Unit 7 The firm and its customers

7.7 Gains from trade: The surplus and how it is divided

economic rent
Economic rent is the difference between the net benefit (monetary or otherwise) that an individual receives from a chosen action, and the net benefit from the next best alternative (or reservation option). See also: reservation option.
joint surplus
The sum of the economic rents of all involved in an economic interaction.
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.
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.

When people engage voluntarily in an economic interaction, they do so because it makes them better off: they obtain a surplus called economic rent. Their joint surplus is a measure of the gains from exchange or gains from trade. In Unit 5, we study the surplus from an interaction between two people (Angela and Bruno). We can analyse the economic interactions between consumers and the owners of a firm in the same way, judging the gains from buying and selling the good in terms of Pareto efficiency and fairness.

We will assume that the rules of the game, which determine how the product is allocated to consumers, are as follows:

  1. The firm decides how many items to produce, and sets a single price.
  2. Individual consumers then decide how many items (if any) to buy.

These rules reflect typical market institutions for consumer goods. We could imagine alternatives: a group of people who wanted cars could get together to produce a specification, then invite manufacturers to tender for the contract. But this might be difficult to arrange in practice.

Consider the interaction between Beautiful Cars and a consumer who is willing to pay $34,000 for a car. The firm has a constant marginal cost, c = 14,400 of producing a car. So a transaction in which the consumer buys the car at a price between these two amounts could benefit them both; the joint surplus is $19,600.

Figure 7.19 shows the joint surpluses on transactions between the firm and two individual consumers, and how they are divided between consumer and producer when the firm chooses its profit-maximizing point E, where P* = $27,200 and Q* = 32. It then shows how we can find the total surplus in the market by adding up the joint surpluses on the 32 cars that are sold.

In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The vertical distance between the marginal cost line and the demand curve at quantity 15 is the total surplus at the 15th consumer. The vertical distance between the marginal cost line and the demand curve at quantity 24 is the total surplus at the 24th consumer.
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Figure 7.19 The surplus in the market for Beautiful Cars.

The surplus for individual transactions: In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The vertical distance between the marginal cost line and the demand curve at quantity 15 is the total surplus at the 15th consumer. The vertical distance between the marginal cost line and the demand curve at quantity 24 is the total surplus at the 24th consumer.
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The surplus How it is divided
WTP Marginal cost, MC Surplus WTP – MC Price, P
Consumer’s share, WTP – P Producer’s share, P – MC
15th consumer 34,000 14,400 19,600 27,200 6,800 12,800
24th consumer 30,400 14,400 16,000 27,200 3,400 12,800

The surplus for individual transactions

There is a surplus on each car equal to the difference between the consumer’s WTP and the producer’s marginal cost. The vertical lines in the figure show the surpluses for the transactions with two of the consumers.

How the surplus is divided: In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The vertical distance between the marginal cost line and the demand curve at quantity 10 is the total surplus at the 10th consumer. This is split between producer surplus from 14,400 to 27,200, and consumer surplus from 27,200 to 36,000. The vertical distance between the marginal cost line and the demand curve at quantity 15 is the total surplus at the 15th consumer. This is split between producer surplus from 14,400 to 27,200, and consumer surplus from 27,200 to 34,000.
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How the surplus is divided

Beautiful Cars sets a price P* (point E). The buyer’s surplus (in red) is the difference between the WTP and the price, WTP – P*, and the producer receives P* – MC (purple).

The total surplus: In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The area enclosed by points (0, 14,400), (0, 40,000), E and (32, 14,400) is the sum of the joint surpluses.
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The total surplus

The shaded area enclosed by the demand curve and the marginal cost curve from 0 to 32 cars represents the sum of the joint surpluses on all 32 cars that are sold at this price.

The total surplus is divided between consumers and producer: In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The area enclosed by points (0, 14,400), (0, 27,200), E and (32, 14,400) is the sum of the producer’s surpluses. The area enclosed by points (0, 27,200), (0, 40,000) and E is the sum of the consumer’s surpluses.
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The total surplus is divided between consumers and producer

The area enclosed by the demand curve and the price of E is the sum of the surpluses obtained by the 32 consumers. The rectangle between the price and MC curve is the sum of the producer’s surpluses on each car, which is equal to (P – MC)Q*.

Profit: In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost) passing through point (32, 16,900), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The area enclosed by points (0, 14,400), (0, 16,900), (32, 16,900) and (32, 14,400) is fixed costs. The are enclosed by points (0, 16,900), (0, 27,200), E and (32, 16,900) is profit. The area enclosed by points (0, 27,200), (0, 40,000) and E is the sum of the consumer’s surpluses.
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Profit

The firm’s profit is (P – AC)Q*. The remaining part of the producer’s surplus covers the fixed costs.

consumer surplus
Each consumer who buys a good receives a surplus equal to their willingness to pay minus the price. The term ‘consumer surplus’ normally refers to the sum of these surpluses across all consumers.
producer surplus
The producer of a good receives a surplus on each unit, equal to the price minus the marginal cost of producing it. The term ‘producer surplus’ normally refers to the sum of these surpluses across all units sold.

In Figure 7.19, the sum of the joint surpluses on every good sold, corresponding to the shaded area between the demand curve and the marginal cost curve, gives us a measure of the total gains from trade in the market. We can split this area into the sum of the surpluses received by all the consumers, which is known as consumer surplus, and the sum of the surpluses received by the firm, known as producer surplus.

Note that these surpluses are rents received when an item is sold, relative to the outside option that it is not sold. In particular, the producer’s surplus on the item is the marginal profit, P – MC, from producing and selling it. So producer surplus doesn’t take account of fixed costs. Remember from Section 7.6 that Beautiful Cars has fixed cost F and constant marginal cost c, and we can write its profit in two ways:

\[\text{profit} = (P - c)\text{Q*} - F = (P - \text{AC)Q*}\]

The first expression tells us that profit is equal to producer surplus minus fixed costs. The second expression shows that the profit corresponds to the area of the rectangle between the price and the average cost in Figure 7.19. The remainder of the producer surplus area is equal to the fixed cost.

Producer surplus tells us the firm’s rent relative to the outside option of not producing the cars, but still incurring the fixed costs. In contrast, profit tells us how much economic rent the firm receives relative to the outside option of leaving the market altogether.

Pareto efficiency and deadweight loss

Figure 7.19 shows that the demand curve lies above the marginal cost curve up to point F, where Q = 64. There are potential gains from trade—positive surpluses—on 64 cars.

This means that when the firm chooses its profit-maximizing point, E, the allocation of cars in this market is not Pareto efficient. Only 32 consumers receive cars. So potential gains from trade have not been exhausted: there are some consumers who do not buy cars at the firm’s chosen price, but are nevertheless willing to pay more than it would cost the firm to produce them.

Pareto improvement
A change that benefits at least one person without making anyone else worse off. See also: Pareto dominant, Pareto criterion.
price discrimination
A selling strategy in which different prices are set for different buyers or groups of buyers based on the buyers’ differing willingness to pay.
deadweight loss
A measure of the total loss of surplus (that is, potential gains from trade) relative to the maximum available in the market.

If the firm made one more car, costing $14,400, it could be sold to the 33rd consumer at a price of—for example—£25,000. This would be a Pareto improvement. The 33rd consumer would be better off; the firm would make the same profit as before on the 32 cars sold for $27,200, plus extra profit on the 33rd car; and no other consumer would be affected.

Why does Beautiful Cars produce only 32 cars, when Pareto improvements would be possible—when both the firm and its consumers could be better off?

The answer is that point E is the best it can do under the rules of the game: it has to set a single price for all consumers. If it could sell 32 cars at $27,200 each to the consumers with highest WTP, and then sell more cars at lower prices to other consumers, it could increase its profit and make these additional consumers better off. But setting different prices for different buyers, known as price discrimination, cannot work unless the firm knows which ones will buy at the higher price. In Exercise 7.3, you can explore the effects of changing the rules of the game to allow price discrimination.

To realise all the potential gains from trade in this market, cars should be allocated to all consumers up to the one at point F on the demand curve, whose WTP is exactly equal to the marginal cost. Beyond point F there are no further potential Pareto improvements—producing another car would cost more than any of the remaining consumers would pay.

In Figure 7.20, the area enclosed by the demand curve and marginal cost curve from 32 to 64 cars represents the total loss of surplus from the firm’s decision to sell 32 cars, at point E, compared with point F, where all the gains from trade would be realised. This measure of lost surplus is called the deadweight loss. It is the sum of all the potential gains that are not realised, represented by the shaded triangular area between E and F.

In this diagram, the horizontal axis shows the quantity of cars, and ranges from 0 to 80. The vertical axis shows the price, and ranges from 0 to 45,000. Coordinates are (quantity, price). A downward-sloping, straight line passes through points (0, 40,000), E (32, 27,200) and F (64, 14,400). This is the demand curve. A horizontal line at price 14,400 is the marginal cost (or isoprofit for a profit of negative 80,000) intersects the demand curve at point F. There are three parallel, downward-sloping convex curves. From the lowest to the highest, these are the isoprofit curves for profits of 0 (average cost), 329,600 and 600,000. The isoprofit curve for profits of 0 lies above the marginal cost line at all points but intersects the demand curve in two points. The isoprofit curve for profits of 329,600 is tangential to the demand curve at point E. The isoprofit curve for profits of 600,000 lies above the demand curve at all points. The area enclosed by points (0, 14,400), (0, 40,000), E and (32, 14,400) is the sum of the joint surpluses. The area enclosed by points (0, 14,400), E and F is the deadweight loss.
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Figure 7.20 The firm’s profit-maximizing decision results in a deadweight loss (DWL).

Efficiency and the distribution of the surplus in markets for differentiated products

The analysis for Beautiful Cars illustrates a general result: the price set by the producer of a differentiated product results in a Pareto inefficient allocation. This happens because it chooses a price P* > MC. Consumers with WTP between P* and MC do not obtain the product, although they would pay more than the cost of producing it.

Note that what matters for efficiency is the quantity of the product that is traded. To assess Pareto efficiency, we need only ask: are all the items for which there is a positive surplus being produced and sold to consumers?

But the price also matters, for two reasons. First, given the rules of the game, it determines how many consumers buy cars. Secondly, the price determines the division of the total surplus sold between the owners of the firm and the customers.

bargaining power
The extent of a person or firm’s advantage in securing a larger share of the economic rents made possible by an interaction.
market power
A firm has market power if it can sell its product at a range of feasible prices, so that it can benefit by acting as a price-setter (rather than a price-taker).

In general, the division of gains from economic interactions depends on the relative bargaining power of the participants: that is, their ability to influence the price in their own favour. The owners of Beautiful Cars have bargaining power—market power—as the only seller of a particular car. They can set a high price, knowing that consumers who value the car highly will accept it. An individual consumer has no power to bargain for a better deal because the firm has many other potential customers. Beautiful Cars’ ability to set a high price increases its own surplus and reduces the gains for consumers.

Can we say anything about fairness? One consideration is whether the high price set by the producer is unfair because it excludes buyers with lower incomes. A lower price for Beautiful Cars could give lower-income households access to a means of transport and a wider range of job opportunities, for example.

But this model provides no further insight into the fairness of the allocation of a differentiated product. We have measured the gain to each consumer in monetary terms, as the difference between the WTP and the price, so it cannot be used to compare the benefit to different consumers. The same monetary surplus may be valued very differently by rich and poor consumers: for example, they would make different judgements about whether the purchase was a bargain, depending on how much money they had left for other spending.

Why you should be careful how you interpret surplus

It is common practice in economics to use consumer and producer surplus to measure ‘welfare’ in a market. But producer surplus can be misleading as a measure of the firm’s benefit, since it ignores fixed costs. And since the monetary gains used to calculate consumer surplus do not mean the same thing to different consumers, adding them together is a poor measure of overall consumer benefit. Adding individual surpluses together can be useful for comparing different outcomes in a market, as we compared point E and point F above. But it tells us little about overall welfare.

Exercise 7.3 Changing the rules of the game

  1. Suppose that Beautiful Cars had sufficient information and so much bargaining power that it could charge each consumer, separately, the maximum they would be willing to pay. Draw the demand and marginal cost curves (as in Figure 7.20), and indicate on your diagram:
    1. the number of cars sold
    2. the highest price paid by any consumer
    3. the lowest price paid
    4. the consumer and producer surplus.
  2. Can you think of any examples of goods that are sold in this way?
  3. Why is this type of pricing not common practice?
  4. Some firms charge different prices to different groups of consumers—for example, airlines may charge higher fares for last-minute travellers. Why would they do this and what effect would it have on the consumer and producer surpluses? What can/cannot we say about the effect on overall welfare in the market?
  5. Suppose a competition policy is implemented that prevents firms from charging different prices to different groups of consumers. How could this change give consumers more bargaining power?
  6. Under these rules, how many cars would be sold?
  7. Under these rules, what would the producer and consumer surpluses be?

Question 7.12 Choose the correct answer(s)

Read the following statements and choose the correct option(s).

  • Consumer surplus is the difference between the consumers’ willingness to pay and what they actually pay.
  • Producer surplus equals the firm’s profit.
  • Deadweight loss is the loss incurred by the producer for not selling more cars.
  • All possible gains from trade are achieved when the firm chooses its profit-maximizing output and price.
  • Correct: to be more precise, each consumer receives a surplus equal to the difference between the WTP and the price, and consumer surplus is the sum of the surpluses of all consumers.
  • Producer surplus is the difference between the firm’s revenue and its marginal costs. This is not the same as profit, because it doesn’t account for the fixed costs of production. The profit is the producer surplus minus the fixed costs.
  • The deadweight loss is the loss of potential total surplus. It is the sum of the surplus losses of both the consumers and the producer.
  • A firm producing a differentiated product chooses a level of output at which some gains from trade are not achieved. There are consumers willing to pay more than the marginal cost of a car who do not receive cars.