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Gasoline market-Demand and supply problem

Let us suppose that US gasoline market has the demand and supply curves
Qd = 10 – 0.5Pd
Qs = -2 + Ps when Ps ≥ 2 and Qs = 0 if Ps < 2,

Here quantities stand for millions of gallons per year and prices refer to the amount of $ per gallon

(i) With no tax, determine the equilibrium price and quantity?

(ii) Assume that the government imposes an excise tax of $3 per gallon. Then what will the new equilibrium quantity? Determine the price which buyers pay? And what price will sellers receive?

(iii) Determine the impact of this tax on the consumer excess and the producer excess. In addition, compute the tax collection from government and the welfare deadweight loss.

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With a $3 tax, setting Qd = Q implies

10 - 0.5 (Ps + 3) = -2 + Ps 

After replacing into the equation for Pd implies Pd = 10.  Replacing this price into the equation for quantity demanded entails  million.  At such prices and quantities, consumer excess is $25 million, producer excess is $12.5 million, and government tax receipts are $15 million. The deadweight loss is $1.5 million. The deadweight loss evaluates the difference among potential net benefits ($54 million) and the total benefits which are really attained ($25 + $12.5 + $15 = $52.5 million).

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