Question

2.    Assume a $1 per unit tax is imposed on a market.

        [a] Under what [i] price elasticity of demand [PED] and [ii] price elasticity of supply [PES] circumstances

               will this tax cause the largest deadweight loss [DWL] in a market?

               [i]   

                [ii]  

        [b] Under what [i] PED and [ii] PES circumstances will this tax cause the smallest gain in government tax

               revenue in the market?

               [i]   

               [ii]  

        [c]   Under what [i] PED and [ii] PES circumstances will this tax cause the least change in the market

               equilibrium quantity?

               [i]   

               [ii]  

        [d]   In light of the above, why do governments typically tax cigarettes, alcohol, and gasoline?

Answer 1

a) The fall in demand and consequent fall in supply and the resulting deadweight loss depends upon the price elasticity of demand and elasticity of supply. If either demand or supply is inelastic the deadweight loss will be smaller. If the demand is elastic and supply is inelastic the producers bear the larger burden of a tax. The price in the market does not increase in the full extent of the tax and there will not be more decrease in demand and production. On the other hand if the demand is inelastic and the supply is elastic the consumers bear larger portion of a tax. The fall in demand will be low and thus the quantity supply does not decrease. This cause low deadweight loss. If both demand and supply are elastic the increase in price due to a tax reduces the demand and supply together. This will cause larger deadweight loss.

i) PED is greater than 1 (elastic demand)

ii) PES is greater than 1 (elastic supply)

b) The tax collection by the government depends upon the relative PED and PES. If both demand and supply are elastic the government gets smallest amount of tax revenue. The reason is that both demand and supply together decrease with the imposition of a tax.

i) PED is greater than 1(elastic demand)

ii) PES is greater than 1(elastic supply)

c) The fall in equilibrium quantity is low in case of inelastic demand and inelastic supply. If either of one is inelastic the government tax does not reduce the equilibrium quantity more. If demand is inelastic the demand does not fall more with increase in price due to a tax. The equilibrium quantity does not decrease more. On the other if the supply is inelastic the price does not increase to the full extent of tax. The producer’s bears larger portion of the tax. Then the demand does not fall more and there is a small decrease in equilibrium quantity.

i) PED is less than 1(inelastic demand)

ii) PES is less than 1(inelastic supply).

d) The demand for alcohol and cigarette is inelastic (PED is less than 1) In case of inelastic demand the demand does not decrease with the same proportion as the increase in price. Thus the government can collect more tax and this amount can be used for the expenses of social cost from the consumption of such goods.

The demand for gasoline is also inelastic. The government can collect more revenue by increasing the tax on gasoline.