Tax Wedge
What is Tax Wedge?
A tax wedge is the gap a per-unit tax drives between the price buyers pay and the price sellers receive, equal to the tax per unit at the new quantity.
When a tax is imposed, buyers pay one price and sellers keep a lower one; the vertical distance between them is the wedge, equal to the tax per unit. The wedge reduces the quantity traded below the efficient level and creates deadweight loss (the triangle whose base is the lost quantity and height is the wedge). How the wedge splits into buyer and seller burden depends on relative elasticities, but the size of the wedge itself equals the statutory tax per unit regardless of who legally pays it.
Tax Wedge: a worked example
Take a market with demand Qd = 100 - 2P and supply Qs = 3P. Before tax, 100 - 2P = 3P gives P = $20 and Q = 60. Now put a $5 per-unit tax on sellers. Sellers keep Pb - 5, so 100 - 2Pb = 3(Pb - 5), giving Pb = $23, Ps = $18 and Q = 54. The wedge is $23 - $18 = $5, exactly the tax. Buyers absorb $3 of it, sellers $2. Quantity falls by 6, so deadweight loss is 0.5 x $5 x 6 = $15, and the government collects $5 x 54 = $270.
The mistake students make with tax wedge
Students read the wedge as the amount the buyer's price rises. In the market above the buyer's price rose only $3 while the wedge was $5; the other $2 came out of the seller's price falling. The wedge is the full gap between the two prices, and it equals the statutory tax per unit no matter which side the law collects it from. Elasticities decide how that fixed gap is split, not how big it is.
Tax Wedge questions
Is the tax wedge the same thing as deadweight loss?
The tax wedge is not the deadweight loss. The wedge is a price gap measured in dollars per unit, while deadweight loss is an area measured in total dollars, found by multiplying half the wedge by the fall in quantity. A $5 wedge that cuts quantity by 6 units creates $15 of deadweight loss; the same $5 wedge in a market where quantity barely moves creates almost none.
Does it matter whether a tax is placed on buyers or on sellers?
A tax wedge is the same size whether the law places the tax on buyers or on sellers. Switching the statutory side changes which curve you shift on the diagram, but the equilibrium quantity, the price buyers pay, the price sellers keep and the revenue all come out identical. Legal incidence is a paperwork question; economic incidence is settled by the relative elasticity of supply and demand.
What makes a tax wedge create a bigger deadweight loss?
A tax wedge causes more deadweight loss when supply and demand are more elastic and when the tax per unit is larger. Elastic curves mean buyers and sellers walk away from trades easily, so the same wedge destroys more of them. Because the loss is half the wedge times the lost quantity, and the lost quantity itself grows with the wedge, doubling a tax roughly quadruples the deadweight loss.
Formula / Example
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