Consider the market for gasoline. In the initial equilibrium, the price is $2.00
ID: 1252762 • Letter: C
Question
Consider the market for gasoline. In the initial equilibrium, the price is $2.00 per gallon and the quantity is 100 million gallons. The price elasticity of demand is 0.70, and the price elasticity of supply is 1.0. Suppose a carbon tax shifts the supply curve upward by $0.34 and to the left by 17 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 $0.34 tax and producers pay the remaining $______________ of the tax.
Explanation / Answer
a) New price is: P = $2.20. New quantity is: (1-0.07)*100 = 93 b) Consumers pay 0.20 while producers pay 0.14 Detailed explanation: Let's use the information given to piece together as much as we can. First, let's recall that a tax can be represented as a wedge between supply and demand. The quantity begins at 100 million gallons and is reduced by 17 percent. This implies that the new quantity is 83 million gallons. 100 - 17 = 83 The price elasticity of demand is 0.7. Let's plug this into the formula for price elasticity. "%d" means percent change. E = %dQ/%dP 0.7 = 17/%dP %dP = 17/0.7 %dP = 24.2857143 Since the price was originally $2, this implies that the new price is: P = 2*1.242857143 P = 2.48571429 or about 2.5 And we are told that the price elasticity of supply is 1. So, let's plug that into the function. E = %dQ/%dP 1 = 17/%dP %dP = 17 This implies that the price that suppliers received decreased by 17% P = 2*(1-0.17) P = 1.66 So, the amount of the tax is: t = 2.48571429 - 1.66 t = 0.82571429 Consumers pay: 2.48571429 - 2 = 0.48571429 Or about $0.50 or as a percentage: 0.48571429/0.82571429 = 58.8235296% Producers pay: 2 - 1.66 = 0.34 or as a percentage: 0.34/0.82571429 = 41.1764704% Whoever wrote this question must have made a mistake. An $0.83 tax is required to reduce the quantity by 17%. If a $0.34 tax were imposed, then consumers would pay: 0.34*0.588235296 = $0.20 and producers would pay: 0.34*41.1764704 = $0.14 These are probably the desired answers, but you should let your professor know you caught a typo. See, a $0.34 tax would represent a percentage change in price received by suppliers of: 1 - (2 - 0.14)/2 = 7% Not 17%! It looks like the 1 was typed by mistake.