# Walras Law

Walras's law is a principle of general equilibrium theory that states that the sum of aggregate demand must equal the sum of aggregate supply, taking prices into account.

This simple economic model works under conditions of perfect competition and what you are looking to find is the equilibrium price.

## Walras law formula

The simplest formula to represent it is the following:

This formula explains that the sum of the aggregate demand is equal to the sum of the aggregate supply, which gives an equalization of 0.

To develop his model, he first relied on Say's law. Where each supply creates its own demand, this can be exemplified as follows. Let's imagine a tailor who sells pants and his sale price is \$ 100. In turn, with the money he gets from the sale of his pants, he becomes a demanding \$ 2000 of other products on the market, since this constitutes his purchasing power. This is Say's law.

## Development of Walras law

Walras wanted to bring this theory to aggregate economics. For him the most important thing was the trial of prices, for that reason he generated his model with a system of equations that:

• Includes n equations and n unknowns.
• It assumes a number of fixed units of products.
• Consider that the goods are limited, say 20 pants.

For him, what should be solved was the price as the main unknown of the model or independent variable. For this economist the price is the one that must be adjusted until the market empties.

To better understand it, let's look at the following graphs:

For price 10, the quantity demanded is 100 and the quantity supplied is 500, causing an excess supply of 400 units.

For price 2, the quantity demanded is 500 and the quantity supplied is 100, resulting in an unmet demand of 400 units.

Price 6 equals the quantity demanded and supplied in 300 units, which implies that there is no shortage or surplus of product. The equalization of the quantity of supply and demand proves the statement of Walras's Law.

### Assumptions of the Walras model

The way Walras determined his model was by considering how rural markets that opened at a certain time and closed at a certain time functioned. In them, the bidders and demanders acted by exercising simultaneous auctions. These auctions allowed the best price to be found for the bidders (the highest) and the best price for the demanders (the lowest).

This model was generated during the emergence of the Neoclassical School of Economics, where mathematical models began to be used to formalize economic science, that means giving it the character of science. For these models to work it is necessary to apply the assumption "Ceteris Pabirús", this is keeping everything constant, therefore an essential condition was that there was perfect competition, this implies infinite competitors and infinite consumers; with the purpose that nobody influenced the price.

## Example Walras law in the stock market

Walras's law could be enforced on the stock market. In that market, there are brokers that represent the bidders and brokers that represent the applicants.

Let's think that in the market for raw materials such as coffee, some offer coffee at \$ 80, others at \$ 70 and others at \$ 60. At the same time, there are applicants who are looking to buy this coffee. Initially a broker representing the plaintiff is willing to pay the lowest price of \$ 60, but another plaintiff appears who wants to keep the product and is willing to pay \$ 70 for the product. For the price of \$ 80 there are no buyers.

If we realize the equilibrium price of \$ 70 is reached, that implies that it is the best price for the offeror, that is, the highest that could be found in that market and the best price for the demander, that is, the lowest that could be obtained. No bidders were found willing to sell at the price of \$ 60 and no bidders were found willing to buy at the price of \$ 80.

In conclusion, we can affirm that all the participants in the transaction benefited, because they found the best prices.

This contribution of the neoclassical school of economics is one of the incentives that moves the markets where each participant wants to maximize his utility, the supplier expects to sell at the highest price and the demander the lowest price.

However, there are critics who claim that the Walras model is not applied one hundred percent in practice, as it is considered a model with ideal assumptions.

Law of supply Demand law

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