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. 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- 0.5y to 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, enter x=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.