Consider the market for gasoline. In the initial equilibrium, the price is $3.00
ID: 1237572 • 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. Consumers pay $_____________ of the $0.30 tax and producers pay the remaining $______________ of the tax. 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 quanitty is ________ million gallons.Explanation / Answer
he tax incidence of the buyer can be calculated as: TI = PES/(PES + PED) TI = 1/(1 + 0.4) TI = 0.714285714 This means that buyers pay about 71% of the tax while sellers pay about 29% of the tax. Buyers pay: 0.3*0.71 = 0.213 Sellers pay 0.3*0.29 = 0.087 A $0.30 tax will increase the price to: New price = 3.00 + 0.3*(1/(1 + 0.4)) New price = $3.21 Using the midpoint formula for elasticity: E = %dQ/%dP E = (Q1 - Q2)/0.5*(Q1 + Q2) / (P2- P1)/0.5*(P1 + P2) 0.4 = (100 - Q2)/(0.5*(100 + Q2)) / (3.21 - 3)/(0.5*(3 + 3.21)) 0.4 = (100 - Q2)/(0.5*(100 + Q2)) / 0.0676328502 0.4*0.0676328502 = (100 - Q2)/(0.5*(100 + Q2)) 0.0270531401 = (100 - Q2)/(0.5*(100 + Q2)) 0.0270531401*0.5*(100 + Q2) = 100 - Q2 0.0270531401*0.5*100 + 0.0270531401*0.5*Q2 = 100 - Q2 Q2*(0.0270531401*0.5 + 1) = 100 - 0.0270531401*0.5*100 Q2 = (100 - 0.0270531401*0.5*100)/(0.0270531401*0.5 + 1) Q2 = 97.3307912 New quantity is about 97 million gallons.