Teaching with Economics Experiments >> Teaching Modules >> Public Finance  Effects of a Per Unit Tax >> Lecture to Accompany Tax ExperimentThe lecture material is developed on the assumption that students have previously been introduced to step function market supply and demand functions that correspond to goods traded in discrete units (as in everyday life).
Definitions
Central Results in the Theory of TaxesGiven the simplifying assumption of zero transactions costs, one can show theoretically that:
Market Equilibrium with No Tax Define Q(p) as the market demand function. For example, if the demand function is linear then
or as
Figure 1. Equilibrium with Linear Demand and Supply and No Tax Figure 2. Equilibrium with Step Function Demand and Supply and No Tax Market Equilibrium with a Per Unit TaxNow assume that a tax of t per unit is imposed on the commodity. In the presence of the tax, the total amount per unit that buyers must pay (the demand price) exceeds the total amount per unit that sellers get to keep (the supply price) by the amount of the tax per unit:
Figure 3. Equilibrium with Linear Demand and Supply and a Per Unit Tax Figure 4. Equilibrium with Step Function Demand and Supply and a Per Unit Tax
Deadweight Loss of a TaxExcept in limiting special cases, a tax imposes a deadweight loss or excess burden on buyers and sellers. The deadweight loss is the amount by which the reduction in buyers' surplus and sellers' surplus exceeds the tax revenue.
Figure 5. Deadweight Loss with Linear Demand and Supply and a Per Unit Tax Figure 6. Deadweight Loss with Step Function Demand and Supply and a Per Unit Tax Equal Incidence of a Tax with Symmetric Demand and SupplyRegardless of whether the liability to pay a tax falls on buyers or on sellers, the incidence of the tax falls on both sides of the market. Figure 7. BL is the Buyers' Loss from the tax and SL is the Sellers' Loss. In this case of symmetric demand and supply, BL = SL regardless of whether the tax liability falls on buyers or sellers.
Unequal Incidence of a Tax with Asymmetric Demand and SupplyWe have observed that the incidence of a tax is independent of whether the liability to pay the tax is on buyers or sellers. Figure 8. If demand is less elastic than supply then tax incidence falls more on buyers than on sellers. Figure 9. If supply is less elastic than demand then tax incidence falls more on sellers than on buyers. Figure 10. If supply is perfectly inelastic then tax incidence falls entirely on sellers. Figure 11. If supply is perfectly elastic then tax incidence falls entirely on buyers. Figure 12. If demand is perfectly inelastic then tax incidence falls entirely on buyers.  
