Jim Whitney Economics 102
 Tax and subsidy geometry
 
Given the formulas for the demand and supply curves and the size of any taxes or subsidies, you can always use algebra to solve for the equilibrium quantity and buyer and seller prices and then diagram the market. But often we just work directly with the diagram, with no formal equations provided. In that case, we need a handy device to quickly find the new equilibrium once a tax or subsidy is imposed.

By convention, we usually show a tax as shifting the supply curve up by the amount of the tax and show a subsidy as shifting the supply curve down by the amount of the subsidy. These are shown in the two lefthand diagrams below. It is important to keep in mind that the only purpose of the shifted curve is to help us quickly find the new equilibrium quantity. True MB and MC have not changed, so we use the original D and S curves to plot the new Pb and Ps at the the new Qt.
 
Sometimes we (and some authors) distinguish between policies imposed on buyers (consumption policies) and sellers (production policies). The differences are shown across each row of diagrams below. Note the bottomline, simplifying lesson: only the total size of a tax or subsidy matters; market forces, not policymakers, determine who actually pays a tax and gets a subsidy.

Three ways of legislating a $6 tax:

 

Three ways of legislating a $6 subsidy: