Suppose that the market for cigarettes in a particular town has the following supply and demand curves: QS = P;QD = 50 − P, where the quantities are measured in thousands of units. Suppose the town council needs to raise $300,000 in revenue anddecides to do this by taxing the cigarette market. What should the excise tax be in order to raise the required amount of money? 2. The tax revenue will be$\displaystyle P_{tax}*Q$, with$\displaystyle Q$determined by the intersection of the Inverse Demand Curve and the New Inverse Supply Curve, which is shifted upward from the original by$\displaystyle P_{tax}$. Prior to the imposition of the excise tax, the equilibrium price$\displaystyle P_{E} = 25, Q_{E} = 25$. However, when the tax is implemented, demand will fall, thus you need to find: You have Four Equations and Four Unknowns:$\displaystyle Q - P_{S} = 0\displaystyle Q + P_{D} = 50\displaystyle P_{tax} + P_{S} - P_{D} = 0\displaystyle Q*P_{tax} = 300,000$From the above, you can write$\displaystyle 2Q^2 - 50Q + 300,000 = 0$, which has complex roots for Q. Thus it will not be possible to raise 300,000. Perhaps you meant 300? If so, Q = 10 units or 15 units. Substituting Q=15 into the above yields$\displaystyle P_{tax}=20$, i.e$\displaystyle P_{S}=15, P_{D}=35, P_{tax}=20\$