IB Economics SL & HLTopic 2.7 — Government InterventionPaper 1 & 2Diagram skill~12 min read
Indirect Taxes and Subsidies
Both of these tools do the same thing to a diagram: they move the supply curve. A tax pushes it left, a subsidy pushes it right. The marks are not in the shift though — they are in the three price points that appear afterwards, and in working out who actually ends up paying.
📚 What you need to know
An indirect tax is paid on spending, not on income. It is collected from producers, which is why supply shifts, not demand.
A specific tax is a fixed amount per unit. An ad valorem tax is a percentage of the price, so the two supply curves fan apart.
A tax creates three prices: the old price P1, the new price buyers pay P2, and what sellers keep P3.
Tax incidence is the share of the tax carried by each side. It is decided by PED, not by who hands the money over.
A subsidy is a payment per unit to producers. Supply shifts right, price falls, quantity rises.
With a subsidy the diagram flips: the producer share is the top box and the consumer share is the bottom one.
Both taxes and subsidies move the market away from the free-market quantity, so both create a welfare loss unless there was a market failure to correct.
Why the supply curve moves
Think about what a tax actually does to a firm. For every unit it sells, it now has to hand over a slice to the government. So to be willing to supply the same quantity as before, the firm needs a higher price — higher by exactly the tax. Draw that and you get the old supply curve lifted straight up by the size of the tax.
A subsidy is the mirror image. The firm receives extra money per unit, so it is happy to supply the same quantity at a lower price. The curve drops by the size of the subsidy.
The shift, in one line
tax → supply moves up by the tax • subsidy → supply moves down by the subsidy
Measure the shift vertically, not sideways. Students who slide the curve across instead of lifting it up end up with a gap that is not equal to the tax, and then every number afterwards is wrong.
A specific tax on the diagram
Here is the diagram you will draw more than any other in this topic. Take your time over the three price points, because every calculation in the exam comes out of them.
P3 is easy to forget. Find it by dropping down from the new quantity onto the original supply curve — that is what the seller actually keeps.
🧩 Drawing it in the exam, in order
Draw S and D and label the first equilibrium P1Q1.
Lift supply straight up by the size of the tax. Label it S + tax.
Read off the new equilibrium where S + tax meets D. That is P2Q2.
Drop a line from Q2 to the original S curve. Where it lands is P3.
Shade the box between P2 and P1 (consumer share) and between P1 and P3 (producer share).
Shade both together and you have the government’s tax revenue.
The three formulas you will actually use
tax revenue = (P2 − P3) × Q2
consumer share = (P2 − P1) × Q2
producer share = (P1 − P3) × Q2
Who really pays? PED decides
The government collects the tax from the firm. That does not mean the firm carries it. A firm passes on as much as buyers will tolerate, and how much they will tolerate depends on how easily they can walk away.
If demand is inelastic — cigarettes, petrol, insulin — buyers stay even when the price jumps, so the firm can pass most of the tax on. If demand is elastic — one brand of biscuit, a restaurant meal — buyers disappear the moment prices rise, so the firm has to swallow most of it.
Same tax, same supply curve, different demand. The whole difference in outcome comes from how willing buyers are to walk away.
The rule in one line: the more inelastic side of the market carries the bigger share of the tax. It works for supply too — inelastic supply means the producer carries more.
Subsidies: the same diagram, upside down
A subsidy pushes supply to the right. Price falls, quantity rises, and the government pays for the gap between what buyers hand over and what sellers receive.
Here is the bit students get wrong every single year. On a tax diagram the consumer box sits on top. On a subsidy diagram the producer box sits on top. It makes sense once you think about it: the producer ends up with a price above the old one, and the consumer ends up paying a price below the old one.
Read the two shaded boxes as a bill. Every dollar in them comes out of tax revenue, which is where your opportunity cost paragraph starts.
A quick memory hook: with a tax the buyer is the one who gets hurt first, so the buyer’s box is on top. With a subsidy the seller is the one being helped, so the seller’s box is on top.
Judging them
Policy
Good points
Problems
Indirect tax
Raises revenue; makes polluters and heavy users pay; cuts consumption of harmful goods; fairly easy to collect
Weak effect if demand is inelastic; hits poorer households hardest as a share of income; can push trade into illegal markets
Subsidy
Lowers price and raises use of good things like vaccines or clean energy; protects jobs; can be targeted at one industry
Costs the government money with a real opportunity cost; can prop up firms that never become efficient; hard to remove once given
A tax on a demerit good is regressive. Two people buy the same packet and pay the same tax, but that tax is a far bigger slice of a low income. That single sentence is a ready-made evaluation point.
Worked examples
WORKED EXAMPLE
Tax revenue and incidence
A government puts a specific tax of $15 per unit on a product. Before the tax, 500,000 units were sold at $40. After the tax, 420,000 units are sold and buyers pay $50. Calculate the tax revenue and the share carried by each side. [4]
Step 1: Find the three prices
P1 = $40, P2 = $50, and P3 = 50 − 15 = $35the seller keeps the buyer’s price minus the taxStep 2: Tax revenue = tax × new quantity15 × 420,000 = 6,300,000Tax revenue = $6.3 millionStep 3: Consumer share(50 − 40) × 420,000 = $4,200,000Step 4: Producer share(40 − 35) × 420,000 = $2,100,000check: 4.2m + 2.1m = 6.3m ✓ buyers carry two thirds, so demand here is fairly inelastic
WORKED EXAMPLE
Welfare loss from the same tax
Using the figures above, calculate the welfare loss caused by the tax. [2]
Step 1: Recognise the shape
It is the triangle between the old and new quantity, with height equal to the tax.
Step 2: Base and height
base = 500,000 − 420,000 = 80,000 units, height = $15Step 3: Area of a triangle(80,000 × 15) ÷ 2 = 600,000Welfare loss = $600,000these are trades that would have made both sides better off, and the tax stopped them
WORKED EXAMPLE
The cost of a subsidy
A government pays a subsidy of $6 per unit on electric bikes. Sales rise to 900,000 units, the price buyers pay falls from $30 to $26, and producers now receive $32. Calculate the total cost to the government and split it between buyers and sellers. [4]
Step 1: Total cost = subsidy × new quantity6 × 900,000 = 5,400,000Cost to government = $5.4 millionStep 2: Gain to buyers (price fell by $4)(30 − 26) × 900,000 = $3,600,000Step 3: Gain to sellers (price received rose by $2)(32 − 30) × 900,000 = $1,800,000check: 3.6m + 1.8m = 5.4m ✓ buyers gained more here because demand is relatively elastic
💡 Exam tip
Always use the new quantity Q2 in every box calculation. Using Q1 is the single most common arithmetic slip in this topic.
Label the axes Price and Quantity and label both curves. Unlabelled diagrams lose easy marks.
For an ad valorem tax, draw the two supply curves fanning apart — the gap must grow as price rises.
If a question mentions cigarettes, alcohol or fuel, bring in inelastic demand straight away.
When you evaluate a subsidy, name what the money could have been spent on instead. That is the opportunity cost mark.
Show the units in your final answer. “$6.3 million” scores; “6,300,000” alone sometimes does not.
⚠ Common mix-up
Shifting demand instead of supply. The tax is collected from producers, so supply moves. Demand only shifts if buyers’ tastes or incomes change.
Thinking the person who hands over the money bears the tax. The firm pays the government, but the incidence depends on PED.
Putting the consumer box on top of a subsidy diagram. On a subsidy it is the producer box on top.
Forgetting P3. Without it you cannot work out the producer share or the government’s total revenue.
Drawing an ad valorem tax as a parallel shift. Parallel means specific. Fanning means ad valorem.
Saying a tax “solves” the problem. It reduces the quantity; it rarely lands exactly on the socially best level.
Up next: Price Ceilings and Price Floors — what happens when the government stops arguing with the market and simply forbids a price.
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