Supply and demand

In microeconomic theory, the partial equilibrium supply and demand economic model originally developed by Alfred Marshall attempts to describe, explain, and predict changes in the price and quantity of goods sold in competitive markets. The model is only a first approximation for describing an imperfectly competitive market. It formalizes the theories used by some economists before Marshall and is one of the most fundamental models of some modern economic schools, widely used as a basic building block in a wide range of more detailed economic models and theories. The theory of supply and demand is important for some economic schools' understanding of a market economy in that it is an explanation of the mechanism by which many resource allocation decisions are made. However, unlike general equilibrium models, supply schedules in this partial equilibrium model are fixed by unexplained forces.

An example: Supply and demand in a 6-person economy

Supply and demand can be thought of in terms of individual people interacting at a market. Suppose the following six people participate in this simplified economy:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• Alice is willing to pay $10 for a sack of potatoes.
• Bob is willing to pay $20 for a sack of potatoes.
• Cathy is willing to pay $30 for a sack of potatoes.
• Dan is willing to sell a sack of potatoes for $5.
• Emily is willing to sell a sack of potatoes for $15.
• Fred is willing to sell a sack of potatoes for $25.

There are many possible trades that would be mutually agreeable to both people, but not all of them will happen. For example, Cathy and Fred would be interested in trading with each other for any price between $25 and $30. If the price is above $30, Cathy is not interested, since the price is too high. If the price is below $25, Fred is not interested, since the price is too low. However, at the market Cathy will discover that there are other sellers willing to sell at well below $25, so she will not trade with Fred at all. In an efficient market, each seller will get as high a price as possible, and each buyer will get as low a price as possible.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Imagine that Cathy and Fred are bartering over the price. Fred offers $25 for a sack of potatoes. Before Cathy can agree, Emily offers a sack of potatoes for $24. Fred is not willing to sell at $24, so he drops out. At this point, Dan offers to sell for $12. Emily won't sell for that amount so it looks like the deal might go through. At this point Bob steps in and offers $14. Now we have two people willing to pay $14 for a sack of potatoes (Cathy and Bob), but only one person (Dan) willing to sell for $14. Cathy notices this and doesn't want to lose a good deal, so she offers Dan $16 for his potatoes. Now Emily also offers to sell for $16, so there are two buyers and two sellers at that price (note that they could have settled on any price between $15 and $20), and the bartering can stop. But what about Fred and Alice? Well, Fred and Alice are not willing to trade with each other, since Alice is only willing to pay $10 and Fred will not sell for any amount under $25. Alice can't outbid Cathy or Bob to purchase from Dan, so Alice will not be able to get a trade with them. Fred can't underbid Dan or Emily, so he will not be able to get a trade with Cathy. In other words, a stable equilibrium has been reached.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

A supply and demand graph could also be drawn from this. The demand would be:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• 1 person is willing to pay $30 (Cathy).
• 2 people are willing to pay $20 (Cathy and Bob).
• 3 people are willing to pay $10 (Cathy, Bob, and Alice).

The supply would be:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• 1 person is willing to sell for $5 (Dan).
• 2 people are willing to sell for $15 (Dan and Emily).
• 3 people are willing to sell for $25 (Dan, Emily, and Fred).

Supply and demand match when the quantity traded is two sacks and the price is between $15 and $20. Whether Dan sells to Cathy, and Emily to Bob, or the other way round, and what precisely is the price agreed cannot be determined. This is the only limitation of this simple model. When considering the full assumptions of perfect competition the price would be fully determined, since there would be enough participants to determine the price. For example, if the "last trade" was between someone willing to sell at $15.50 and someone willing to pay $15.51, then the price could be determined to the penny. As more participants enter, the more likely there will be a close bracketing of the equilibrium price.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

It is important to note that this example violates the assumption of perfect competition in that there are a limited number of market participants. However, this simplification shows how the equilibrium price and quantity can be determined in an easily understood situation. The results are similar when unlimited market participants and the other assumptions of perfect competition are considered.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~