Unit 8 Supply and demand: Markets with many buyers and sellers

8.3 Competitive equilibrium and price-taking

equilibrium price
This term normally refers to the price at which supply and demand for a good are equalized, so that the market is in equilibrium (also known as the market-clearing price). But it could refer to the level of the price in the equilibrium of other economic models. See also: market-clearing price.
equilibrium
An equilibrium is a situation or model outcome that is self-perpetuating: if the outcome is reached it does not change, unless an external force disturbs it. By an ‘external force’, we mean something that is determined outside the model.
excess supply
A situation in which the quantity of a good supplied is greater than the quantity demanded at the current price. See also: excess demand.
competitive equilibrium
A market is in competitive equilibrium if the quantity supplied is equal to the quantity demanded at the prevailing price, and all buyers and sellers are price-takers, so that no-one can benefit from attempting to trade at a different price.
price-taker
A buyer or seller acts as a price-taker if they cannot benefit from attempting to trade at any other price than the prevailing market price. A price-taker has no power to influence the market price, but can buy or sell as many items as they wish at that price.

Marshall called the market-clearing price the equilibrium price. We say that the market for second-hand books is in equilibrium when P* = 8. In everyday language, something is in equilibrium if the forces acting on it are in balance, so that it remains unchanged. A market is in equilibrium if the actions of buyers and sellers have no tendency to change the price or the quantities bought and sold. Figure 8.4 explains why the market-clearing price P* is the only price where there is no tendency for change.

In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A. When the price is above $8, there are more people selling books than people buying. When the price is below $8, there are more people buying a book than people selling.
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Figure 8.4 Equilibrium in the market for second-hand books.

The market-clearing price: In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A.
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The market-clearing price

The market-clearing price is P* = 8. At this price, the quantity supplied is equal to the quantity demanded: Q* = 24.

A price above the market-clearing price: In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A. When the price is above $8, there are more people selling books than people buying.
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A price above the market-clearing price

At a price greater than $8, there would be an excess supply of books. More students would wish to sell, but not all of them would find buyers, so these sellers would want to lower their prices.

A price below the market-clearing price: In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A. When the price is above $8, there are more people selling books than people buying. When the price is below $8, there are more people buying a book than people selling.
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A price below the market-clearing price

At a price less than $8, there would be excess demand for books—more buyers than sellers. So some buyers would want to find a seller by offering to pay more, and some sellers could do better by raising their prices.

The equilibrium price and quantity: In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A. When the price is above $8, there are more people selling books than people buying. When the price is below $8, there are more people buying a book than people selling.
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The equilibrium price and quantity

Only at P* = $8 is there no tendency for change. At this price, every seller who wants to sell can find a buyer, and every buyer who wants to buy can find a seller, so none of them would want to change the price. The market is in equilibrium, and the equilibrium quantity is Q* = 24.

Not all markets for second-hand books are in equilibrium. In one case when the conditions for equilibrium were not met, automatic price-setting algorithms raised the price of a book to $23 million! Michael Eisen, a biologist, noticed a classic but out-of-print text, The Making of a Fly, was listed for sale on Amazon by two reputable sellers, with prices starting at $1,730,045.91 (+$3.99 shipping). He watched over the next week as the prices rose rapidly, eventually peaking at $23,698,655.93, before dropping to $106.23. Eisen explains why in his blog.

excess demand
A situation in which the quantity of a good demanded is greater than the quantity supplied at the current price. See also: excess supply.

In Figure 8.4, there is excess demand for books if the going price is below P*, and excess supply if it is above P*. At these prices, some buyers or sellers could do better by trading at different prices. P* is the equilibrium price, where all those who wish to buy or sell can do so, and there is no tendency for change.

Competitive equilibrium

Marshall’s supply and demand model can be applied to markets with many buyers and sellers of identical goods. The requirement for many buyers and sellers is important because it implies that the amount each individual buys or sells is small relative to the market as a whole. This, together with the requirement that goods are identical, means that in equilibrium, no individual has the power to influence the market price. At the prevailing market price, everyone can buy or sell as many items as they like, and they can always find someone else to trade with if they don’t like the deal that a particular seller or buyer is offering. On both sides of the market, competition eliminates bargaining power.

So the best each individual can do is to trade at the prevailing equilibrium price. For example, in the equilibrium of the textbook market no student would trade with a seller asking more than $8 for a book, because they can find an alternative seller asking $8. And the seller would not benefit from lowering the price, because they can find a buyer willing to pay $8.

Nash equilibrium
A Nash equilibrium is an economic outcome where none of the individuals involved could bring about an outcome they prefer by unilaterally changing their own action. More formally, in game theory it is defined as a set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else. See also Game theory.

In this situation, we say that the market is in competitive equilibrium, and the buyers and sellers are acting as price-takers.

A competitive equilibrium is a Nash equilibrium, because given what all other actors are doing (trading at the equilibrium price), no actor can do better than to continue what he or she is doing (also trading at the equilibrium price).

In general, we expect buyers to be price-takers if there are many other buyers, and sellers to be price-takers if there are many sellers selling an identical product. Figure 8.5 compares competitive equilibrium, where there is price-taking on both sides of the market, with the case of a differentiated product discussed in Unit 7.

Market for a differentiated product, e.g. Cheerios One seller Price setter Despite competition from similar products, no-one else sells Cheerios. The seller can vary the price and still attract buyers.
Many buyers Price-takers If a buyer offered a lower price, the seller would not accept, because there are many alternative buyers willing to pay.
Market in competitive equilibrium, e.g. a second-hand textbook Many sellers Price-takers If a seller set a price above $8, their book would not sell; buyers would go to other sellers. And $8 is better than a lower price.
Many buyers Price-takers If a buyer offered to pay less than $8, no seller would accept: they would find other buyers. And $8 is better than a higher price.

Figure 8.5 Buyers and sellers, price-taking and price setting.

Do markets with many buyers and sellers reach competitive equilibrium?

For second-hand books we have argued, as Marshall did, that if supply and demand were not equal, buyers and sellers would adjust their prices until the equilibrium was reached.

Economists have studied the behaviour of buyers and sellers in laboratory experiments to assess whether prices are adjusted to equalize supply and demand. In the first such experiment, in 1948, Edward Chamberlin gave each member of a group of Harvard students a card designating them as ‘buyers’ or ‘sellers’ and stating their willingness to pay, or reservation price, in dollars. They could then bargain among themselves, and he recorded the trades that took place. He found that prices tended to be lower, and the number of trades higher, than the equilibrium levels. Chamberlin repeated his experiment every year. One of the students who took part in 1952, Vernon Smith, later conducted his own experiments and won a Nobel Prize in economics as a result.

He modified the rules of the game so that participants had more information about what was happening: buyers and sellers called out prices that they were willing to offer or accept. When anyone agreed to a proposed deal, a trade took place and the two participants dropped out of the market. His second modification was to repeat the game several times, with the participants keeping the same card in each round.

Figure 8.6 shows his results. There were 11 sellers, with reservation prices between $0.75 and $3.25, and 11 buyers with WTP in the same range. The diagram shows the corresponding supply and demand functions. (With just 11 buyers and sellers, these are drawn more accurately in steps, rather than approximated by a smooth line.)

In equilibrium, six trades will take place at a price of $2. But the participants did not know this, since they did not know the price on anyone else’s card. The right-hand side of the diagram shows the price for each trade that occurred. In the first period, there were five trades—all at prices below $2. But by the fifth period, most prices were very close to $2, and the number of trades was equal to the equilibrium quantity.

There are two diagrams. In diagram 1, the horizontal axis shows the quantity, and ranges from 0 to 12 in increases of 1. The vertical axis shows the price in dollars, and ranges from 0 to 4. Coordinates are (quantity, price). A step function connecting points (0, 4), (0, 3.3), (1, 3.3), (1, 3), (2, 3), (2, 2.7), (3, 2.7), (3, 2.5), (4, 2.5), (4, 2.2), (5, 2.2),  (5, 2), (6, 2), (6, 1.8), (7, 1.8), (8, 1.5), (8, 1.2), (9, 1.2), (9, 1), (10, 1), (10, 0.8), (11, 0.8), and (11, 0) is the demand function. A step function connecting points (0, 0), (0, 0.8), (1, 0.8), (1, 1), (2, 1), (2, 1.2), (3, 1.2), (3, 1.5), (4, 1.5), (4, 1.8), (5, 1.8), (5, 2), (6, 2), (6, 2.2), (7, 2.2), (7, 2.5), (8, 2.5), (8, 2.7), (9, 2.7), (9, 3), (10, 3), (10, 3.3), (11, 3.3), and (11, 4) is the supply function. In diagram 2, the horizontal axis shows the number of transactions in 5 different periods. In periods 1 to 3 there are 5 separate transactions. In period 4 there are 7 separate transactions. In period 5 there are 6 separate transactions. The vertical axis shows the price in dollars at which each transaction happened, ranging from 0 to 4. The price fluctuated around $1.8 per transaction for all transactions until the third transaction in period 3, after which it fluctuated around $2 per transaction for the remaining transactions.
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Figure 8.6 Vernon Smith’s experimental results.

Vernon L. Smith. 1962. ‘An Experimental Study of Competitive Market Behavior’Journal of Political Economy 70 (3) (January): p. 322.

Smith’s experiment provides some support for applying the model of competitive equilibrium to markets where goods are identical, if there are enough buyers and sellers who are well-informed about the trading of others. The outcome was close to equilibrium even in the first period, and converged quickly towards it in subsequent periods as the participants learned more about supply and demand.

Exercise 8.2 Price-takers

Think about a good that you buy regularly, for example, different kinds of food, clothes, transport tickets, or electronic goods.

  1. Are there many sellers of this good?
  2. When you purchase this good, which factors influence your decision? For example, do you usually try to find the seller with the lowest price, or are there other criteria you consider to be important?
  3. Use your answers to Questions 1 and 2 to help you determine whether the sellers of that good are likely to be price-takers.
  4. As a buyer, explain whether you are/are not a price-taker of this good. Give some examples of goods for which buyers may not necessarily be price-takers.

Question 8.3 Choose the correct answer(s)

The diagram shows the demand and the supply curves for a textbook. The curves intersect at (Q*, P*) = (24, 8). Using this information, read the following statements and choose the correct option(s).

In this diagram, the horizontal axis shows quantity of books, denoted Q, and ranges from 0 to 45. The vertical axis shows sellers’ reservation price in dollars, denoted P (price), ranging from 0 to 25. Coordinates are (quantity of books, price). An upward-sloping line originates from point (0, 2) and passes through point A (24, 8). A downward-sloping line connects the points (0, 20) and (40, 0) and is labelled demand curve. The demand curve intersects the supply curve at point A.
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  • At a price of $10, there is excess demand for the textbook.
  • At $8, a seller would benefit if they increased their selling price to $9.
  • Point A is a Nash equilibrium.
  • The total number of books sold is determined by the maximum level of demand (40 books).
  • At $10, the price is above the equilibrium price of $8, and there is an excess supply of books.
  • At $8, all buyers with a WTP at $8 or above can be matched with all sellers with a WTA of $8 or less. If one of these sellers raised their price to $9, the buyer could find another seller willing to accept less.
  • At point A, the quantity demanded is equal to the quantity supplied—that is, the market clears. No buyer or seller has an incentive to change their current behaviour, so this situation is a Nash equilibrium.
  • The maximum level of demand is 40, but 16 of these will be unfulfilled as their willingness to pay is below the market-clearing price of $8.