Léon Walras and General Equilibrium Theory

Léon Walras and General Equilibrium Theory:

This theory considers all prices as being interdependent. It views all prices as a vast, complex system. It does not, therefore, deal with individual prices. On the contrary, it depicts general prices. It also studies the forces which determine the general prices and in doing so, it often uses mathematical methods. The procedure for such a mathematical analysis is to lay down a series of simultaneous algebraic equations in which the tastes and desires of the consumers, the available quantities of productive factors, and the technical requirements of the industries for these factors are the known magnitudes whilst the prices of finished goods, raw materials, and productive factors are the unknown magnitudes. The simultaneous algebraic equations are then worked out to determine the values of the unknown magnitudes. In other words, the general prices or the prices of all the goods are determined simultaneously with the help of algebraic equations. It goes without saying that a very advanced type of mathematics is involved in the construction of algebraic equations to determine general prices. Consequently, economists, with training in advanced mathematics, alone can make use of this highly mathematical method. To the person not initiated in higher mathematics, the general equilibrium theory sounds highly abstract, though it highlights the conception of the interdependence of prices.

The first scientific treatment of general equilibrium analysis was made by a French economist, Leon Walras (1834-1910) of the Laussane School. It was a new venture in an entirely new and unexplored field. Beginning with the concept of marginal utility, Walras soon built up a new theory of exchange, not for one commodity as was customary then among the economists, but for any number of commodities. It was a novel thing never attempted before. As Prof. Boulding says, “Walras is the Laplace of economics; just as Laplace transformed astronomy from a system in which the movement of each heavenly body was attached to its own particular cause to a system in which the mutual interaction of all bodies upon each other determines the behavior of all, so Walras transformed economics from the system in which each value was attached to its own particular cause to a system in which all values, whether of finished goods, intermediate products or factors of production, are mutually determined by the interaction of the innumerable forces of desire upon the innumerable resistances of scarcity.”

The ideas of Walras were later absorbed by Vilfredo Pareto (1843-1923), who further developed and deepened the general equilibrium theory, and cast it in a suitable mathematical model. Although the general equilibrium theory is nearly a century old, it has been developed and deepened by a small number of theorists on the continent of Europe. The British and American economists mostly became interested in the general equilibrium theory after the Second World War. In more recent years, economists like J. R. Hicks, R. G. D. Allen, and others have made further additions to the general equilibrium theory. Despite all this, Walras’ model of the general equilibrium of a competitive economy still remains the classic. Others have no doubt, tried to refine Walras’ model, but no radical modifications have yet been made. What follows is a simple, non-mathematical description of Walra’s model of the general equilibrium of a perfectly competitive economy. It gives us a vision of the interdependence of prices in a competitive economy. 

According to Walras, households and firms are the two sectors of the competitive economy which is self-sufficient in itself. Perfect competition prevails in all the markets whether they are commodity markets or factor markets. The prices prevalent in these markets link the respective actions of the household and the firms. The household sell resources (say land, labor, and capital equipment) to the firms, which in turn, sell their manufactured goods to the households. This underlines the dependence of the firms on the households and vice versa. The model assumes that there is full employment of labor and other resources in the economy. (There is nothing surprising about this in so far, as all classical theories are based on the assumption of full employment.)

The tastes and desires of households or consumers are assumed to be constant. Each household buys quantities of each commodity according to its tastes, money income, the price of the commodity in question, and the prices of all other commodities. Please note this point carefully. The household, when buying a commodity, takes into account the price not only of that commodity but also the prices of all other commodities, which generally enter into its consumption. A change in any of the other prices may affect its purchase of the commodity concerned. (Incidentally, this brings out the interdependence of all prices). For example, a household, when buying sugar has to consider the price not only of sugar but also the prices of other commodities like cotton textiles. the money income of the household is limited. If the price of cotton textiles rises and the household spends more money on it, it is obvious that less money would be available for being spent on sugar. The demand for sugar will consequently decline. If all households react in this manner, the total demand for sugar, as well as its price, will fall. The price of sugar is thus influenced not only by its demand and supply but also by the prices of other commodities. A change anywhere in the price of any commodity will affect the budget of the household, obliging it to rearrange it in light of the changed price situation. it is not necessary that a change in the price of a commodity will inevitably have heavy repercussions on the budget of the household. If the commodity involved is unimportant and the change in its price is small, the repercussions on the household’s budget may be almost negligible.

Walras’ model assumes that the households do not save, but, on the contrary, spend their entire income on consumption. The incomes of the households are derived from the sale of their resources to the firms. Changes in the prices of the resources sold by the households affect their incomes and consequently their budgets. It is not necessary that a household sells only one resource to the firms. It may sell more than one resource, in case it possesses them. A change in the price of one resource causes a change in the price of the other because the households can make substitutions in their capacity as sellers in the same manner in which they can do in their capacity as buyers. Thus, the prices of resources are interconnected in the same manner as the prices of commodities. The household is actually faced with two networks of prices. One is the network of commodity prices and the other is the network of resource prices. At the time of buying commodities, it is confronted with the network of commodity prices. At the time of selling resources, it has to face the network of resource prices. The purchases of commodities by the households, accordingly, are governed by the two networks of prices- on the income side by the network of resource prices, and on the expenditure side, by the network of commodity prices. The two networks of prices are related to each other through the action of the households.

The total demand in the market for each commodity is the sum total of the demands of all the households in the economy. The market demands for various commodities are also governed by the same two networks of prices.

The various firms operating in the economy produce goods by hiring the productive resources of the households. Since perfect competition exists everywhere, the prices of the goods tend to equal their costs of production. Unit costs are assumed to be constant in Walras’ model. Thus, average costs and marginal costs are equal and constant. The price of each commodity, as said above, equals its cost of production. The total cost of production of a commodity comprises all those items on which the firm incurs expenditure. The expenditure incurred on each item can be found out by multiplying the quantity of resources (used in one unit of the commodity) by its price. Let us suppose that in the manufacture of a pair of shoes, two types of labor are used- skilled and unskilled. The manufacture of a pair of shoes involves, let us assume, 30 minutes of skilled labor and 15 minutes of unskilled labor. Skilled labor is paid, let us suppose, at the rate of $3 per hour while unskilled labor is paid at the rate of $1 per hour. Then in the manufacture of a pair of shoes, $1.50 worth of skilled and $0.25 worth of unskilled labor will be used. In other words, the money cost of a pair of shoes on account of labor charges would come to $1.75. In this way, the money cost of the various items can be worked out. The physical resources used in the manufacture of a pair of shoes, such as labor, raw materials, etc., are referred to as co-efficient of production in the Walrasian model. In this example, 30 minutes of skilled labor and 15 minutes of unskilled labor are the coefficients of production. The coefficients of production are assumed to be fixed by Walras.

Like the households, the firms, are also confronted with two networks of prices. As suppliers, the firms’ actions are governed by the network of commodity prices. As buyers of productive resources like labor, raw materials, capital equipment, etc., their actions are governed by the network of resource prices. The resource prices along with the coefficients of production determine the costs of the firms. The firms act as the connecting link between the two networks of prices.

Since Walras’ model assumes the non-existence of unemployment, the demand for each productive resource must equal its supply. The demand for productive resources, as said above comes from the firms, while their supply comes from the households. The network of resource prices functions in such a manner as to make the demand for each resource equal to its supply. It also makes all productive resources compatible with one another. Each resource market attains equilibrium, all resource markets are in a general equilibrium. Likewise, the demand for each commodity equals its supply. The demand for commodities, as said above, comes from households, while their supply comes from firms. The network of commodity prices establishes equilibrium not only in each commodity market but in all the commodity markets taken together. All commodity markets are in general equilibrium. The equilibria in the commodity markets and the equilibria in the resource market are joined together in one grand general equilibrium by the operation of the two networks of prices in the economy. In this grand general equilibrium, the entire economy finds itself in full equilibrium. All prices are in equilibrium. All demands equal all supplies. All households as well as all firms are in equilibria. For each household, the price of each commodity equals its marginal utility, or in the alternative, the ratio of the prices of any two goods equals their marginal rate of substitution. For each household, the marginal rate of substitution between income and leisure is equal to the price ratio between income and work. For each firm, the marginal cost of each commodity equals its price. The cost of production for each firm is at a minimum.

The gist of the general equilibrium theory is that the desires and tastes of the households and the productive resources available to the firms mutually determine the quantities of the various commodities to be produced.

The question, however, arises: What force brings about equality between all demands and all supplies in the economy? Walras’ reply is that it is a process of “groping” which brings about equality between demands and supplies in the economy. To illustrate this process of groping, let us suppose that the price of commodity ‘A’ is out of equilibrium due to maladjustments between its demands and supply, say, the supply is in excess of the demand. The price of ‘A’ is, therefore, low in the market. The demand will consequently rise up. The rise in the price of ‘A’ will cause an increase in the demands of other commodities, say ‘B’ and ‘C’, particularly when they happen to be its substitutes. In addition, the rise in the price of ‘A’ will cause a decline in the supplies of other commodities like ‘B’ and ‘c’, because productive resources will now flow to ‘A’. The prices of the other commodities will change now. The change in their prices will have their repercussions back on the demand and supply of ‘A’. These changes and counter-changes will ultimately result in the establishment of an equilibrium, between all demands and all supplies, according to Walras.

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