [[John Maynard Keynes|Keynes]]{{refn|group=note|"The general theory of employment, interest and money", especially the appendix to Chapter 14. Page numbers refer to the widely available edition published by Macmillan for the Royal Economic Society as part of Keynes's collected writings, which appear to correspond to those of the first edition.}} whose remarks nonetheless made a positive contribution to it.

Mill's theory is set out the chapter "Of the rate of interest" in his "Principles of political economy".{{refn|group=note|See also his chapters "Of the law of the increase of capital" and "Of profits"}} He says that the interest rate adjusts to maintain equilibrium between the demands for lending and borrowing.<ref>"Of the rate of interest", §1.</ref> Individuals lend in order to defer consumption or for the sake of the greater quantity they will be able to consume at a later date owing to interest earned. They borrow in order to anticipate consumption (whose relative desirability is reflected by the [[time value of money]]), but entrepreneurs also borrow to fund investment and governments borrow for their own reasons. The three sources of demand compete for loans.<ref>§2.</ref>

For entrepreneurial borrowing to be in equilibrium with lending:
<blockquote>The interest for money... is... regulated... by the rate of profits which can be made by the employment of capital...<ref>Ricardo, chapter "On currency and banks"</ref></blockquote>
Ricardo's and Mill's 'profit' is made more precise by the concept of the marginal efficiency of capital (the expression, though not the concept, is due to Keynes{{refn|group=note|Chapter 11 of The General Theory is titled "The Marginal Efficiency of Capital." [[Alfred Marshall|Marshall]] used the term ''marginal utility of capital'' and Fisher ''rate of return over cost''. Fisher also referred to it as representing the "investment opportunity side of interest theory".}}), which may be defined as the annual revenue which will be yielded by an extra increment of capital as a proportion of its cost. So the interest rate ''r'' in equilibrium will be equal to the marginal efficiency of capital ''r{{'}}''. Rather than work with ''r'' and ''r{{'}}'' as separate variables, we can assume that they are equal and let the single variable ''r'' denote their common value.

[[File:Millinterestrate.svg|thumb|Classical theory of the determination of the interest rate. The solid red curve in the diagram shows the desired level of saving ''s'' as a function of ''r'' for the current income ''y&#x0302;''.]]

The investment schedule ''i'' (''r'') shows how much investment is possible with a return of at least ''r''.{{refn|group=note|Keynes called this function the 'schedule of the marginal efficiency of capital' and also the 'investment demand schedule'.}} In a stationary economy it is likely to resemble the blue curve in the diagram, with a step shape arising from the assumption that opportunities to invest with yields greater than ''r&#x0302;'' have been largely exhausted while there is untapped scope to invest with a lower return.<ref name="Mill §3; Longfield">Mill §3; Longfield.</ref>

Saving is the excess of deferred over anticipated consumption, and its dependence on income is much as described by Keynes (see [[The General Theory of Employment, Interest and Money#bookiii|The General Theory]]), but in classical theory definitely an increasing function of ''r''. (The dependence of ''s'' on income ''y'' was not relevant to classical concerns prior to the development of theories of [[unemployment]].) The rate of interest is given by the intersection of the solid red saving curve with the blue investment schedule. But so long as the investment schedule is almost vertical, a change in income (leading in extreme cases to the broken red saving curve) will make little difference to the interest rate.

In some cases the analysis will be less simple. The introduction of a new technique, leading to demand for new forms of capital, will shift the step to the right and reduce its steepness.<ref name="Mill §3; Longfield"/> Or a sudden increase in the desire to anticipate consumption (perhaps through military spending in time of war) will absorb most available loans; the interest rate will increase and investment will be reduced to the amount whose return exceeds it.<ref>§3.</ref> This is illustrated by the dotted red saving curve.

====<span id=keynescriticisms>Keynes's criticisms</span>====
In the case of extraordinary spending in time of war the government may wish to borrow more than the public would be willing to lend at a normal interest rate. If the dotted red curve started negative and showed no tendency to increase with ''r'', then the government would be trying to buy what the public was unwilling to sell at any price. Keynes mentions this possibility as a point "which might, perhaps, have warned the classical school that something was wrong" (p.&nbsp;182).

He also remarks (on the same page) that the classical theory does not explain the usual supposition that "an increase in the quantity of money has a tendency to reduce the rate of interest, at any rate in the first instance".

Keynes's diagram of the investment schedule lacks the step shape which can be seen as part of the classical theory. He objects that
<blockquote>the functions used by classical theory... do not furnish material for a theory of the rate of interest; but they could be used to tell us... what the rate of interest will have to be, if the level of employment [which determines income] is maintained at a given figure.<ref>p181.</ref></blockquote>

Later (p.&nbsp;184) Keynes claims that "it involves a circular argument" to construct a theory of interest from the investment schedule since 
<blockquote>the 'marginal efficiency of capital' partly depends on the scale of current investment, and we must already know the rate of interest before we can calculate what this scale will be.</blockquote>