Question

3.Consider the market for gasoline in the U.S. Suppose that the price elasticity of demand has been estimated to be 0.3,while the priceelasticity of supply is estimated to be 0.6. Answer the following questions.

a)Construct a supply-and-demand diagram that illustrates the free-market equilibrium. How much do buyers pay? How much do sellers receive? Is there a difference between the price paid by buyers and the price received by sellers?

b)Suppose the federal government imposes a gasoline tax of $0.50 per gallon. Construct a supply-and-demand diagram that illustrates the effect of the tax on the market for gasoline. How does the tax impactthe price buyers pay? How about the effective price received by sellers? Is there a difference between the price paid by buyers and the price received by sellers? What happens to the number of transactions between buyers and sellers?

c)How is the gasoline tax distributed between buyers and sellers? That is, do buyers pay more or less of the $0.50 per-unit tax than sellers? Prove your answer with the pre-tax and post-tax equilibrium prices paid by buyers and received by sellers from (b) part.

d)Identify the areas of the graph that represent tax revenue and deadweight loss? Describe the intuition behind the concept of deadweight loss.

e)If the government repealed the gasoline tax, how would this change affect the price paid by buyers and the price received by sellers? What would happen to the deadweight loss?

Answer 1

3.

a)

In the figure below, DD is the demand curve and SS is the supply curve. The intersection of DD and SS that is E* is the equilibrium point where Price is P* and Quantity is Q*.

Buyers will pay P*

Sellers will receive P*

No, there is no difference between the price paid by buyers and the price received by sellers.

b)

As federal government imposes a gasoline tax of $0.50 per gallon it will cause supply to decrease. This will result into leftward shift of supply curve from SS to SS'. Now New equilibrium is at E** where price pay by buyers is Pb and Price received by Seller is Ps(Pb-0.5).

Yes, there is a difference of 0.5 between what the buyer pay and seller receive.

The number of transactions between buyer and seller also decreases from Q* to Q**.

c) From the graph in part b), the difference between the initial equilibrium price P* and Pb is more than the difference between P* and Ps that is

Pb-P* > P*-Ps

It implies that buyers are paying more part of the tax as compare to seller who bear less part of the tax.

Generally this is also dependent upon Elasticities:

If elasticity of demand > Elasticity of supply then Seller will bear more of tax and If elasticity of demand < Elasticity of supply then Buyer will bear more of tax. Here as well

Elasticity of demand (0.3) is less than the Elasticity of supply(0.6) so buyer will bear more part of $0.5 tax.

d) Tax revenue is the product of the difference between the Price paid by buyer and receive by seller and Quantity that is

Tax revenue= (Pb-Ps)(Q**) (Area in red in graph below)

Deadweight loss is the decrease in total surplus from the initial situation to after tax situation. This is the area(in blue in graph below) computed by difference between the Price paid by buyer and receive by seller and difference in Q* and Q**.