Question

Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If Congress mandates that cars have to get 36 miles per gallon, by what percentage will this lower the costs of driving? If the elasticity of total miles driven (per year) with respect to the cost of driving is –1, by how much will total miles driven per year increase, assuming it is 10,000 miles at the beginning? How much will total annual gas consumption of the average car change as a result of the mandated program?

Answer 1

An average car gets 28 miles per gallon. The cost of gas is $3 a gallon.

So,

Cost of driving per mile = 3/28 = $0.11 per mile

Now,

Congress mandates that an average car must get 36 miles per gallon.

So,

Cost of driving per mile = 3/36 = $0.08 per mile

Calculate the percentage decrease in cost of driving -

Percentage decrease = [($0.11 - $0.08)/$0.11] * 100 = 27.27%

Thus,

The mandated program lower the costs of driving by 27.27%.

Elasticity of total miles driven (per year) with respect to the cost of driving = -1

Percentage decrease in cost of driving = 27.27%

Percentage increase in total miles driven per year = Elasticity of total miles driven (per year) with respect to the cost of driving * Percentage decrease in cost of driving

Percentage increase in total miles driven per year = 1 * 27.27 = 27.27

Thus,

The total miles driven per year will increase by 27.27%.

Initially, miles driven per year = 10,000 miles

Percentage increase in miles driven = 27.27%

Increase in miles driven = 10,000 * 0.2727 = 2,727

Thus,

The total miles driven per year would increase by 2,727 miles.

Initially,

Miles driven = 10,000 miles

Average = 28 miles per gallon

Total gallon of gas needed = 10,000/28 = 357.14 gallons

Thus,

The total annual gas consumption before mandated program is 357.14 gallons.

After mandated program,

Miles driven = 12,727 miles

Average = 36 miles per gallon

Total gallon of gas needed = 12,727/36 = 353.53 gallons

Thus,

The total annual gas consumption after mandated program is 353.53 gallons.

Change in annual gas consumption = Annual gas consumption before mandated program - Annual gas consumption after mandated program

Change in annual gas consumption = 357.14 gallons - 353.53 gallons = 3.61 gallons

The total annual gas consumption will decrease by 3.61 gallons as a result of the mandated program.