Unit 8 Supply and demand: Markets with many buyers and sellers
8.5 Gains from trade in competitive equilibrium: Allocation and distribution
- gains from trade, gains from exchange
- The benefits that each party gains from a transaction compared to how they would have fared without the transaction.
Buyers and sellers of bread voluntarily engage in trade because both benefit. The gains from trade can be measured in the same way as in Unit 7, by the surpluses obtained by buyers and sellers. There is a potential surplus whenever a buyer will pay more for a loaf than the marginal cost of producing it.
Figure 8.12 shows the market supply and demand curves for bread. Remember that bakeries differ in their marginal costs of producing bread, and the supply curve tells us the marginal cost of each loaf produced. The demand curve shows the consumers’ willingness to pay. For every loaf up to the 5,000th one produced, there is a consumer who is willing to pay more than the marginal cost of producing it.
In the competitive equilibrium at point A, 5,000 loaves are sold at €2 each. All consumers up to the 5,000th receive a monetary surplus equal to their WTP minus the price; and producers of all loaves up to the 5,000th receive a surplus equal to the price minus the marginal cost of producing the loaf.
The whole shaded area in Figure 8.12—the sum of consumer and producer surplus—is the total surplus from trade in the bread market. All potential gains from trade are exhausted at the competitive equilibrium—in other words, the total surplus is maximized.
Joel Waldfogel, an economist, gave his chosen discipline a bad name by suggesting that gift-giving at Christmas may result in a deadweight loss.1 If you receive a gift that is worth less to you than it cost the giver, you could argue that the surplus from the transaction is negative. Do you agree?2
- If fewer loaves were produced, there would be unexploited gains from trade: some consumers without bread would be willing to pay more than the cost of producing another loaf.
- If any more than 5,000 loaves were produced, the total surplus would decrease, because the surplus on the extra loaves would be negative: they would cost more to make than consumers would pay.
- At the equilibrium, the marginal cost of the last loaf produced—the 5,000th—is equal to the willingness to pay of the last consumer who buys, so all potential gains from trade are exploited.
This property holds in general: a competitive equilibrium allocation maximizes the total surplus available in the market. It contrasts with the allocation of a differentiated good (Figure 7.20), where there is a deadweight loss because the producer sets a price above the marginal cost of the last item produced.
Pareto efficiency
Building block
For an introduction to Pareto efficiency, read Section 4.5.
Since all potential gains from trade are exploited at the competitive equilibrium, we know that it is not possible to change the allocation (the amount of bread produced, and who buys and sells it) to make a consumer or firm better off without making any of them worse off.
- Pareto efficient, Pareto efficiency
- An allocation is Pareto efficient if there is no feasible alternative allocation in which at least one person would be better off, and nobody worse off.
- external effect, externality
- An external effect occurs when a person’s action confers a benefit or imposes a cost on others and this cost or benefit is not taken into account by the individual taking the action. External effects are also called externalities.
- complete contract
- A contract is complete if it a) covers all of the aspects of the exchange in which any party to the exchange has an interest, and b) is enforceable (by the courts) at close to zero cost to the parties.
Does this mean the equilibrium allocation is Pareto efficient? The answer is yes, provided that no one other than the consumers and bakeries is affected by trade in the bread market. But if, for example, producing bread involved a lot of noise or pollution which affected the people living nearby, then to find a Pareto efficient allocation, we would have to allow for these additional costs of bread production (known as external effects).
The Pareto efficiency of a competitive equilibrium allocation is often interpreted as a powerful argument in favour of markets as a means of allocating resources. But we should be careful not to exaggerate the value of this theoretical result. It holds only under the following stringent conditions:
- In a market with many buyers and sellers of identical goods
- At the equilibrium, when all participants are price-takers
- When trade in the market has no external effects
- Where there is a complete contract between each buyer and seller.
Building block
For an introduction to incomplete contracts, see Section 6.6 on incomplete contracts in the labour market.
The fourth condition can be assumed to hold in our example: the exchange of a loaf of bread for money is governed by a complete contract. If you find there is no loaf of bread in the bag marked ‘bread’ when you get home, you can get your money back. But in other cases, it may be impossible to ensure that all the important aspects of the exchange are covered by a legally enforceable contract.
In practice:
- Most firms sell goods that are somehow differentiated from those of other firms—even bakeries selling identical loaves differ in location, and the service and range of goods they offer.
- Evidence of price-taking is hard to find (Section 8.10).
- Many goods have external effects—such as carbon emissions that contribute to climate change.
- Contracts are often incomplete: for example, the buyer of a second-hand car may not know whether it is reliable and roadworthy.
The implications for Pareto efficiency of external effects and incomplete contracts are analysed in Unit 10.
The distribution of the gains from trade
There are two criteria for assessing an allocation: efficiency and fairness (Unit 5). Even if we think that a market allocation is Pareto efficient, we should not conclude that it is necessarily a desirable one. As we explain in Unit 7, consumer and producer surplus do not tell us about fairness, because the sum of monetary gains is a poor measure of the overall benefits. But we can assess how the monetary gains are distributed between the producers and the consumers, by comparing the consumer and producer surplus. In Figure 8.12, consumer surplus is slightly higher than producer surplus. This happens because the demand curve is relatively steep (inelastic).
Just as we measure the responsiveness of consumers to price changes using the elasticity of demand, we can use the elasticity of supply to measure the responsiveness of producers. In Figure 8.12, demand is less elastic than supply. In general, the distribution of the total surplus between consumers and producers depends on the relative elasticities of demand and supply.
Exercise 8.3 Maximizing the surplus
Consider a market for the tickets to a football match. Six supporters of the Blue team would like to buy tickets; their valuations of a ticket (willingness to pay) are 8, 7, 6, 5, 4, and 3. The diagram below shows the demand ‘curve’. Six supporters of the Red team already have tickets, for which their reservation prices (willingness to accept) are 2, 3, 4, 5, 6, and 7.
Suppose all trades are to take place at a single price as in a competitive market where buyers and sellers are price-takers.
- Draw the supply and demand ‘curves’ on a single diagram. (Hint: the supply curve is also a step function, like the demand curve.)
- Show that four trades take place in equilibrium.
- What is the equilibrium price?
- Calculate the following by adding up the surpluses of each individual trade: consumer (buyer) surplus, producer (seller) surplus, total surplus in equilibrium.
Now suppose that the market operates through bargaining between individual buyers and sellers.
- Find a way of matching the buyers and sellers so that more than four trades occur. (Hint: suppose the highest WTP buyer buys from the highest WTA seller.)
- Using the scenario you found in step 5, work out the surplus from each trade and compare it to the equilibrium surplus from step 4.
- Starting from the allocation of tickets you obtained through bargaining, in which at least five tickets are owned by Blue supporters, is there a way through further trade to make one of the supporters better off without making anyone worse off?
Exercise 8.4 Gains from trade, deadweight loss, and elasticity of supply
- Consider the bread market in Figure 8.12, where the equilibrium price is €2.00 and 5,000 loaves are sold. Suppose that the bakeries get together to form a cartel (a group of firms that collude in order to increase their joint profits). They agree to raise the price to €2.70, and jointly cut production to supply the number of loaves that consumers demand at that price. Sketch a diagram to illustrate the market outcome under the cartel. Shade the areas on your diagram to show the consumer surplus, producer surplus, and deadweight loss caused by the cartel.
- Describe some features of goods that are likely to have highly elastic supply curves, and give some examples.
- Draw two diagrams, one where the supply curve is highly elastic, and one where the supply curve is highly inelastic. Use your diagrams to explain how the share of the gains from trade obtained by producers depends on the elasticity of the supply curve.
Question 8.6 Choose the correct answer(s)
In Figure 8.12, the market equilibrium output and price of the bread market is shown to be at (Q*, P*) = (5,000, €2). Suppose that the mayor decrees that bakeries must sell their bread at a price of €1.50. Based on this information, read the following statements and choose the correct option(s).
- Producer surplus is lower, because producers who would have sold bread at prices between €1.50 and €2 no longer sell their bread.
- Producer surplus is lower, because producers who would have sold bread at prices between €1.50 and €2 no longer sell their bread.
- Consumer surplus is lower, because fewer trades occur (consumers are no longer able to buy bread from the producers who would have sold at prices between €1.50 and €2).
- There is a deadweight loss, equal to the area of the triangle between the supply and demand curves to the left of equilibrium.
Question 8.7 Choose the correct answer(s)
Read the following statements about a competitive equilibrium allocation and choose the correct option(s).
- The allocation maximizes the total surplus, but that does not mean it is best for everyone in the market—for example, we may think it is unfair.
- This must be true, since the allocation maximizes the total surplus.
- The equilibrium allocation may not be Pareto efficient if it affects someone other than the buyers or sellers.
- This is a general property of competitive equilibrium.
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Joel Waldfogel. 1993. ‘The Deadweight Loss of Christmas’. The American Economic Review 83 (5) (December): pp. 1328–1336. ↩
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The Economist. 2009. ‘Is Santa a Deadweight Loss?’. Updated 14 December 2009. ↩