In 2019, North Carolina consumed 114,576 thousand barrels of gasoline which is about 4.8 billion gallons.Gasoline demand and supply are both quite inelastic, which means that they don't respond much to changes in prices.Short-run demand elasticities have been estimated around -0.2.This means that if the price of gasoline increases by 10%, consumption of gasoline decreases by 2%.Supply elasticities are estimated around 0.1 which means that if the price of gasoline increases by 10%, the supply of gasoline increases by 1%.The supply and demand curves below are roughly consistent with these facts.

Driving your car has many negative externalities, for example:

the negative externality from emissions of carbon dioxide and nitrogen

oxides, the negative externality from increasing traffic congestion, and the

negative externality from causing accidents.Economists have estimated

that these externalities are about $1.60-$2.00 per gallon.

Assume annual demand for gasoline in North Carolina is given by

D(p)= 6 - 0.5p where demand is measured in billions of gallons and p is the

price in $ per gallon.This demand is equivalent to the marginal benefit

curve, MB=12- 2q where marginal benefit is measured in $ per gallon and q is

measured in billions of gallons.Assume annual supply in North Carolina is

given by S(p)=4.2 +0.4p, where supply is also in billions of gallons.This

supply is equivalent to the private marginal cost curve, PMC=2.5q-10.5 where

marginal cost is measured in $ per gallon and q is measured in billions of

gallons.Assume the external cost from the negative externalities is $1.80

per gallon.

This problem analyzes a Pigouvian tax for gasoline consumption

in North Carolina. Be sure to briefly explain any calculations.

1)Market inefficiency

a.Solve for the market equilibrium

gasoline consumption and gasoline price by setting MB=PMC.

i.Hint:I

recommend desmos.com.Don't forget the units!

ii.Calculate

the consumer expenditure on gasoline.(Note that this is also the

producers' revenue.)How much is this expenditure per capita? (There are

10.5 million people in North Carolina.)

b.Solve for the efficient gasoline consumption

by setting MB=SMCwhere social marginal cost is the sum of the private

marginal cost and the external cost: SMC=PMC+XT=2.5q-10.5+1.8.

i.Hint:I

recommend desmos.com.Don't forget the units!

2)Pigouvian tax.The Pigouvian tax

equals the externality cost of $1.80 per gallon.With a Pigouvian tax of

$1.80, the sellers (gas stations or refineries) only receive a portion of the

price you pay at the pump.For example, if the buyer pays p the seller

only receives p-1.8 .Use the following steps to calculate the market

equilibrium with the Pigouvian tax.

a.Graph the demand curve, D(p)= 6 - 0.5p.(Hint:

In desmos.com, enter x=6- 0.5yto get the axes correct.)

b.The seller only receives p-1.8 for every

gallon of gasoline they sell.So supply is now S(p)=4.2+0.4(p-1.8).Graph

the supply curve (Hint: In desmos.com, enterx=4.2+0.4(y-1.8) to get the

axes correct.)

c.Solve for the Pigouvian tax

equilibrium gasoline price and gasoline consumption. Use either desmos.com,

wolframalpha or algebra.

i.Calculate

the total consumer expenditure on gasoline and the total tax revenue.Also

calculate the per capita values.

d.Compare the Pigouvian tax equilibrium

to the market equilibrium in 1.a.

i.Does

the price go up by $1.80?Why or why not?

ii.Explain

what happens to consumer expenditure?(use numbers)

iii.Explain

what happens to producer revenue net of taxes? (use numbers)

e.Compare the Pigouvian tax

equilibrium to the efficient gasoline consumption in 1.b.

f.Calculate the deadweight loss of

the market equilibrium.Provide the value in total and in per capita

terms.