The law of supply and the supply curve — Economics

Before this

Supply — how much sellers offer · coming soon
Consumer and producer surplus
The law of demand

This leads to

What shifts supply
Price elasticity of supply
Finding equilibrium algebraically

Why would a café make more coffee just because the price rose?

Buyers obey the law of demand for reasons you can feel: a higher price hurts your budget, so you buy less. Sellers are harder to understand. Suppose the price of coffee in a town rises from $4 to $6 a cup. Why should the cafés make more cups? Their coffee machines did not get faster. Their staff did not multiply.

And yet, in almost every market, a higher price brings out more of the good. This lecture explains why, from the inside of a café. The answer is about cost, and it is the same answer the lecture on consumer and producer surplus borrowed without explaining.

The law of supply

Other things being equal (ceteris paribus), when the price of a good rises, the quantity supplied rises. When the price falls, the quantity supplied falls.

Price and quantity supplied move in the same direction. That is the opposite of demand, where they move in opposite directions. Quantity supplied always means a plan: how much sellers are willing and able to sell at a given price, in a given time.

The lecture on consumer and producer surplus introduced the town's coffee supply as $Q_{s} = 100 P - 100$ , with quantity in cups per week. Here is its schedule:

Price ($)	Quantity supplied (cups per week)
2	100
4	300
6	500
8	700

Plot it with price on the vertical axis, as for demand, and you get the supply curve, S. It slopes upward from left to right. That slope is the law of supply in a picture.

The coffee supply schedule, plotted. Each point is one row of the table. The line meets the price axis at $1: below that price, no café would sell a single cup.

The reason: each extra cup costs more to make

That lecture promised to explain why the lowest acceptable price rises as more cups are made. Here is the explanation. It is the hard part of this lecture, so spend time here.

Think about a café owner, Tunde, deciding how many cups to make each week. The first batch is cheap. His machine is already on, his staff are already working, and the beans are in the cupboard. The extra cost of that batch is small.

Making more is different. To make a second and third batch, he must keep staff late and pay them overtime. For even more, he must hire a second machine or buy beans in a hurry at a higher price. Each extra batch costs more than the one before. Economists call the cost of one extra unit the marginal cost, and for most firms it rises as output rises.

Now the logic is simple. Tunde makes an extra batch only if the price covers its extra cost. At $4, he makes every batch that costs $4 or less to produce, and stops. If the price rises to $6, the batches that cost between $4 and $6 now pay for themselves too. So he makes more. That is it. That is the whole idea: a higher price makes more of the expensive-to-produce units worth producing.

Read the supply curve upwards, as you read the demand curve. Its height above any quantity is the lowest price at which that unit would be supplied, and that is its extra cost. For the 250th cup, the height is $1 + 250 \div 100 = $3.50$ . Try it below.

Explore — why a higher price brings out more cups

Move the price. Each bar is a batch of 100 cups, as tall as its extra cost to the town's cafés. A batch is made only when the price covers its cost.

Price: $4

At a price of $4 (the dashed line), the batches whose extra cost is below $4 are made.

The batches cost $1.50, $2.50, $3.50, $4.50 and so on. At $4, three batches (300 cups) are made. The darker parts, between each bar's top and the price, add up to the producer surplus: 100 × ($2.50 + $1.50 + $0.50) = $450.

Notice two things. First, as the price rises, more bars pass the test, so more cups are supplied. Second, the darker area between the price and the bars is the producer surplus you have already met. It lies above the supply curve and below the price. Some books wrongly call it the area under the supply curve. The area under the supply curve is the extra cost of making the cups, not the sellers' gain.

There is a second reason the curve slopes up, and it works across the whole market. A higher price draws new sellers in. At $4, a café with high costs may not find it worth opening. At $6, it may. When it opens, its cups add to the market's quantity supplied. So a higher price brings out more cups in two ways: existing cafés make more, and new cafés join. This is the mirror image of demand, where a higher price made some buyers leave the market.

Market supply is the sellers added together

The town's supply is built from its cafés, just as market demand was built from individual buyers. At each price, add the quantities that each café would supply.

Suppose Mei's café supplies $60 P - 60$ cups and Tunde's supplies $40 P - 40$ cups. At $4, Mei supplies 180 and Tunde supplies 120, so the market supplies 300. At every price, the two add to $100 P - 100$ , the town's supply. On a graph, this means adding the curves sideways: at each height (price), add the distances along the quantity axis.

Along the curve, or a new curve?

The same distinction from demand applies, for the same reason. The supply curve is drawn for one set of conditions: one level of costs, one technology, one number of sellers.

A change in the good's own price causes a movement along the supply curve: a change in quantity supplied. A higher price moves the point up and to the right.
A change in anything else that affects sellers, such as the cost of beans, new technology or the number of cafés, causes a shift of the whole curve: a change in supply. A rightward shift is an increase in supply. A leftward shift is a decrease.

Why does a cost change shift the curve? Because the curve is the extra cost of each unit. If beans become more expensive, every batch costs more to make. So every point on the curve moves up, and at each price fewer batches pay for themselves. The next lecture goes through every factor that shifts supply. For now, practise the distinction below.

Sorter — movement along supply, or a shift?

Each card describes a change. Choose a card, then choose the box. Think about what happens to the coffee supply curve.

Each change, and what it does to the supply curve for coffee:

Change	Effect on S
The price of coffee rises	movement up along S
Coffee beans become more expensive	shift left
A faster espresso machine is invented	shift right
Three new cafés open in town	shift right
The price of coffee falls	movement down along S
Café staff wages rise	shift left
Buyers' incomes rise, and the price of coffee goes up	movement up along S
A storm damages the town's coffee machines	shift left

Stop and think

A drought destroys part of a country's wheat crop, and the price of wheat rises. A student says: "The price rose, so this is a movement along the supply curve." Is that right?

Show the answer

No. The drought is not a price change. It reduces what farmers can supply at every price, so the supply curve shifts left. The rise in price is the result of that shift. Buyers then respond to the higher price by buying less, which is a movement along the demand curve. One event, two different curves: supply shifts, and the market moves along demand to its new equilibrium.

Worked examples

Worked Example 1 — Reading a supply equation both ways

For coffee, $Q_{s} = 100 P - 100$ . Find the quantity supplied at $5. Then find the lowest price at which the 450th cup would be supplied.

Across: at $P = 5$ , $Q_{s} = 100 \times 5 - 100 = 400$ cups.

Upwards: rearrange to find the price. $Q_{s} + 100 = 100 P$ , so $P = (Q_{s} + 100) \div 100 = 1 + Q_{s} \div 100$ . For the 450th cup, $P = 1 + 450 \div 100 = 5.5$ . So the 450th cup costs $5.50 extra to make, and it is supplied only if the price is at least $5.50.

Check by substituting back: $100 \times 5.5 - 100 = 450$ . Correct. Notice that the 450th cup needs a higher price than $5, where only 400 cups are supplied. That matches the upward slope.

Worked Example 2 — Movement or shift, with the diagram

(a) The price of phones rises. (b) Memory chips, a key input for phones, become much more expensive. What happens to the supply of phones in each case?

(a) The good's own price changed. This is a movement up along the supply curve. Quantity supplied rises, because more phones now earn more than their extra cost. On the diagram, an arrow runs up along S.

(b) An input cost rose. Every phone costs more to make, so the whole supply curve shifts left, from S₁ to S₂. At every price, fewer phones are supplied. This is a decrease in supply.

Worked Example 3 — A real case: US crude oil, 2014 to 2016

The change. Between June and late November 2014, the price of US crude oil fell by more than 31%. It fell by a further 13% after the oil producers' group OPEC decided to keep its own production unchanged (US Energy Information Administration, December 2014). The EIA noted that at $60 a barrel, prices were near or below the costs of some of the most expensive US wells.

The prediction. The law of supply predicts a movement down along the supply curve. When the price no longer covers the extra cost of the most expensive wells, those wells stop being drilled, and quantity supplied should fall.

What happened. Not at first. In 2015, US crude oil production averaged 9.4 million barrels a day, more than in 2014. Wells that were already drilled kept pumping. Only in 2016 did production fall, to an average of 8.9 million barrels a day, about 5% lower. Late in 2016, as prices rose again, monthly production started to grow again (EIA, March 2017).

The verdict. The law of supply held, but slowly. A café can make fewer cups tomorrow. An oil company cannot un-drill a well, and starting or stopping new drilling takes months. So supply responded weakly at first and more strongly later. Other things were also changing, such as cheaper drilling methods, so not every movement in the data comes from price alone. How much and how fast supply responds to price is measured by the price elasticity of supply, in a later lecture.

Three classic mistakes

Trap 1 — "The price rose, so supply increased"

A higher price increases the quantity supplied: a movement along the curve. "An increase in supply" means the whole curve shifts right. The two phrases describe different events, and examiners check which one you use.

Trap 2 — Producer surplus under the supply curve

Producer surplus is the area above the supply curve and below the price. The area under the supply curve is the cost of producing the units. Shading the wrong region is one of the most common errors on welfare diagrams.

Trap 3 — Letting a buyers' change shift supply

A rise in incomes, a change in tastes or a fall in the price of a complement affects buyers. It shifts demand. Supply only feels the result, a change in price, and moves along its curve.

Try it yourself

Work each one on paper first. Open a hint only when you are stuck.

For coffee, $Q_{s} = 100 P - 100$ . Find the quantity supplied at $3.50, and the lowest price at which the 150th cup would be supplied.

Hint 1
For the first part, substitute $P = 3.5$ .

Hint 2
For the second part, use $P = 1 + Q_{s} \div 100$ .

Full answer
At $3.50: $Q_{s} = 350 - 100 = 250$ cups. For the 150th cup: $P = 1 + 150 \div 100 = $2.50$ . Check: $100 \times 2.5 - 100 = 150$ . Correct.
A town has two bakeries. Bakery A supplies $20 P - 20$ loaves and Bakery B supplies $30 P - 60$ loaves, but neither can supply fewer than zero. Find the market quantity supplied at $1.50, $3 and $4.

Hint 1
Work out each bakery separately at each price. If a formula gives a negative number, that bakery supplies nothing.

Hint 2
Bakery B supplies nothing until the price reaches $2, because $30 \times 2 - 60 = 0$ .

Full answer
At $1.50: A supplies 10, B supplies 0, market 10. At $3: A supplies 40, B supplies 30, market 70. At $4: A supplies 60, B supplies 60, market 120. Bakery B only joins the market once the price passes $2, which is the "new sellers join" reason for the upward slope. Check at $4: $20 \times 4 - 20 = 60$ and $30 \times 4 - 60 = 60$ .
In the market for tea, say whether each change is a movement along the supply curve or a shift, and in which direction. (a) The price of tea rises. (b) A new picking machine is used on tea farms. (c) Floods ruin tea fields. (d) A health report makes buyers want more tea, and the price rises.

Hint 1
Ask of each change: is it the price of tea itself, or something that changes what farmers can supply at every price?

Hint 2
In (d), the report changes buyers' tastes. Which curve do tastes belong to?

Full answer
(a) Movement up along S. (b) Shift right: better technology lowers the extra cost. (c) Shift left: less can be supplied at every price. (d) Movement up along S: the report shifts demand right, and sellers respond to the higher price by moving along their supply curve.
In the coffee market, the price rises from $4 to $6. Producer surplus rises from $450 to $1 250. Split the $800 increase into two parts, and explain each.

Hint 1
Part of the gain comes from the 300 cups that were already being made. Part comes from the new cups.

Hint 2
The old cups each earn $2 more. The new cups, from 300 to 500, form a small triangle between the old price, the new price and the supply curve.

Full answer
The 300 cups already made each earn $2 more: $300 \times 2 = $600$ . The 200 new cups each earn a little over their extra cost; together they form a triangle of area $\frac{1}{2} \times 200 \times 2 = $200$ . Total increase $= 600 + 200 = $800$ . Check: $\frac{1}{2} \times 500 \times (6 - 1) = $1 250$ , and $1250 - 450 = 800$ .

The bigger idea

The supply curve and the demand curve are built the same way, from the inside. Demand is the value of each extra unit to buyers. Supply is the cost of each extra unit to sellers. Where value meets cost, the market settles, and the lecture on surplus showed that this is exactly where total surplus is largest.

The oil case adds a lesson that the diagram hides: time. A supply curve describes plans for one period. Over a few weeks, sellers can change little. Over a few years, they can build, drill, hire and invest. So the same price change can bring a small response at first and a large one later.

Key concepts in this lesson

The law of supply says that, other things being equal, a higher price raises the quantity supplied and a lower price reduces it.
The supply curve slopes upward mainly because the extra (marginal) cost of each unit rises as output rises, so a higher price makes more units worth producing.
A higher price also draws new sellers into the market, and market supply is the sum of every seller's quantity at each price.
A change in the good's own price is a movement along the supply curve, while a change in costs, technology or the number of sellers shifts the whole curve.
Producer surplus is the area above the supply curve and below the price, not the area under the supply curve.