The Underlying Theory of Modern Orthodox Neoclassical Economics: Walras - Part 5

Now, as already indicated, Walras develops his theory of general equilibrium on the basis of these two parts of the ‘marginalist’ or ‘neoclassical’ picture of the market economy of capitalism in Jevons’s ‘mathematical’ theory of exchange and Menger’s ‘non-mathematical’ theory of production. However, as pointed out by Vivian Walsh and Harvey Gram, Walras does this for two reasons. The first is because they only sketched out the basic features of the two ‘[i]ndividual components’ (Walsh and Gram, 1980: 142) of the ‘marginalist’ or ‘neoclassical’ picture of the market economy of capitalism. The second is because they failed to present their theories within a more ‘complete system of general equilibrium’ (Walsh and Gram, 1980: 142), viz., one which shows the interrelationships between the consumers’ market and the resources’ market and how they might operate together in a more complete, general economic system. Despite these criticisms of Walras’s, he nevertheless, as I shall now show, develops his theory of general equilibrium on the basis of a pure exchange model (á la Jevons) without any use of social class categories (á la Jevons and, especially, Menger) in order to construct a theory about the allocation of ‘given resources’ which meet ‘consumers’ demand’.

I begin with some preliminary comments on Walras’s theory of general equilibrium as presented in his Elements of Pure Economics, or Theory of Social Wealth.

Central to Walras’s theory of general equilibrium is, as pointed out by Vivian Walsh and Harvey Gram, his concept of ‘scarcity (rareté)’ (1980: 143). Scarcity, according to Walras, refers to the ‘intrinsic value’ of something (like ‘land and its services’ for instance [Walsh & Gram, 1980: 143]): meaning, it has such a ‘value’ as the result of it possessing a particular ‘utility’ which is also of a ‘limited supply’ (Walsh & Gram, 1980: 143). In other words, if something of use which is desired by others is scarce because of its limited stock (meaning, in other words, that the scarcer something is, the more valuable, or desirable, or wanted it is), then it is deemed to have a ‘scarcity value’. So, if item X is scare because of its limited supply or stock, and it is something that most people want in order to produce item Y, then it will elicit or fetch a greater demand and therefore ‘scarcity value’ for it.

Now, as pointed out by Vivian Walsh and Harvey Gram (via the quotes of Arrow and Hahn in their text), Walras conceives the ‘“economic system”’ that he is investigating as being comprised of ‘“households and firms”’ (1980: 149). As such, he sees ‘“each household”’ as ‘“owning a set of resources”’, viz., ‘“commodities”’ which are ‘“useful in both production and consumption”’, especially, ‘“different kinds of labour”’ (Walsh & Gram, 1980: 149). Accordingly, for Walras, it is his position that for ‘“any given set of prices”’, any ‘“household”’ will derive a specific ‘“income from the sale of its resources”’, and, as a consequence of having this particular ‘“income”’, it will thus be able to ‘“choose among alternative bundles of consumer goods whose cost”’ in terms of their ‘“given prices”’ will not ‘“exceed the household’s income”’ (Walsh & Gram, 1980: 149). Thus, for Walras, this particular economic system, as outlined here by the quotes from Arrow and Hahn, describes a ‘general equilibrium system’ or economic state affairs in which the ‘given resources’ of the economic system is allocated in order to meet the demands of consumers, which are the households of the economic system (Walsh & Gram, 1980: 149).

As Vivian Walsh and Harvey Gram point out, Walras, like Jevons, begins with a model of pure exchange – meaning, there is no treatment of production. Walras does this in two stages: first, in terms of a simple model in which there are only two commodities or goods being exchanged amongst many traders; and secondly, in terms of an extended model in which there are many commodities or goods being exchanged amongst many traders. Once Walras has finished presenting his model of pure exchange in both these ways (viz., in terms of a simple and extended model of pure exchange), in which it is posited that all ‘trading parties’ are, as in the case of Jevons, endowed with ‘given stocks’ of exchangeable ‘goods’ (Walsh & Gram, 1980: 149), he then presents his ‘expanded model’ of production. (How these ‘trading parties’ come to have these ‘given stocks’ of ‘goods’ is not mentioned or discussed by Walras; they are just a ‘given’ in the model, something which we do not need to worry about.) In doing so, Walras’s aim is to show how it is that the commodities or ‘these goods are themselves produced by the exchange of the services of the given resources in return for claims to income’ (Walsh & Gram, 1980: 149). Thus, the model of production as developed by Walras is presented by him as a model of indirect exchange between the given resources or the factors of production and the commodities or goods in the consumers’ market. (This is, it is worth noting, the Mengerian aspect of Walras’s general equilibrium theory or model of a market economy, like capitalism. Furthermore, in presenting his model of production as an indirect form of exchange, Walras, like Menger, but unlike Marx, is not interested in presenting a model of production which is grounded on how products for the market are produced by wage-labour under capitalist relations or conditions of productions. Instead, as will become apparent, Walras’s focus is, like Menger’s, on the ‘inputs’ and ‘outputs’ of production.)

I shall now expand on all of this.

Walras starts with a simple model of pure exchange in which there are only two commodities or goods being exchanged amongst many traders. In doing so, Walras assumes, as pointed out by Vivian Walsh and Harvey Gram, that ‘the total stock of goods in the hands of the participants in exchange are given’ (1980: 150). In other words, how they come to have these commodities or goods in the first place or how there comes to be a total stock of these goods in the first place is not a question which needs exploration. Such things are meant to be taken for granted, i.e., as ‘givens’. So, on the basis of this assumption, Walras considers what happens within a model of pure exchange in which there are only two commodities being exchanged amongst the various traders or participants within the exchange market for goods or commodities. In so doing, Walras introduces the following terms into his simple or basic model of pure exchange. On the one hand, he introduces ‘“the term effective offer”’ which applies or refers ‘“to any offer made… of a definite amount of a commodity at a definite price”’; while, on the other, he introduces ‘“the term effective demand””, which in turn applies to or refers to ‘“any such demand for a definite amount of a commodity at a definite price”’ (Walsh & Gram, 1980: 150). These two terms, the ‘effective offer’ and the ‘effective demand’, are Walras’s terms for what is ordinarily called supply and demand in modern economics. It is subsequently on the basis of these two opposite terms that Walras formulates:

“the law of effective offer [supply] and effective demand [demand] or the law of the establishment [or emergence] of equilibrium prices in the case of the exchange of two commodities [the law of equilibrium prices]” (Walsh & Gram, 1980, p. 150).

In short, what is commonly called in modern economics the basic economic law of supply and demand or the basic law of equilibrium.

This law is, accordingly, stated by Walras as follows. First, Walras states that:

“… given two commodities, for the market to be in equilibrium with respect to these commodities, or for the price of either commodity to be stationary in terms of the other, it is necessary and sufficient that the effective demand be equal to the effective offer of each commodity.” (Walsh & Gram, 1980: 150)

Then, Walras states that:

“Where this equality does not obtain, in order to reach equilibrium prices, the commodity having an effective demand (demand] greater than its effective offer [supply] must rise in price, and the commodity having an effective offer [supply] greater than its effective demand [demand] must fall in price.” (Walsh & Gram, 1980: 150)

But how does all this happen? That is, how do the ‘individual economic agents’ arrive at such an ‘equilibrium price’ or equilibrium state of affairs? Well, according to Walras, it happens, as Vivian Walsh and Harvey Gram point out, by:

“… each holder attain[ing] maximum satisfaction of wants… when the ratio of the intensities of that last wants satisfied [by each of these goods], or the ratio of their raretés [scarcity values], is equal to the price.” (Walsh & Gram, 1980: 150)

Consequently, for Walras:

“Until this equality has been reached, a party to the exchange will find it to his advantage to sell the commodity the rareté [scarcity value] of which is smaller than its price multiplied by the rareté [scarcity value] of the other commodity and to buy the other commodity the rareté [scarcity value] of which is greater than its price multiplied by the first commodity.” (Walsh & Gram, 1980: 150)

Thus, this all happens on the basis of ‘maximum satisfaction’ on the part of both traders. Neither will sell or buy a commodity unless it maximises the level of satisfaction they will derive from either selling or buying it at a certain ‘equilibrium price’. Of course, what they are prepare to trade is dependent on the scarcity value (rareté) of the commodity or good in question.

In this, Walras is basically following Jevons, albeit in a more refine and explicit way in that he talks in terms of the laws of supply and demand and the law of equilibrium price. The suggestion here is that in such a market, even for two commodities, there will be nothing traded until a certain equilibrium price is reached, which means in turn a situation in which the market ‘clears’.

Significantly, as Vivian Walsh and Harvey Gram point out, this all happens on the assumption of ‘perfect competition among traders’ (1980: 150), meaning, none of them can affect or influence the price of the commodity supplied (offered) and demanded in the market. That is, none of them (these traders), as pointed out by Vivian Walsh and Harvey Gram, can do this either by their own individual actions or by forming ‘coalitions’ (1980: 150).

So, for Walras, what is shown by his initial basic model of a pure exchange market economy in which there are only two commodities or goods being exchanged amongst many traders is that this is how a market ‘clears’ in terms of an equilibrium price via the laws of supply and demand – which is in turn predicated on individual agents (traders) seeking to maximise their satisfaction (their marginal utility as Jevons would put it).

Now, it is on the basis of this initial, basic model of a pure market exchange of two goods or commodities amongst many traders that Walras presents his extended model of a pure market exchange economy. In this extended model, Walras considers the case in which there are ‘many goods’ to be exchanged amongst many traders. In doing so, Walras once again bases his model on the principle of maximum satisfaction (scarcity [rareté]). As a consequence, he states that under ‘the condition of “maximum satisfaction”’ (Walsh & Gram, 1980: 150), it will be found that this condition will:

“… always consist in the attainment of equality between the ratio of the raretés [scarcity values] of any two commodities and the price of one in terms of the other, for otherwise it would be advantageous to make further exchanges of these commodities for each other”. (Walsh & Gram, 1980: 150)

Hence, as Vivian Walsh and Harvey Gram perceptively point out, ‘the demand, and the offer, of any commodity is a function, not simply of the price of that commodity, but of the prices of all commodities’ (1980: 150). In other words, the prices of all commodities or goods determines how much one commodity or good is exchanged at a certain equilibrium price in terms of the laws of supply and demand.

So, for Walras, not only will there be an equilibrium price reached amongst many traders over the exchange of two commodities, but also amongst many traders over many commodities being exchanged within the market. Thus, for Walras, whether it is two commodities or goods or many commodities or goods, an equilibrium price will be attained in the sense that the supply or offer of a commodity or good and the demand for it balance each other. Whenever this happens, an equilibrium price will be attained and the market for that commodity or good or for many commodities or goods will ‘clear’ – clear at that equilibrium price which reflects the ‘maximum satisfaction’ of the traders involved in the exchange process, i.e., the exchange of commodities or goods in the market amongst many traders who are endowed with them (i.e., a bundle of commodities or goods).

Now, it is on the basis of these two models of a pure market exchange economy (the simple and extended models of pure exchange in which there is a ‘pure exchange of given stocks of many commodities among many traders under competition’ [Walsh & Gram, 1980: 151]) that Walras consequently develops his expanded model of a market exchange economy which takes into account the production side of the economy.

First, as Vivian Walsh and Harvey Gram point out, Walras draws a distinction between what he calls ‘capital goods’ and ‘income goods’ (1980: 151-2). Accordingly, for Walras, a ‘capital good’ is anything which is deemed to be a ‘durable’ (Walsh & Gram, 1980: 151); meaning, it is something which can be re-used over an extended period of time within the production of commodities or goods, such as a piece of land or a machine. An ‘income good’, however, is anything which is a ‘non-durable’ (Walsh & Gram, 1980: 152); meaning, anything which is used up immediately in the production of commodities or goods, like raw materials such as seeds used to sow a field or fuel used to drive machines.

Now, for Walras, it is the ‘capital goods’ (the ‘durables’ of production), and not the ‘income goods’ (the ‘non-durables’ of production), which are subsequently held to be the things which provide the ‘services’ (Walsh & Gram, 1980: 152) utilised in the production of commodities or goods, which in turn are to be sold in the consumers’ market (the market in which ‘goods and services’ are exchanged or traded for a certain ‘equilibrium price’ as determined by the laws of supply and demand and in accordance with the economic principle of ‘scarcity [rareté]’). So, for Walras, ‘capital goods’ are conceived as the ‘inputs’ of production which in turn produce the ‘outputs’ of production, viz., certain ‘quantities’ of commodities or goods (Walsh & Gram, 1980: 152) – which in turn can become, as Walras tells us, the ‘income goods’ used alongside of the ‘capital goods’ of production (Walsh & Gram, 1980: 152).

It is thus in terms of this model of the inputs (the ‘services of the capital goods’) and the outputs (the ‘quantities of income goods’) of production (Walsh & Gram, 1980: 152) that Walras extends the law of equilibrium. First, Walras, as Vivian Walsh and Harvey Gram point out, distinguishes between two types of market: the ‘services market’ and the ‘products market’ (1980: 153). The services market is the place where, as Walras tells us:

“land-owners, workers and capitalists appear as sellers, and entrepreneurs as buyers of the various productive services, i.e., land-services, labour and capital-services”. (Walsh & Gram, 1980: 152)

While, as Walras also tells us, the products market is the place where:

“the entrepreneurs appear as sellers, and the land-owners, labourers and capitalists as buyers of products. These products are exchanged, like services, with the aid of a numéraire and in accordance with the mechanism of free competition”. (Walsh & Gram, 1980: 152)

It is Walras’s assertion that there will be an equilibrium between these two aspects of production as long as the ‘selling prices’ of the outputs of production (the various quantities of income goods, i.e., commodities or goods) ‘equal’ the ‘costs’ of the inputs of production (the various quantities of capital goods, i.e., the ‘productive services’ of, specifically, ‘land-service, labour and capital-service’) that have been used by the ‘entrepreneurs’ in order to produce products for the consumers’ market.

So, for Walras, like the pure exchange models of the simple and extended varieties, his model of production as just articulated here is also an equilibrium model. It too is an economic state of affairs in which there is a market balance between the amount of capital goods used to produce commodities for the consumers’ market and the amount of commodities produced on the basis of these capital goods. And all this is, according to Walras, reflected in the prices of commodities and the costs of the capital goods. Consequently, for Walras, in such markets of ‘indirect exchange’ between the sellers of productive services and the buyers of commodities (i.e., between the ‘households’ themselves) there will also be an equilibrium state of affairs.

Yet, none of these different market models of Walras’s can on their own, as he points out, establish a ‘general equilibrium’ state of affairs. For this to happen, according to Walras, then they must all be in equilibrium at once.

As pointed out by Vivian Walsh and Harvey Gram, Walras describes and/or summarises a market system as being in a state of ‘general equilibrium’ whenever the following market properties hold. On the assumption that ‘“equilibrium in production… implies equilibrium in exchange”’, a ‘“general equilibrium”’ state can be ‘“defined”’ as one in which (Walsh & Gram, 1980: 153), firstly:

“it is a state in which the effective demand and offer of productive services are equal and there is a stationary current price in the market for these services.” (Walsh & Gram, 1980: 153)

Hence, there is an equilibrium state in the resources or the factors of production market (productive services). Secondly:

“it is a state in which the effective demand and supply of products are also equal and there is a stationary current price in the products market.” (Walsh & Gram, 1980: 153)

Thus, there is an equilibrium state in the products market (consumer’s goods and service). And thirdly:

“it is a state in which the selling prices of products equal the costs of the productive service that enter into them.” (Walsh & Gram, 1980: 153)

In short, there is an equilibrium state between the costs of production and the selling prices of products, i.e., between the ‘inputs’ and the ‘outputs’ of production.

Accordingly, for Walras:

“The first two conditions relate to equilibrium in exchange; the third to equilibrium in production.” (Walsh & Gram, 1980: 153)

Thus, for Walras, all markets in terms of consumers’ goods and services, productive services and the ‘inputs’ and ‘outputs’ of production are simultaneously in balance with each other. As a consequence, all markets simultaneously ‘clear’ at a general equilibrium price in terms of the laws of supply and demand and in accordance with the economic principle of ‘scarcity (rareté)’.

It is subsequently within this general equilibrium framework or model of a market economy (like capitalism) that Walras purports to show how the ‘given resources’ of society are allocated in order to meet the demands of consumers. They are allocated in the specific quantities that they are and for the specific costs that they fetch as a result of the specific prices that commodities attain in the consumers’ market. Accordingly, for Walras, this proves to be the most efficient and most optimal way in which a market society like capitalism can produce what consumers want at a ‘general equilibrium price’ in which all markets simultaneously ‘clear’. This means, therefore, that the supply and demand of commodities (the ‘goods and services’ of the consumers’ market) are never below or above the ‘general equilibrium price’ (whatever that is). Equally, it means that the supply and demand of the productive services of a market society (the services of land, labour and capital) are never below or above the ‘general equilibrium price’ either (whatever that is).

Now, as Vivian Walsh and Harvey Gram point out, this purportedly efficient allocation of the ‘given resources’ of society, which takes place as a result of meeting consumers’ demand, is predicated on the existence of the following core feature of such a ‘system of general equilibrium’ (1980: 142): ‘the households’ (1980: 155; my italics). As Vivian Walsh and Harvey Gram say: it is through the pursuit of ‘maximizing’ their individual ‘satisfaction’ in terms of wanting certain commodities in the consumers’ market that they consequently ‘determine what shall be the composition of output’ and in so doing ‘influence the relative prices’ (1980: 155) of not just what is produced as output, but also the costs of the inputs and, in turn, the respective ‘incomes’ that are paid to the households themselves when offering up their particular services in the services market (i.e., the resources or factors of production market). As a consequence, ‘social classes play no analytical role’ in Walras’s general equilibrium model, since ‘the main actors are individual resource-owning households who derive incomes from the sale of resource services and spend these incomes on commodities’ (Walsh & Gram, 1980: 155). Thus, within such a general equilibrium system of a market economy (like capitalism), the ‘[p]roducers [i.e., the firms of the system] thus act simply as agents for resource-owning households, transforming given factor services into consumption goods’ (Walsh & Gram, 1980:. 155).

In sum, then, this is how Walras brings together a ‘complete system of general equilibrium’ (Walsh & Gram, 1980: 142) in which the problem has been to establish the means by which the ‘given resources’ of a market-based society (like capitalism) can be most efficiently allocated in order to meet the demands of consumers. In doing so, Walras does it by abandoning any analytical use of social classes. As a result, he has constructed what can be called, as Vivian Walsh and Harvey Gram do, a ‘pure economic theory in terms of a general equilibrium model’ (1980: 138).