Consider the market for gasoline. In the initial equilibrium, the price is $3.00
ID: 1253021 • Letter: C
Question
Consider the market for gasoline. In the initial equilibrium, the price is $3.00 per gallon and the quantity is 100 million gallons. The price elasticity of demand is 0.40, and the price elasticity of supply is 1.0. Suppose a carbon tax shifts the supply curve upward by $0.30 and to the left by 20 percent.A) After reviewing the price-change formula in the earlier chapter on elasticity, compute the new price and quantity. The new price is $_________ per gallon and the new quantity is _____________ million gallons.
B) Consumers pay $_____________ of the $0.30 tax and producers pay the remaining $______________ of the tax.
Explanation / Answer
The tax incidence can be calculated using the pass through fraction. TI = PES/(PES + PED) TI = 1/(1 + 0.4) TI = 0.714285714 This means that about 71% of a tax is paid by the buyer and 29% is paid by the seller. So, of a $0.30 tax, the buyer pays: 0.30*0.71 = $0.213 And the seller pays: 0.30*0.29 = $0.087 This means that the new price of gasoline is: 3 + 0.213 = $3.213 As a percentage change, this is: 0.213/3 = 7.1% And with a price elasticity of demand of 0.4, we can calculate the new quantity of gasoline: E = %dQ/%dP, where "%d" means "percent change." 0.4 = %dQ/7.1 %dQ = 0.4*7.1 %dQ = 2.84 So, the new quantity of gasoline is: 100*(1 - 0.0284) = 97.16 million gallons. This negates that supply shifted to the left by 20%, exposing an error in the problem. A $0.30 tax would not shift supply by 20%. It would only shift supply by 2.84%. To organize the answers: A)$3.213 and 97.16 million gallons. B) $0.213 and $0.087