Question

The market demand for gasoline can be represented by the equation Q=120-2P, where quantity Q is measured in gallons/week and price P is measured in dollars per gallon. The supply curve for gasoline, however, depends on whether the time frame is the short run or the long run. A per-gallon tax of $6 is imposed on the gasoline market.

a. In the short run, the supply function for gasoline is represented by

80 if P>5

Q = anything between 0 and 80, inclusive, if P = 5

0, if p<5

Please calculate the equilibrium prices and quantity of gasoline in the short run, both before and after the introduction of the tax. Calculate the deadweight loss of the tax. Please provide a graph to illustrate your answer.

b. In the long run, the supply curve for gasoline is horizontal at P=20. Please calculate the equilibrium prices and quantity of gasoline in the long run, both before and after the introduction of the tax. Calculate the deadweight loss of the tax. Please provide a graph to illustrate your answer.

Do buyers or sellers tend to bear more of the burden of the tax? Does your answer depend on whether the market is looked at in the short run or the long run? Why or why not?

Thank you!

Answer 1

a) From the construction of the supply function, find that the before tax equilibrium is found at

120 – 2P = 80

40 = 2P

P* = 20 and the quantity is fixed at 80 gallons.

When the tax is imposed on buyers, new demand function is 120 – 2(P + 6) or 108 – 2P. The new after tax quantity and prices are

108 – 2P = 80

Ptax = 14 received by sellers and price paid by buyers is fixed at 20. Qtax is unchanged at 80. There is no deadweight loss when demand or supply are perfectly inelastic or elastic

b)

b. In the long run, the supply curve for gasoline is horizontal at P=20. Here demand is again 108 – 2P and so the equilibrium price is fixed at 20. Now quantity demanded and supplied is Q = 108 – 2*20 = 68 units. At this quantity, price paid by buyers is 20 + 6 = $26 and price received by sellers is $20. There is no deadweight loss as supply is perfectly elastic.

In the short run supply is perfectly inelastic so sellers bear the entire tax burden. In the long run when supply is perfectly elastic, it is the buyer who bears the full bear of burden.