What shifts supply — the determinants — Economics

Before this

This leads to

Tax incidence
Subsidies
Price elasticity of supply

A $1 tax: how far does supply move?

A town's council puts a tax of $1 on every cup of coffee sold. The cafés must pay it. Every textbook agrees on the first part of the answer: the supply curve for coffee shifts to the left.

But by how much? One cup? A dollar? A hundred cups? Many students write "supply shifts left by the amount of the tax". Look at that sentence closely. The tax is measured in dollars. A shift to the left is measured in cups. The sentence mixes two different units, so it cannot be right as it stands.

This lecture answers the question exactly. On the way, it goes through every factor that shifts supply, as the last lecture promised. They all follow from one test, and the tax question is the clearest way into that test.

One curve, two ways to read it

In the last lecture, the town's coffee supply was $Q_{s} = 100 P - 100$ , with quantity in cups per week. You can read this curve in two directions.

Across: at a given price, how many cups are supplied? At $4, the answer is 300 cups.

Upwards: for a given cup, what is the lowest price at which it is supplied? That height is the extra (marginal) cost of making that cup. For the 300th cup, it is $1 + 300 \div 100 = $4$ .

Now add the $1 tax. Every cup now costs the café $1 more to sell, because $1 of the price goes to the council. So the lowest acceptable price for every cup rises by exactly $1. The 300th cup needed $4 before. Now it needs $5. Every point on the curve moves up by $1.

Read the new curve across instead. At $4, a café keeps only $3 after the tax. Before the tax, $3 brought out 200 cups. So at $4, only 200 cups are now supplied, 100 fewer than before. The curve has also moved left by 100 cups, at every price.

The $1 tax moves every point of the coffee supply curve up by $1 (the short upward arrow). Read across at $4, the same new curve is 100 cups to the left (the short arrow pointing left). The new curve is

Q_{s} = 100 P - 200

That is it. That is the whole idea. "Up" and "left" are not two different shifts. They are two ways of reading one new curve. The upward shift is exactly the tax: $1. The leftward shift depends on the slope. On this curve, every $1 changes the quantity by 100 cups, so the $1 tax moves it 100 cups left. On a steeper curve, the same $1 tax would move it fewer cups. Try it below.

Graph — a tax or a subsidy on the supply curve

Choose a tax or a subsidy, and a gentle or a steep supply curve. Then change the amount per cup. Compare the shift up or down with the shift sideways.

Amount per cup: $1.00

The same $1 per cup, on two supply curves of different slopes. The gentle curve is Qₛ = 100P − 100, and the steep curve is Qₛ = 50P − 50.

Change	New curve	Shift	Cups at $4
Gentle, $1 tax	Qₛ = 100P − 200	up $1	300 → 200
Steep, $1 tax	Qₛ = 50P − 100	up $1	150 → 100
Gentle, $1 subsidy	Qₛ = 100P	down $1	300 → 400

The vertical shift is always the amount per cup. The sideways shift is 100 cups on the gentle curve and 50 cups on the steep one.

Did you see it? On both curves, the shift up or down always equals the amount per cup. The sideways shift halves when the curve is steep. So the correct sentence is: a tax of $t per unit moves the supply curve up by exactly $t; how far it moves to the left depends on the slope. A subsidy is the mirror image. It moves the curve down by the subsidy, which is a shift to the right.

Stop and think

Café wages rise. One student says, "The supply curve shifts up." Another says, "The supply curve shifts left." Who is right?

Show the answer

Both of them. Higher wages raise the cost of every cup, so the lowest acceptable price for every cup rises: the curve moves up. Read across, at every price fewer cups now cover their cost: the same curve is further left. Up and left describe one shift, a decrease in supply. In the same way, "down" and "right" both describe an increase in supply.

The test behind every determinant

The tax shows the test that works for everything else. The supply curve is the extra cost of each unit, read upwards. So ask one question of any change:

The test for a supply shift

Does the change alter the full cost of supplying each unit today, including what the seller gives up by supplying it? Or does it change the number of sellers?

If costs rise, or sellers leave, supply decreases: the curve moves up and to the left. If costs fall, or sellers join, supply increases: the curve moves down and to the right.

The phrase "what the seller gives up" matters. Two of the determinants below do not change the money a seller spends at all. They change what the seller loses by selling this good today instead of something else, or instead of later.

Seven determinants, each with its reason

Textbooks count the determinants of supply differently: six, seven or eight. The count does not matter. The test does. Here are seven, each checked against the test.

1. The cost of inputs

Wages, raw materials, energy and rent are the inputs to production. If any of them becomes more expensive, every unit costs more to make. Supply decreases: the curve moves up and left. If an input becomes cheaper, supply increases. For example, a fall in the price of oil lowers the cost of plastics and of running factories, so the supply of many manufactured goods increases.

2. Technology

Better technology means more output from the same inputs: a faster machine, a better seed, smarter delivery routes. Each unit then costs less to make, so supply increases. Technology almost always moves supply to the right, because firms rarely choose a worse method once they have a better one.

3. Indirect taxes and subsidies

A tax per unit sold adds to the cost of supplying each unit, so it moves the curve up by exactly the tax. A subsidy is a payment from the government for each unit produced. It works like a cut in cost, so it moves the curve down by exactly the subsidy. Many countries subsidise farming, which increases the supply of food. What a tax or a subsidy does to the market price is a separate question, studied in the lectures on tax incidence and subsidies.

4. The prices of other goods the seller could make

A farmer's field can grow wheat or maize. If the price of maize rises, every field used for wheat now gives up more maize income. So the full cost of growing wheat has risen, even though seeds and wages cost the same. Farmers switch some fields to maize, and the supply of wheat decreases. Goods that compete for the same resources like this are called substitutes in production.

Some goods come out of the same process: beef and leather both come from cattle. They are in joint supply. If the price of beef rises, farmers raise more cattle, and the supply of leather increases, even though nothing happened in the leather market.

5. Expectations of future prices

This one surprises many students, so it has its own section below. If sellers can store their good and expect a higher price later, selling today means giving up that higher price. Supply today decreases.

6. The number of sellers

Market supply is the sum of every seller's quantity. When new sellers join, supply increases at every price. When sellers leave, it decreases. Ride-hailing apps, for example, brought many new drivers into city transport, which increased the supply of taxi-like rides.

7. Weather and natural conditions

A drought, a flood or a frost means fewer crops from the same land, seed and work. Each unit of output then costs more, so supply decreases. A good growing season increases supply. The same idea applies to natural resources: the discovery of a new oil field increases supply, and an overfished sea decreases it.

Expectations: the determinant that seems backwards

Before reading the explanation, make a prediction.

Predict — sellers expect a higher price

Rice farmers have rice stored in dry sheds. News arrives that the price of rice will probably rise sharply next month. What happens to the supply of rice in the market today? Choose one, then read the explanation.

The answer, with the reasoning:

Supply today decreases: the curve shifts left. Rice can be stored, so every bag sold today is a bag that cannot be sold next month at the higher price. That lost chance is part of the full cost of selling today. So at every price today, farmers offer less, and keep more in their sheds. A common wrong answer is that supply increases because "prices are rising". But the price has not risen yet; only the expectation has changed. Another wrong answer is "no change, because nothing has happened today". The expectation itself is the change.

Notice the condition hidden in the question: the rice could be stored. Expectations matter most for goods that keep, such as grain, oil, metals and gold. For fresh bread, there is little sense in holding back today's loaves, because they will be stale tomorrow. The determinant works through what sellers give up, so it is strong only when waiting is possible.

This is the mirror image of buyers. In the demand lectures, buyers who expected a lower price later bought less today. Here, sellers who expect a higher price later sell less today. In both cases, people move their trading to the time that suits them better.

Worked examples

Worked Example 1 — A cost rise, with numbers

The price of coffee beans rises, so every cup costs the town's cafés $0.50 more to make. Before, $Q_{s} = 100 P - 100$ . Find the new supply equation and the quantity supplied at $4.

Every cup's lowest acceptable price rises by $0.50. Before, the lowest price for a cup was $P = 1 + Q_{s} \div 100$ . Now it is $P = 1.5 + Q_{s} \div 100$ . Rearranging, $Q_{s} = 100 P - 150$ .

At $4: $Q_{s} = 400 - 150 = 250$ cups, down from 300. The curve moved up by $0.50 and left by 50 cups.

Check: the 250th cup needed $1 + 2.5 = $3.50$ before the rise, and needs $1.5 + 2.5 = $4$ now. That is $0.50 more, as it should be.

Worked Example 2 — Two changes pulling different ways

In a farming region, a new seed variety gives bigger harvests from the same land. In the same year, a drought hits. What happens to the supply of the crop?

The new seed is better technology: supply increases, to the right. The drought is a natural condition: supply decreases, to the left. The two changes push the curve in opposite directions. So the final shift depends on which is larger, and the theory alone cannot tell you. A good answer says this clearly, and names what you would need to know: how much the seed raises yields, and how much the drought cuts them.

Worked Example 3 — Wheat, maize and leather

(a) The price of maize rises. What happens to the supply of wheat? (b) The price of beef rises. What happens to the supply of leather?

(a) Wheat and maize are substitutes in production: they compete for the same fields. Growing wheat now means giving up more maize income, so the full cost of supplying wheat rises. Supply of wheat decreases: the curve shifts left.

(b) Beef and leather are in joint supply: they come from the same animals. A higher beef price leads farmers to raise and sell more cattle, and more hides come with them. Supply of leather increases: the curve shifts right.

In both cases, the price of the good itself (wheat, leather) did not change first. A change in another market moved this one.

Worked Example 4 — A real case: the UK Soft Drinks Industry Levy

The policy. In March 2016, the UK government announced a levy on sugary soft drinks, which started in April 2018. Drinks with more than 8 g of sugar per 100 ml pay 24p per litre (24 pence, in British money). Drinks with 5 to 8 g pay 18p per litre. Drinks with less than 5 g pay nothing. Pure fruit juices and milk drinks are not covered. The levy is paid by the companies that make or import the drinks, not by shoppers at the till.

What the determinants predict. For a high-sugar drink, the levy is a tax per unit paid by the seller. So its supply curve moves up by the levy per litre. But the levy also gave producers a way out. The same factory can make a drink with less sugar, and below 5 g that drink pays nothing. So the two recipes are substitutes in production. The levy raises the full cost of supplying the high-sugar recipe compared with the low-sugar one. The prediction: the supply of high-sugar drinks decreases, and the supply of low-sugar drinks increases.

What happened. A study of UK sales data compared 2015 with 2018, a period that includes the two years between the announcement and the start (Bandy and others, BMC Medicine, 2020). The share of soft drinks sold with more than 5 g of sugar per 100 ml fell from 31% to 15%. The average sugar in each 100 ml sold fell from 4.4 g to 2.9 g. The total sugar sold in soft drinks fell by 29%, while the total volume of soft drinks sold rose by 7%.

The verdict. The prediction held. People did not stop buying soft drinks; they bought more. What changed was what the producers chose to make. The levy worked largely on the supply side, by changing recipes, and not only through higher prices for shoppers. One caution: a study of sales shows what changed, but other things were changing too, such as public health campaigns. So it cannot prove that the levy alone caused every gram of the fall.

Three classic mistakes

Trap 1 — "A tax shifts supply left by the amount of the tax"

The tax is in dollars, and a leftward shift is in units. A tax of $t per unit moves the curve up by exactly $t. How far it moves to the left depends on the slope of the curve.

Trap 2 — "Down means less"

When costs fall, or a subsidy is paid, the supply curve moves down. That is an increase in supply, because the same curve is further to the right. Describe a supply change as left or right, and use up or down only to explain why.

Trap 3 — "Sellers expect higher prices, so they supply more now"

If the good can be stored, the opposite is true. Selling today means giving up the higher price later, so supply today decreases. The higher quantity comes later, when the price has actually risen.

Try it yourself

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

For a bakery's bread, say whether supply increases or decreases, and give the reason. (a) The price of electricity for its ovens rises. (b) It buys a faster mixing machine. (c) The price of cakes, which the same ovens can bake, rises. (d) The government pays the bakery $0.20 for each loaf.

Hint 1
Use the test: does the change raise or lower the full cost of supplying each loaf today?

Hint 2
In (c), think about what the bakery gives up when it uses an oven for bread instead of cakes.

Full answer
(a) Decreases: an input cost rose. (b) Increases: better technology lowers the cost of each loaf. (c) Decreases: bread and cakes are substitutes in production, so each oven-hour of bread now gives up more cake income. (d) Increases: a subsidy of $0.20 moves the curve down by $0.20, which is a shift to the right.
The supply of mangoes in a market is $Q_{s} = 50 P - 100$ , in kilograms per week. The government puts a tax of $2 per kilogram on sellers. Find the new supply equation, and the quantity supplied at a price of $6 before and after the tax.

Hint 1
At any price $P$ , the seller now keeps only $P - 2$ . So replace $P$ with $P - 2$ .

Hint 2
$Q_{s} = 50 (P - 2) - 100$ . Expand the bracket.

Full answer
New supply: $Q_{s} = 50 (P - 2) - 100 = 50 P - 200$ . At $6: before, $300 - 100 = 200$ kg; after, $300 - 200 = 100$ kg. Check upwards: the 100th kilogram needed $(100 + 100) \div 50 = $4$ before, and needs $(100 + 200) \div 50 = $6$ now. That is $2 more, exactly the tax.
The coffee cafés receive a subsidy of $0.50 per cup. Starting from $Q_{s} = 100 P - 100$ , find the new supply equation, the quantity at $4, and the new lowest price for the 300th cup.

Hint 1
With the subsidy, a café receives $P + 0.5$ for each cup. Replace $P$ with $P + 0.5$ .

Hint 2
The lowest acceptable price for every cup falls by $0.50.

Full answer
$Q_{s} = 100 (P + 0.5) - 100 = 100 P - 50$ . At $4: $400 - 50 = 350$ cups, up from 300. The 300th cup needed $4 before. Now it needs $(300 + 50) \div 100 = $3.50$ , which is $0.50 less. The curve moved down by $0.50 and right by 50 cups.
A council wants a tax that shifts the coffee supply curve, $Q_{s} = 100 P - 100$ , 150 cups to the left at every price. What tax per cup does it need? Another town's coffee supply is $Q_{s} = 50 P - 50$ . How far left would the same tax shift that curve, and why is it different?

Hint 1
On the first curve, each $1 of tax moves the curve 100 cups to the left.

Hint 2
On the second curve, each $1 changes the quantity by only 50 cups.

Full answer
A tax of $t moves the first curve $100 t$ cups to the left. For 150 cups, $100 t = 150$ , so $t = $1.50$ . On the second curve, the same $1.50 tax moves it $50 \times 1.5 = 75$ cups to the left. Both curves move up by exactly $1.50, but the second curve is steeper: each $1 of price changes its quantity by only 50 cups. So the same tax moves it half as far sideways. This is the first sign of an idea you will meet as the price elasticity of supply: how strongly quantity supplied responds to price decides how much a tax changes the quantity.

The bigger idea

Every determinant in this lecture is really one idea: the supply curve is the full cost of each unit, and anything that changes that cost moves the curve. Input prices and taxes change the money spent. Other goods and expectations change what the seller gives up. Economists call that the opportunity cost, and it is one of the most important ideas in the subject.

The sugar levy shows why this matters for policy. A government that taxes a good does not only raise its price. It changes what sellers find worth making. Sometimes the biggest effect of a tax is a product that changes before the buyer ever sees a higher price.

Key concepts in this lesson

A supply curve can be read across, as the quantity at each price, or upwards, as the lowest acceptable price for each unit, which is its extra cost.
A shift up and a shift left are the same decrease in supply, and a shift down and a shift right are the same increase.
A tax of $t per unit moves the supply curve up by exactly $t, while how far it moves to the left depends on the slope of the curve.
Supply shifts when the full cost of supplying each unit today changes, or when the number of sellers changes. Costs change through inputs, technology, taxes and subsidies, other goods the seller could make, expectations and the weather.
When sellers can store a good and expect a higher price later, supply today decreases, because selling now means giving up that higher price.