Consider the market for gasoline. In the initial equilibirum, the price is $2.00
ID: 1099135 • Letter: C
Question
Consider the market for gasoline. In the initial equilibirum, the price is $2.00 per gallon and the quantity is 100 million gallons. The price elasticity of demand is 0.7, 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.
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 the producers pay the remaining $________ of the tax.
Explanation / Answer
a)
P = $2.20
New quantity is:
(1-0.07)*100=93
b)
Consumers pay 0.20 while producers pay 0.14
This implies that the new quantity is 83 million gallons.
100 - 17 = 83
The price elasticity of demand is 0.7
"%d" means percent change.
E = %dQ/%dP
0.7 = 17/%dP
%dP = 17/0.7
%dP = 24.2857143
$2,
this implies that the new price is:
P = 2*1.242857143
P = 2.48571429
or about 2.5
the price elasticity of supply is 1
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 = 1.6
So, the amount of the tax is:
t = 2.48571429 - 1.66
t = 0.82
Consumers pay:
2.48571429 - 2 = 0.4
Or about $0.50
or as a percentage: 0.48571429/0.82571429 = 58%
Producers pay:
2 - 1.66 = 0.3
or as a percentage: 0.34/0.82571429 = 41%
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
$0.34 tax would represent a percentage change in price received by suppliers of:
1 - (2 - 0.14)/2 = 7%
Not 17%!