A tax on sellers: who really pays it?

In this video, we work out how a tax on sellers affects the prices buyers pay and sellers keep.

Question one. Demand is quantity demanded equals one hundred minus ten P and supply quantity supplied equals ten P. A tax of two rupees a unit is put on sellers: what do buyers pay and sellers keep?

First, put quantity on the horizontal axis and price in rupees on the vertical axis. Draw demand, D: price equals ten minus quantity divided by ten. Draw supply, S: price equals quantity divided by ten.

Their initial equilibrium, E zero, has a price of five rupees and a quantity of fifty units.

The tax shifts supply upward by two rupees to S one, because sellers need two extra rupees to supply each quantity. Call the buyer price P b and the seller price P s: the buyer price minus the seller price equals two.

Equating demand and supply gives one hundred minus ten P b equals ten times P b minus two, in brackets.

Collecting terms, twenty P b equals one hundred and twenty.

Dividing by twenty, buyers pay six rupees per unit.

Sellers keep six minus two, which is four rupees per unit, shown at point A on the original supply curve.

The new equilibrium, E one, has a buyer price of six rupees and a quantity of forty units.

Check: demand at six rupees and supply at four rupees both equal forty units. Hence, buyers pay six rupees per unit, and sellers keep four rupees per unit.