How to Calculate the Cost of an Export Subsidy
An export subsidy raises the domestic price to the world price plus the subsidy, and it costs taxpayers the subsidy per unit times the quantity exported after it.
The Export Subsidy formula
Calculator
Enter the world price, the subsidy and domestic quantities at both prices to get exports, the taxpayer bill and the net loss.
The price on the world market, which the domestic price matches under free trade.
What the government pays producers on each unit sold abroad.
Read off the domestic supply curve at the free-trade price.
Read off the domestic demand curve at the free-trade price.
Domestic supply once the price is world price plus subsidy.
Domestic demand at that same higher price.
The government pays $70 million, the subsidy on every exported unit and nothing on units sold at home.
- Domestic price with the subsidy
- $6
- Exports after the subsidy
- 70
- Gain to domestic producers
- $110
- Loss to domestic buyers
- $55
- Net welfare loss
- $15
Home buyers now pay $6, the world price plus the whole subsidy.
Exports move from 40 million to 70 million units, widened by more domestic output and less domestic buying at once.
Producer surplus rises by $110 million, since the higher price is earned on every unit, not only the exported ones.
Consumer surplus falls by $55 million, because home buyers face the same raised price as foreign ones.
Producer gain minus the buyer loss and the taxpayer bill leaves the country $15 million worse off, the two distortion triangles added together.
How to calculate Export Subsidy, step by step
- 1Start at the world price. Under free trade the domestic price equals the world price. Exports are the gap between what domestic producers supply and what domestic buyers want at that price.
- 2Add the subsidy to the price. A producer can earn the world price plus the payment by shipping a unit abroad, so nobody sells at home for less. The domestic price rises by the full subsidy.
- 3Read both domestic quantities at the new price. Go up the supply curve for the larger quantity supplied and up the demand curve for the smaller quantity demanded.
- 4Subtract to get the new exports. Exports after the subsidy = quantity supplied − quantity demanded at the subsidized price. The gap is wider than it was under free trade, from both directions at once.
- 5Multiply for the taxpayer bill. Government cost = subsidy per unit × exports after the subsidy. The payment is made on exported units, so multiplying by total domestic output overstates it.
- 6Measure the two triangles. Net loss = ½ × subsidy × the rise in output, the production distortion, plus ½ × subsidy × the fall in domestic purchases, the consumption distortion.
Worked example: Export Subsidy
The world price of wheat is $5 a bushel. At $5 domestic farms supply 100 million bushels while domestic buyers want 60 million, so exports are 40 million. A subsidy of $1 a bushel lifts the domestic price to $6, supply climbs to 120 million and domestic purchases fall to 50 million, so exports rise to 70 million. The taxpayer bill is $1 × 70 million = $70 million. Producers gain $1 × (100 + 120) ÷ 2 = $110 million and domestic buyers lose $1 × (60 + 50) ÷ 2 = $55 million, so the net loss is 110 − 55 − 70 = $15 million. That matches the two triangles: ½ × 1 × 20 = $10 million on the production side and ½ × 1 × 10 = $5 million on the consumption side.
Export Subsidy questions
Why does the domestic price rise by the full subsidy?
Because a producer can always earn the world price plus the payment by exporting, so no unit is sold at home for less than that. In the small-country model the world price itself does not move, so the whole increase lands on domestic buyers.
Do you multiply the subsidy by total output or by exports?
By the quantity exported after the subsidy, since the payment is made per unit shipped abroad. Multiplying by total domestic production counts units that never cross a border and overstates the bill, which is the most common error on this question.
Who gains and who loses from an export subsidy?
Domestic producers gain, because they receive the higher price on every unit they sell. Domestic buyers lose, since they pay world price plus subsidy at home, and taxpayers fund the payment. The gain is smaller than the two losses combined, leaving the exporting country worse off overall.
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