"If costs are stated in terms of alternative commodities and all reference either to "sacrifice" or "outlays" simply omitted, we retain the scientific content of cost of production theory while side-tracking the sources of a century and a half of controversy."
(Frank H. Knight, Journal of Political Economy, 1928: p.355).
(A) Opportunity Cost
(B) The Austrian-Marshallian Debate
(A) Opportunity Cost
Philip H. Wicksteed's (1910, 1914) depiction of "demand-and-supply" in pure exchange was geared to demonstrate the supremacy of the Austrian alternative cost (or opportunity cost or displacement cost) doctrine over the Marshallian real cost (or disutility cost or pain cost) doctrine.
The concept of opportunity cost can be found in the works of many early economists (e.g. J.H. von ThEen, 1823; J.S. Mill, 1848; and, most notably, L. Walras, 1874), yet the opportunity cost doctrine was only explicitly introduced as an all-encompassing theory of cost in a seminar paper by Friedrich von Wieser (1876) and expounded in his later books (Wieser, 1884, 1889). It was quickly embraced by fellow Austrian economists such as Eugen von Böhm-Bawerk (1889, 1894), Paul Rosenstein-Rodan (1927) and, notably, Gottfried von Haberler (1930, 1933). The alternative cost doctrine was popularized in the English-speaking world by D.L. Green (1894), Frank A. Fetter (1904), Herbert J. Davenport (1908, 1913), Philip H. Wicksteed (1910, 1914), Frank H. Knight (1921, 1928) and Lionel Robbins (1930, 1932, 1934).
The Austrian opportunity cost doctrine is simple enough to explain: it boils down to claiming that relative prices reflect foregone opportunities. In terms of pure exchange, this is easy: for agent h, the cost of demanding D 1h units of good x1 is the offer of O2h units of good x2 he has to make. Thus, the price of good x1 in terms of x2 is the amount of good x2 that has to be offered (and thus foregone) to obtain a unit of good x1, i.e.
p1/p2 = O2h/D1h
So, for example, if to obtain 5 units of good x1, agent h needs to give up 15 units of good x2, then the price of good x1 in terms of x2 is 3. As market prices reflect the trade-off between goods a consumer faces, then perhaps we can be a bit more precise by analyzing it at the infinitesimal margin rather than taking clunky increments of net demands and offers. Doing so, we will find it is more convenient to simply write that, at the margin:
p1/p2 = -dx2h/dx1h
where dx1 is an infinitesimal net demand for good x1 and -dx2 is the corresponding offer. This was baptized by John Hicks (1939) as as the marginal rate of substitution between x1 and x2 The rest is well-known: the hedonistic, rational consumer will choose net demand and offers where -dx2h/dx1h = u1h/u2h, where u1h = ¶uh /¶x1 is the marginal is the marginal utility of good x1h and u2h = ¶ uh/¶ x2h is the marginal utility of good x2. So:
"The ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degrees of utility [i.e. ratio of marginal utilities] of the quantities of the commodity available for consumption after exchange is completed."
(W.S. Jevons, 1871: p.95).
This has been baptized by Maffeo Pantaleoni (1889: p.184) as "Wieser's Law".
All this is well-known and pretty much accepted by all modern Neoclassical economists. Why the fuss? The fuss arises when we consider the opportunity cost principle in the context of production. Suppose we have two goods, x1 and x2, but only one factor (call it v). Suppose that a unit of the factor can produce a unit of good x1, while a unit of the factor can produce two units of good x2. Consequently, in order to produce one unit of good x1, one foregoes the production of two units of x2; simlarly, to produce one unit of x2, one foregoes a half-unit of x1. Thus, in opportunity cost terms, x1 = 2x2 and x2 = x1/2. If prices must equal opportunity cost, then notice that it must be that p1/p2 = 2.
Now, suppose output prices such that p1/p2 = 3, i.e. a unit of x1 sells for 3 units of x2. In this case, a smart agent would try to produce an enormous amount of x1 and exchange it all for x2. For each unit of x1 produced, he receives 3 units of x3, thus he makes a "profit" of one unit of x3. Conversely, a stupid agent who specialized in the production of x2, would need to produce three units of x2 in order to acquire a unit of x1. Yet, if he simply modified his production process and produced the other good instead, he would be able to obtain 1.5 units of x1 by producing it using the same factors it would take to acquire 1 unit of x1 on the market. Thus, if output price ratio p1/p2 is greater than the opportunity cost of good x1 in terms of x2, then we would expect everyone to produce x1 and nobody to produce x2. Similarly, if p1/p2 is less than the opportunity cost, we would expect nobody to produce x1 and everybody to produce x2.
There might be a slight twinge in the heart of a true Neoclassical: it seems as if prices are determined "objectively" by opportunity costs; where does subjective things like utility and thus demand come into play as the determinant of price? The truth of the matter is that we have not necessarily established that output prices must equal opportunity costs in our example. In order to obtain price-opportunity cost equality, we must actually go to a wider example, one which uses at least two different factors (e.g. capital and labor) in the production of both goods x1 and x2.
To see why, consider Figure 1, where have drawn two production possibilities frontiers, PPF (straight line) and PPF¢ (bowed out from the origin) (the production possibility frontier is originally due to Abba Lerner (1932) and Gottfried von Haberler (1933: p.176)). The bowed-out shape of PPF¢ reflects the fact that the proportion in which factors are released when reducing the production of good x1 are different from the proportions in which they are absorbed when increasing the production of good x2. In our earlier example, there was only one factor (v), and two outputs. Thus, when moving from the production of x1 to x2, the factor was absorbed in the same proportion as it was released, thus the relevant production possibilities frontier would be the linear PPF in Figure 1.
Fig.1 - Production Possibilities Frontiers
The slope of any PPF is the opportunity cost of x1 in terms of x2. In the linear case of only one factor, the slope is constant -- in our example, simply -2. Thus, the linear case which is obtained when we have only one factor and two outputs is often referred to as the constant cost case.
In the concave PPF¢ case, the opportunity cost changes as we change combinations of x1 and x2 produced. Specifically, the concave shape of PPF¢ indicates that the more that is produced of good x1, the more and more we have to give up of x2, i.e. the greater the opportunity cost of x1 in terms of x2. Intuitively, this reflects, as Joan Robinson aptly put it, that "an increase in the output of any commodity turns the relative factor prices against itself" (Robinson, 1941). In a general context, if x1 is relatively intensive in capital and x2 is labor intensive, then as we move towards greater output of x1 and less of x2 (e.g. points e to f in Figure 1), the tighter the capital market becomes and the looser the labor market gets. Thus, as we increase x1 the price of capital rises relative to labor so that it becomes costlier and costlier to produce more x1.
We can now see where demand begins to play a role. Consider first the linear case. Suppose conditions in the output market are such that p1/p2 = 2 is the output price. In this case, the entire linear PPF locus denotes the output combinations of x1 and x2 that will ensue. In other words, positions c = (x1c, x2e) and d = (x1d, x2f) in Figure 2 are equally possible. Obviously, then, the output level is indeterminate.
If, however, output prices are such that p1/p2 > 2, then we have determinacy of an extreme sort: we will go to the corner solution x1m, where all factors are dedicated to the production of x1 and none for x2. If p1/p2 < 2, we go to the other corner, x2m, and produce nothing of x1 and as much as possible of x2. These extremities were already alluded to earlier in our earlier linear example. Note that in these extreme cases, prices are not necessarily equal to costs.
The linear or constant cost case reflects exactly Adam Smith's famous example in his Wealth of Nations:
"If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day's or one hour's labour."
(A. Smith , 1776: p.65).
Notice the crucial importance that Smith's example has two outputs (beaver and deer) and one input (labor), thus implying that we must necessarily have a linear PPF as in Figure 1. As insisted by Knight (1928), Smith's argument that exchange values reflect relative labor costs can be reintrepreted in opportunity cost terms: a deer is worth two beaver not because of the fact that labor is involved, but rather because the cost of catching a deer were the two beavers that could be alternatively caught: "the cost of beaver is deer and the cost of deer is beaver, and that is the only objective and scientific content of the cost notion". (F.H. Knight, 1928).
Smith's assertion that prices equal relative labor costs (or, in Knightian interpretation, opportunity costs), implies that he is ruling out the corner solutions x1m and x2m in Figure 1, and thus the only thing that remains is that p1/p2 = 2, thus making demand irrelevant for the determination of prices. In such a case, prices are completely determined by the "objective" relative costs of production of beaver and deer. Note that, in this case, relative output levels are indeterminate, or rather must be determined by something else - exactly as the Classical theory argues they should be.
Suppose, however, that we have two inputs and two outputs, so that we obtain the concave PPF¢ in Figure 1. If prices are (p1/p2)*, then the price line will be tangent to PPF¢ at point e = (x1e, x2e). Equivalently, if prices are (p1/p2)¢ , then the price line will be tangent to PPF¢ at point f = (x1f, x2f). These are, in fact, the only efficient combinations of outputs corresponding to the relevant price ratio. Thus, output price are equal to opportunity costs, and yet utility-based demand, which helps determine output price, is really the main determinant of everything. Thus, Wieser's "Neoclassical" twist on the old Smithian cost theory seems to reduce itself to changing the technology of the system.
Why would we necessarily produce at e in Figure 1 if prices were (p1/p2)*? Suppose not. Suppose we chose f instead at those prices. If so, then output prices are lower than the opportunity cost of x1 in terms of x2 implied by the slope of PPF¢ at point f¢ . This would lead to the kind of instability we saw earlier: people would move away from the production of x1 and towards the production of x2, i.e. driving us right back up the PPF¢ curve to point e.
In sum, when viewed from the prism of opportunity costs, output prices must equal opportunity costs and thus it seems as if prices are governed by the "objective" phenomena of opportunity cost. But a more careful look indicates that it is demand, with its influence on output prices, that determines which opportunity costs are to prevail. Thus, prices and outputs, everything else are subjectively determined. In short, the opportunity cost doctrine is an "objective theory of value which is subjective". We find this stated clearly in Wieser:
"The phenomena of [alternative] costs are, therefore, a new proof of how greatly the objective conditions of the existence of goods influence the value of goods. How far the value of goods, in its final form of "cost value", is from being the mirror of that subjective fact from which it is derived -- the value of wants! The circumstance that cognate products are produced by different quantities of the same productive elements, brings their subjective valuations into a ratio, the terms of which are derived entirely from the objective conditions of production; while the impulses which call for their emergence...remain subjective, and thus prove the subjectivity of the source and nature of value."
(F. von Wieser, 1889: p.185)
and even more clearly in Knight:
"When any two commodities can be produced with the aid of the same resources of whatever sort, freely transferable from one use to the other, the prices of those commodities must in equilibrium be such that the alternative products of the same or equal units of resources exchange for each other. Price is determined by cost rather than utility, but by cost in a physical technical sense, not that of pain or sacrifice...Comparisons of sacrifice, however, may be and commonly are involved in greater or lesser degree, and the operation of the utility principle is the basis of the whole process of adjustment. This is the alternative cost theory which is definitely the product of the utility approach."
(F.H. Knight, 1931)
What about factors of production? These are governed by the Austrian principle of imputation (due to Carl Menger (1871) and Friedrich von Wieser (1889)): given output prices, we can determine what the factor prices will be. More specifically, a given point on the production possibilities curve will determine a particular division of factors between industries which, in turn, will determine the proportional factor prices (for a demonstration of this, see our survey of Paretian general equilibrium theory).
One can go on with the exploitation of opportunity cost idea. As demonstrated famously by Gottfried von Haberler (1933), the principle of comparative advantage in international trade can be couched in opportunity cost terms. To see this consider the following simple linear example. Suppose there are two agents (A and B), each of which is endowed with an hour of labor which can be spent either on rabbit-hunting or deer-hunting. In one hour, A can catch 5 rabbits or 1 deer while B can catch 20 rabbits or 2 deer (they can do a little bit of both, but they each only have an hour to spend). Notice that B is more efficient at catching both rabbits and deer than A is, thus B has an absolute advantage in the production of both goods. The opportunity costs faced by agent A are easily computed: the opportunity cost of a deer is 5 rabbits, or, equivalently, the opportunity cost of a rabbit is 1/5 of a deer. For agent B, the opportunity cost of deer is 10 rabbits or, conversely, the opportunity cost of rabbit is 1/10 of a deer.
Haberler argues that an agent has a comparative advantage in a good if he has a lower opportunity cost in that good. In this example, as is obvious, agent A has a lower opportunity cost (and thus a comparative advantage) of catching deer, while B has a lower opportunity cost (and thus a comparative advantage) of catching rabbits (in general, in any two-good, two-agent scenario, it will always be the case that if one agent has a lower opportunity cost in one thing, the other agent will necessarily have a lower opportunity cost in the other).
Consequently, if specialization is to ensue according to the principle of comparative advantage, agent B should dedicate her entire hour to catching rabbits (20 of them), while agent A should dedicate his hour to catching deer (1 of them). They can then trade. Suppose B offers A six rabbits in exchange for the entire deer A has caught: such an offer can be made by B and will be accepted by A because both will better off as a result. To see this, note that after trading, A will have six rabbits (while before the trade, the best he could do was 5 rabbits). In contrast, after trading, B will have 1 deer and 14 rabbits (before trade, the best she could do was 1 deer and 10 rabbits). Thus, after specializing and trading, A is better off by a rabbit while B is better off by four rabbits.
(B) The Austrian-Marshallian Debate
Alfred Marshall was a compromiser: he did not consider the Marginalist Revolution of 1871-4 to be a complete repudiation of the Classical doctrines of Smith, Ricardo and Mill. Instead, Marshall believed in the continuity between Classical and Neoclassical economics; that both theories, in the end, agreed that equilibrium prices were determined by demand and supply, but that each of them had been too "one-sided" about it. In particular, Marshall (1890: App.I) argued that the sole fault of the Classicals was that they concentrated too much on supply as a determinant of price and thus tended to ignore or understate the role of demand; in contrast, the fault of William Stanley Jevons and other Marginalists was that they concentrated far too much on demand and had ignored supply. Thus, he goes on to conclude, the Marginalist Revolution is less revolutionary that it makes itself seem: supply is determined by cost of production in the Ricardian fashion, demand is determined by utility in the Jevonian fashion, place both together and we have the determination of equilibrium price. As Marshall famously writes:
"We might as reasonably dispute whether it is the upper or the lower blade of a pair of scissors that cuts a piece of paper, as whether value is governed by utility or cost of production. It is true that when one blade is held still, and the cutting is effected by moving the other, we may say with careless brevity that the cutting is done by the second; but the statement is not strictly accurate, and is to be excused only so long as it claims to be merely a popular and not a strictly scientific account of what happens."
(A. Marshall, 1890: p.290)
The fact that Marshall was English and that the Marginalist Revolution was largely of Continental derivation may have had something to do with his reluctance to abandon the English Classical tradition. The convese fact that the Austrians were Continental Europeans may also have had something to do with their keen interest in debunking Ricardo and Mill. Whatever the reason, Marshallians and Austrians came to loggerheads over the "ultimate" determinant of value.
The Austrians and their allies did not dispute that there were "two blades to the scissors" in the determination of price in any one market; instead, they disputed Marshall's assertion that supply was determined by "cost of production". As Wicksteed (1910, 1914) so clearly demonstrated, viewed from the prism of opportunity cost, "supply is reverse demand". Thus:
"The only sense, then, in which cost of production can affect the value of one thing, is the sense in which it is itself the value of another thing. Thus, what has been variously termed "utility", "ophelimity", or "desiredness", is the sole and ultimate determinant of all exchange values"
(P.H. Wicksteed, 1910: p.391).
The Marshallians, notably Francis Y. Edgeworth (1894) and Jacob Viner (1932, 1937) took exception to the assertion that all cost was opportunity cost. What they noted was in fact, quite simple: if to acquire anything, one must "give up" something else, then we are effectively implying that there is ultimately a "fixed" amount of everything. But this, the Marshallians noted, is not necessarily true. Resources, they argued, can be regarded as fixed "in the short-run". But in the "longer run", more resources can be made available. For instance, capital may be built; labor can be increased, etc.
A great amount of ink was spent particularly on labor supply. Labor supply, the Marshallians claimed, was rather flexible. Increase the payments to labor, and "more" would be supplied. Consider the production of, say, scissors. As the output of scissors increases, costs of production increase because higher wages must be paid to labor to induce them to increase their supply. These are not, the Marshallians asserted, "opportunity costs", but "real costs": they compensate laborers for the "disutility" of work (a concept originally introduced by Jevons (1871: Ch. Ch.5)).
The Austrians were not caught off-guard by these examples. The resolution to the "alternative cost" vs. "real cost" dispute is readily apparent: what is the "disutility of labor" other than "displaced leisure"? Labor supply may be flexible, but time is fixed and so the worker must choose between work and leisure. Wages are paid not because producers must compensate workes for the "irksomeness" of labor, but rather because they must compensate laborers for foregoing leisure. Thus, Marshallian real costs are reducible to Austrian opportunity costs.
[Note: in a moment of doubt, Frank Knight (1934) poses the question whether opportunity cost captures the idea that wages in agreeable jobs are lower than wages in irksome jobs? The resolution here is even simpler if we consider the jobs and their irksomeness/agreeableness to be joint goods: the higher wages paid to the laborer in the "irksome job" does not compensate for greater disutility of that job, but rather for the displaced "agreeable job".]
[Another note: the alternative cost-real cost debate flared up with particular vehemence in international trade theory, pitting the Austrian economist Gottfried von Haberler (1930, 1933: Ch. 12; 1951) versus real-cost advocate Jacob Viner (1932, 1937: Ch. 7), and seems to have lingered on for a while in that area. For a modern restatement and resolution in this context see Vanek (1959).]
In reducing the Marshallian examples of real costs to opportunity costs, the Austrians may seem to have won the upper hand, but they were forced to admit one thing: namely, that in the end, for this reduction to be possible, one must impose the assumption that something is fixed in availability which cannot be increased. In our labor example, time was fixed; if time was "extendable" by some way or another, the opportunity cost doctrine would collapse once again. Thus, the Austrians recognized that for the opportunity cost doctrine to work, there must always be a fixed stock of everything.
In sum, with their examples, the Marshallians demonstrated time and time again that the opportunity cost doctrine relies on fixed resources. As such, the Marshallians crowed that the opportunity cost doctrine must necessarily be a "special case". When resources are fixed, then indeed "the ultimate standard of value", to use Böhm-Bawerk's term, is opportunity cost, but when resources are flexible, they argued, Marshallian theory comes into its own.
We find some proponents of the alternative cost doctrine, such as Frank H. Knight (1934) and Lionel Robbins (1930, 1934), a bit troubled by the prospect of flexible resources. In terms of our earlier Figure 1, what will be the prices when the PPF is allowed to move around? However, their resolution was not to rethink the theory of costs to accommodate flexible resources but rather to claim that any economic problem is always ultimately characterized by fixed resources. This was particularly emphasized by Lionel Robbins in his famous Essay on the Nature and Significance of Economic Science (1932). Economics, he insisted, is exclusively concerned with scarcity: "Economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses." (Robbins, 1932: p.16).
Robbins's limitation of the scope of economics to the issue of allocation of fixed resouces was a wildly successful coup and summarized quite well the full meaning of the Marginalist Revolution. Value, as Jevons, Walras, Menger and virtually every Neoclassical since has asserted, derives from scarcity and scarcity cannot arise unless resources are fixed in one way or another. The entire Walrasian-Paretian general equilibrium edifice clearly stands only (and thus perhaps uneasily) on this concept. Of course, the Marginalists also noted that it is not enough that something is fixed in availability in order to have value; it must also be desired, i.e. scarcity is subjective. If value is derived from scarcity, then value is merely "the phenomena of demand acting on fixed stocks -- either of products, or factors or time -- or human capacity." (Robbins, 1933).
It is evident that Robbins's reasoning is a bit circular. He claims that if something is not scarce, it does not have value and thus is not an economic concern. Thus, economics necessarily deals only with the allocation of fixed resources. However, we only obtain the conclusion that value derives from scarcity if we assume there are fixed resources. But the Classical economists - Smith, Ricardo, Mill, etc. - would dispute this vehemently. For Classicals, at least since Cantillon, economics is about finding the rates of exchange between goods and the division of income between factors such that the economy can maintain a balanced circulation of goods and incomes. This is not about the "allocation of fixed resources": in Classical economics, all resources (labor and capital) are endogenous and thus not scarce over time. Yet the absence of scarcity does not stop the Classicals from deriving the "value" of goods quite explicitly, as was demonstrated with remarkable virtuosity by Piero Sraffa (1960).
In sum, the alternative cost-real cost dispute between the Austrians and Marshallians can only be said to have been resolved in favor of the Austrians if the basic premise of the Marginalist Revolution, that value derives from scarcity, is held to be true. Thus, the main contribution of the alternative cost debate was that it clarified what was the essence of the Marginalist Revolution of 1871-4 and to re-assert its fundamental message: that value is subjective (i.e. derived from scarcity) and not objective (i.e. from the need to maintain balanced circulation). Viewed from this vantage point, Marshall's musings are somewhat misleading: yes, Virginia, there was a Marginalist Revolution and it was very revolutionary indeed.
[Note: some commentators (e.g. Robbins, 1930) have argued that, underneath it all, Alfred Marshall held a theory of value which is closer in spirit to the Classical notion of balanced circulation than the Neoclassical one of scarcity. If one did make the argument the Marshall's "long-run" theory (flexible resources) is Classical, while his "short-run" theory (fixed resources) is Neoclassical, one could plausibly argue that then demand-and-supply determine prices only in the short-run, and not the long-run. Yet this would immediately remove Marshall from the Neoclassical pantheon: the argument that supply-and-demand determine exchange values only in the short-run is not novel, but taken right out of Ricardo and Mill! More acute attempts to account for Marshall's theory of value without sacrificing his Neoclassical credentials are found in Ragnar Frisch (1950) and Peter Newman (1960).]
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