Question

D: P=10

S: P= 1 + 2Q

Tax=5

a.) Solve for the original market clearing price and quantity

b.) Calculate the price elasticity of demand at the intital price

c.) Calculate the price elasticity of supply at the intial price

d.) On the basis of these two elasticity coefficents, anticipate the distribtuion of the burden of the tax

Answer 1

A) At original equilibrium, D=S

Therefore, 10=1+2Q

Or, Q=9/2=4.5

And at this quantity, price = 10

It means, original market clearing price is $10 and quantity is 4.5 units

B) Demand is constant at P=10, which indicates demand is perfectly elastic (i.e. price elasticity of demand = infinite) at the initial price.

C) For the supply curve, Qs= (P-1)/2 = P/2 - 0.5

d(Qs)/dP = 1/2 = 0.5

At, P= 10, Qs= 4.5

Therefore, price elasticity of supply = 0.5 * (10/4.5) = 1.11

D) From the elasticity coefficients, we get to know that supply curve is elastic but demand curve is perfectly elastic. It means, after imposition of tax the price paid by consumers remains P=10(at pre-tax level) and price received by sellers is P-tax = (10-5)=5. Suppliers have to bear the entire burden of tax because consumers has no willingness to pay higher price (demand is perfectly elastic, consumers will not buy any amount above P=10).