Prices, quantity and where the surplus goes, before the tax and with it. The last column is the change.
Before the tax
With the tax
Change
Price buyers pay
$68.00
$72.00
$4.00
Price sellers keep
$68.00
$62.00
-$6.00
Quantity
16
14
-2
Consumer surplus
$256.00
$196.00
-$60.00
Producer surplus
$384.00
$294.00
-$90.00
Tax revenue
$0.00
$140.00
$140.00
Deadweight loss
$0.00
$10.00
$10.00
Enter the demand and supply equations, or two rows of each schedule, and the tax per unit. The default is the textbook market P = 100 − 2Q and P = 20 + 3Q, the same one the Market Equilibrium Calculator starts from, with a $10 tax. The results give the price each side faces as well as the split.
Calculated in your browser — the numbers you enter are never sent to our servers.
What it calculates: Share of the tax borne by buyers, Share borne by sellers, Price buyers pay, tax included, Price sellers keep.
A $10 tax in a $68 market: buyers pay $4 more and sellers keep $6 less
In the default market, demand P = 100 − 2Q and supply P = 20 + 3Q cross at 16 units and $68. A tax of $10 a unit means buyers’ price and sellers’ price must now differ by $10. The quantity where that happens is (100 − 20 − 10) ÷ (2 + 3) = 14 units.
At 14 units buyers pay 100 − 2 × 14 = $72, which is $4 more than before, and sellers keep 72 − 10 = $62, which is $6 less. So buyers bear 40% of the tax and sellers 60%, although the full $10 is sent to the government in one payment.
The government collects $10 × 14 = $140. Consumer surplus falls from $256 to $196 and producer surplus from $384 to $294, a loss of $150 against $140 of revenue: the missing $10 is the deadweight loss.
FigureBuyers bear $4 of the $10 and sellers $6: demand is the more elastic side here, so it passes less of the tax on.
Tax of $10
Q = (100 − 20 − 10) ÷ 5 = 14
Buyers: $72 (+$4); sellers: $62 (−$6)
Revenue $140; deadweight loss $10
The side that responds less to price pays more: buyers’ share = supply elasticity ÷ (supply + demand elasticity)
OpenStax puts the rule plainly: if demand is more inelastic than supply, consumers bear most of the tax, and if supply is more inelastic, sellers do. Its examples are cigarettes, where addicted buyers keep buying and the tax is passed on in higher prices, and beachfront hotels, whose owners cannot move and absorb the tax in lower prices.
At the default market’s old equilibrium, demand has an elasticity of 2.13 and supply 1.42. Buyers’ share is 1.42 ÷ (1.42 + 2.13) = 40%, the same figure the prices gave. With straight-line curves the two routes always agree, because both reduce to the slopes: b ÷ (b + d).
Make demand steep (a large b) and buyers’ share climbs toward 100%; make supply steep and it falls toward 0%. A tax falls hardest on whoever has the fewest alternatives.
It does not matter who sends the tax to the government: only the price tag changes
Economists separate statutory incidence, who is legally required to send the tax in, from economic incidence, who ends up paying it through prices. Switch “Who sends the tax to the government” and every result stays the same except the price on the tag.
If sellers remit the tax, the tag shows $72 and sellers pass $10 of it on. If buyers remit it, the tag shows $62 and buyers add $10 at the register. Either way buyers part with $72 and sellers keep $62. Laws can decide who writes the check; the market decides who bears the cost.
Deadweight loss: the trades a tax prevents
The tax cuts the quantity from 16 to 14. Each of those 2 units was worth more to a buyer than it cost a seller to make, so the trade would have created value; with the tax it no longer happens. That lost value is the deadweight loss, ½ × $10 × 2 = $10.
DWL = ½ × t × (Q before − Q after)
It grows with the square of the tax: double the tax to $20 and the quantity falls to 12, the loss to ½ × $20 × 4 = $40. That is why broad taxes at low rates cost less in lost trade than narrow taxes at high ones.
This page and the Market Equilibrium Calculator run on one engine and answer one question each
The Market Equilibrium Calculator has a tax-and-subsidy module inside the full supply-and-demand lab, and it uses the same engine, so its figures match this page. This page is built for incidence: the share each side bears, the elasticity route to the same answer, and the remitter switch that shows who writes the check makes no difference.
For a legal price limit instead of a tax, the Price Ceiling and Floor Calculator shows the shortage or surplus; for the lost-trade triangle on its own, the Deadweight Loss Calculator takes it directly.
Frequently Asked Questions
What is tax incidence?
How the burden of a tax is actually shared between buyers and sellers through the prices each faces, as opposed to who is legally required to pay it.
How do you calculate who pays a tax?
Buyers’ share is the rise in the price they pay divided by the tax; sellers’ share is the fall in the price they keep divided by the tax. With linear curves, buyers’ share is b ÷ (b + d), the demand slope over the sum of the slopes.
Does it matter whether the tax is collected from buyers or sellers?
No. The prices buyers pay and sellers keep, the quantity, the revenue and the deadweight loss are the same either way. Only the price printed on the tag differs.
Who bears more of a tax, buyers or sellers?
Whichever side is less elastic, meaning less able to change how much it buys or sells when the price moves. Inelastic demand, as for cigarettes, puts most of the tax on buyers.
What is the elasticity formula for tax incidence?
Buyers’ share = supply elasticity ÷ (supply elasticity + the absolute demand elasticity), and sellers’ share is the rest.
Why does a tax cause deadweight loss?
It makes fewer units trade, and those lost trades were worth more to buyers than they cost sellers. The value of the trades that no longer happen is the deadweight loss, ½ × tax × the fall in quantity.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Straight-line demand and supply, and a competitive market in which both sides take the price as given.
A fixed tax per unit (an excise), not a percentage of the price.
The tax is collected in full, whoever sends it in.
Where it stops
Elasticities differ between the short and the long run, so the split can shift over time; the model shows one moment.
A percentage (ad valorem) tax, or a market with a single seller, splits differently.
The burden that falls on sellers is ultimately borne by the owners, workers and suppliers behind them, which this one-market model does not trace.
Related Calculators
Market EquilibriumSolve equilibrium price and quantity from linear demand and supply, with surplus, a shift simulator, and tax incidence.
Deadweight LossSize the welfare triangle a per-unit tax destroys, alongside the tax revenue it actually raises.
Price Ceiling and FloorA legal maximum or minimum price on any market: whether it binds, the shortage or surplus, what still trades, who gains and loses, and the deadweight loss.
Consumer SurplusFind the value buyers gain above what they pay, from the choke price, market price, and quantity sold.
Producer SurplusFind the value sellers gain above their minimum acceptable price, from the market price and quantity sold.
Tax MultiplierHow far a tax change moves GDP — simple, or with income tax, imports and induced spending.
Comparative AdvantageFind comparative and absolute advantage between two producers and two goods, plus the mutually beneficial trade range.
GDPGross domestic product by the expenditure method (C + I + G + NX) or the income method — wages, rent, interest, profit, taxes and depreciation.
Published the tax incidence calculator: how a per-unit tax splits between buyers and sellers, the price each side faces, the revenue and the deadweight loss, the elasticity route to the same split, and a switch showing that who sends the tax in changes only the price on the tag.
Runs on the Market Equilibrium Calculator’s engine; checked against OpenStax’s rule that the more inelastic side bears more of the tax, in 3,000 random markets.
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