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It is sometimes the case that the supply curve is vertical, that is the quantity supplied is fixed, no matter what the market price. For example, the amount of land in the world can be considered fixed. In this case, no matter how much someone would be willing to pay for one more acre of land, the extra cannot be created. Also, even if no one wanted all the land, it still would exist. These conditions create a vertical supply curve, giving it zero elasticity (ie. - no matter how large the change in price, the quantity supplied will not change).
In the short run near vertical supply curves are even more common. For example, if the Super Bowl is next week, increasing the number of seats in the stadium is almost impossible. The supply of tickets for the game can be considered vertical in this case. If the organizers of this event underestimated demand, then it may very well be the case that the price that they set is below the equilibrium price. In this case there will likely be people who paid the lower price who only value the ticket at that price, and people who could not get tickets, even though they would be willing to pay more. If some of the people who value the tickets less sell them to people who are willing to pay more (i.e. scalp the tickets), then the effective price will rise to the equilibrium price.
The graph below illustrates a vertical supply curve. When the demand 1 is in effect, the price will p1. When demand 2 is occurring, the price will be p2. Notice that at both values the quantity is Q. Since the supply is fixed, any shifts in demand will only affect price.
In a situation in which there are many buyers but a single monopoly supplier that can adjust the supply or price of a good at will, the monopolist will adjust the price so that his profit is maximised given the amount that is demanded at that price. This price will be higher than in a competitive market. A similar analysis using supply and demand can be applied when a good has a single buyer, a monopsony, but many sellers.
Where there are both few buyers or few sellers, the theory of supply and demand cannot be applied because both decisions of the buyers and sellers are interdependent - changes in supply can affect demand and vice versa. Game theory can be used to analyse this kind of situation. See also oligopoly.
The supply curve does not have to be linear. However, if the supply is from a profit maximizing firm, it can be proven that supply curves are not downward sloping (i.e. if the price increases, the quantity supplied will not decrease). Supply curves from profit maximizing firms can be vertical, horizontal or upward sloping. While it is possible for industry supply curves to be downward sloping, supply curves for individual firms are never downward sloping).
Standard microeconomic assumptions cannot be used to prove that the demand curve is downward sloping. However, despite years of searching, no generally agreed upon example of a good that has an upward sloping demand curve has been found (also known as a giffen good). Non-economists sometimes think that this would not be the case for certain goods. For example, some people will buy a luxury car because it is expensive. In this case the good demanded is actually prestige, and not a car, so when the price of the luxury car decreases, it is actually changing the amount of prestige so the demand is not decreasing since it is a different good (see Veblen good). Even with downward sloping demand curves, it is possible that an increase in income may lead to a decrease in demand for a particular good, probably due to the existence of more attractive alternatives which become affordable: a good with this property is known as an inferior good.
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:
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:
The supply would be:
And here is the graph:
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.
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