Producer Surplus and the Supply Curve

Just as some buyers of a good would have been willing to pay more for their purchase than the price they actually pay, some sellers of a good would have been willing to sell it for less than the price they actually receive. So just as there are consumers who receive consumer surplus from buying in a market, there are producers who receive producer surplus from selling in a market.

Cost and Producer Surplus

Consider a group of students who are potential sellers of used textbooks. Because they have different preferences, the various potential sellers differ in the price at which they are willing to sell their books. The table in Figure 4-6 shows the prices at which several different students would be willing to sell. Andrew is willing to sell the book as long as he can get at least $5; Betty won’t sell unless she can get at least $15; Carlos, unless he can get $25; Donna, unless she can get $35; Engelbert, unless he can get $45.

The Supply Curve for Used Textbooks The supply curve illustrates seller’s cost, the lowest price at which a potential seller is willing to sell the good, and the quantity supplied at that price. Each of the five students has one book to sell and each has a different cost, as indicated in the accompanying table. At a price of $5 the quantity supplied is one (Andrew), at $15 it is two (Andrew and Betty), and so on until you reach $45, the price at which all five students are willing to sell.

The lowest price at which a potential seller is willing to sell has a special name in economics: it is called the seller’s cost. So Andrew’s cost is $5, Betty’s is $15, and so on.

Using the term cost, which people normally associate with the monetary cost of producing a good, may sound a little strange when applied to sellers of used textbooks. The students don’t have to manufacture the books, so it doesn’t cost the student who sells a used textbook anything to make that book available for sale, does it?

A seller’s cost is the lowest price at which he or she is willing to sell a good.

Yes, it does. A student who sells a book won’t have it later, as part of his or her personal collection. So there is an opportunity cost to selling a textbook, even if the owner has completed the course for which it was required. And remember that one of the basic principles of economics is that the true measure of the cost of doing something is always its opportunity cost. That is, the real cost of something is what you must give up to get it.

So it is good economics to talk of the minimum price at which someone will sell a good as the “cost” of selling that good, even if he or she doesn’t spend any money to make the good available for sale. Of course, in most real-world markets the sellers are also those who produce the good and therefore do spend money to make it available for sale. In this case, the cost of making the good available for sale includes monetary costs, but it may also include other opportunity costs.

Individual producer surplus is the net gain to an individual seller from selling a good. It is equal to the difference between the price received and the seller’s cost.

Getting back to the example, suppose that Andrew sells his book for $30. Clearly he has gained from the transaction: he would have been willing to sell for only $5, so he has gained $25. This net gain, the difference between the price he actually gets and his cost—the minimum price at which he would have been willing to sell—is known as his individual producer surplus.

Just as we derived the demand curve from the willingness to pay of different consumers, we can derive the supply curve from the cost of different producers. The step-shaped curve in Figure 4-6 shows the supply curve implied by the costs shown in the accompanying table. At a price less than $5, none of the students are willing to sell; at a price between $5 and $15, only Andrew is willing to sell, and so on.

As in the case of consumer surplus, we can add the individual producer surpluses of sellers to calculate the total producer surplus, the total net gain to all sellers in the market. Economists use the term producer surplus to refer to either individual or total producer surplus. Table 4-2 shows the net gain to each of the students who would sell a used book at a price of $30: $25 for Andrew, $15 for Betty, and $5 for Carlos. The total producer surplus is $25 + $15 + $5 = $45.

Potential seller

Cost

Price received

Individual producer surplus = Price received – Cost

Andrew

$5

$30

$25

Betty

15

  30

  15

Carlos

25

  30

    5

Donna

35

  —

  —

Engelbert

45

  —

  —

All sellers

Total producer surplus = $45

Table : TABLE 4-2 Producer Surplus When the Price of a Used Textbook = $30

Total producer surplus is the sum of the individual producer surpluses of all the sellers of a good in a market.

Economists use the term producer surplus to refer both to individual and to total producer surplus.

As with consumer surplus, the producer surplus gained by those who sell books can be represented graphically. Figure 4-7 reproduces the supply curve from Figure 4-6. Each step in that supply curve is one book wide and represents one seller. The height of Andrew’s step is $5, his cost. This forms the bottom of a rectangle, with $30, the price he actually receives for his book, forming the top. The area of this rectangle, ($30 − $5) × 1 = $25, is his producer surplus. So the producer surplus Andrew gains from selling his book is the area of the red rectangle shown in the figure.

Producer Surplus in the Used-Textbook Market At a price of $30, Andrew, Betty, and Carlos each sell a book but Donna and Engelbert do not. Andrew, Betty, and Carlos get individual producer surpluses equal to the difference between the price and their cost, illustrated here by the shaded rectangles. Donna and Engelbert each have a cost that is greater than the price of $30, so they are unwilling to sell a book and so receive zero producer surplus. The total producer surplus is given by the entire shaded area, the sum of the individual producer surpluses of Andrew, Betty, and Carlos, equal to $25 + $15 + $5 = $45.

Let’s assume that the campus bookstore is willing to buy all the used copies of this book that students are willing to sell at a price of $30. Then, in addition to Andrew, Betty and Carlos will also sell their books. They will also benefit from their sales, though not as much as Andrew, because they have higher costs. Andrew, as we have seen, gains $25. Betty gains a smaller amount: since her cost is $15, she gains only $15. Carlos gains even less, only $5.

Again, as with consumer surplus, we have a general rule for determining the total producer surplus from sales of a good: The total producer surplus from sales of a good at a given price is the area above the supply curve but below that price.

This rule applies both to examples like the one shown in Figure 4-7, where there are a small number of producers and a step-shaped supply curve, and to more realistic examples, where there are many producers and the supply curve is smooth.

Consider, for example, the supply of wheat. Figure 4-8 shows how producer surplus depends on the price per bushel. Suppose that, as shown in the figure, the price is $5 per bushel and farmers supply 1 million bushels. What is the benefit to the farmers from selling their wheat at a price of $5? Their producer surplus is equal to the shaded area in the figure—the area above the supply curve but below the price of $5 per bushel.

Producer Surplus Here is the supply curve for wheat. At a price of $5 per bushel, farmers supply 1 million bushels. The producer surplus at this price is equal to the shaded area: the area above the supply curve but below the price. This is the total gain to producers—farmers in this case—from supplying their product when the price is $5.

How Changing Prices Affect Producer Surplus

As with the case of consumer surplus, a change in price alters producer surplus. But the effects are opposite. While a fall in price increases consumer surplus, it reduces producer surplus. And a rise in price reduces consumer surplus but increases producer surplus.

To see this, let’s first consider a rise in the price of the good. Producers of the good will experience an increase in producer surplus, though not all producers gain the same amount. Some producers would have produced the good even at the original price; they will gain the entire price increase on every unit they produce. Other producers will enter the market because of the higher price; they will gain only the difference between the new price and their cost.

Figure 4-9 is the supply counterpart of Figure 4-5. It shows the effect on producer surplus of a rise in the price of wheat from $5 to $7 per bushel. The increase in producer surplus is the sum of the shaded areas, which consists of two parts. First, there is a red rectangle corresponding to the gains to those farmers who would have supplied wheat even at the original $5 price. Second, there is an additional pink triangle that corresponds to the gains to those farmers who would not have supplied wheat at the original price but are drawn into the market by the higher price.

A Rise in the Price Increases Producer Surplus A rise in the price of wheat from $5 to $7 leads to an increase in the quantity supplied and an increase in producer surplus. The change in total producer surplus is given by the sum of the shaded areas: the total area above the supply curve but between the old and new prices. The red area represents the gain to the farmers who would have supplied 1 million bushels at the original price of $5; they each receive an increase in producer surplus of $2 for each of those bushels. The triangular pink area represents the increase in producer surplus achieved by the farmers who supply the additional 500,000 bushels because of the higher price. Similarly, a fall in the price of wheat from $7 to $5 generates a reduction in producer surplus equal to the sum of the shaded areas.

If the price were to fall from $7 to $5 per bushel, the story would run in reverse. The sum of the shaded areas would now be the decline in producer surplus, the decrease in the area above the supply curve but below the price. The loss would consist of two parts, the loss to farmers who would still grow wheat at a price of $5 (the red rectangle) and the loss to farmers who cease to grow wheat because of the lower price (the pink triangle).

!worldview! ECONOMICS in Action: High Times Down on the Farm

High Times Down on the Farm

The average value of an acre of Iowa farmland hit a record high of $8,716 in 2013, an increase of 5% from the previous year. This followed three years in a row in which prices had increased by more than 15%. Figure 4-10 shows the explosive increase in the price of Iowa farmland from 2009 to 2013. And there was no mystery as to why: it was all about the high prices being paid for corn, wheat, and soybeans. From 2009 to 2013, the price of corn had jumped by 75%, soybeans by 45%, and wheat by 40%.

Why were Iowa farm products commanding such high prices? There are three main reasons: ethanol, rising incomes in countries like China, and poor weather in other foodstuff-producing countries like Australia and Ukraine.

The Price of Iowa Farmland, 1950-2013
Source: Iowa State University Iowa Land Value Survey.

Ethanol—a product made from corn and the same kind of alcohol that’s in beer and other alcoholic drinks—can also fuel automobiles. And in recent years government policy, at both the federal and state levels, has encouraged the use of gasoline that contains a percentage of ethanol. There are a couple of reasons for this policy, including some benefits in fighting air pollution and the hope that using ethanol will reduce U.S. dependence on imported oil. Since ethanol comes from corn, the shift to ethanol fuel has led to an increase in the demand for corn.

But Iowa farmers have also benefited greatly from events in the global economy. Changes in the demand for and supply of foodstuffs in world markets have led to rising prices for American corn, wheat, and soybeans. Rising incomes in countries like China have led to increased food consumption and increased demand for these foodstuffs. Simultaneously, very bad weather in food-producing countries like Australia has led to a fall in supply. Predictably, increased demand coupled with reduced supply has led to a surge in foodstuff prices and a windfall for Iowa farmers.

What does this have to do with the price of land? A person who buys a farm in Iowa buys the producer surplus generated by that farm. And higher prices for corn, soybeans, and wheat, which raise the producer surplus of Iowa farmers, make Iowa farmland more valuable. According to an Iowa State University survey, the average price of an acre of Iowa farmland has surged 383% in 10 years.

Quick Review

  • The supply curve for a good is determined by the cost of each seller.

  • The difference between the price and cost is the seller’s individual producer surplus.

  • The total producer surplus is equal to the area above the market supply curve but below the price.

  • When the price of a good rises, producer surplus increases through two channels: the gains of those who would have supplied the good at the original price and the gains of those who are induced to supply the good by the higher price. A fall in the price of a good similarly leads to a fall in producer surplus.

4-2

  1. Question 4.2

    Consider again the market for cheese-stuffed jalapeno peppers. There are two producers, Cara and Jamie, and their costs of producing each pepper are given in the accompanying table. (Neither is willing to produce more than 4 peppers at any price.) a. Use the accompanying table to construct the supply schedule for peppers for prices of $0.00, $0.10, and so on, up to $0.90. b. Then, calculate the total producer surplus when the price of a pepper is $0.70.

    Quantity of peppers

    Cara’s cost

    Jamie’s cost

    1st pepper

    $0.10

    $0.30

    2nd pepper

    0.10

    0.50

    3rd pepper

    0.40

    0.70

    4th pepper

    0.60

    0.90

Solutions appear at back of book.