Suppose the demand curve for a good is given by the equation P = 200 - 1/2 Q and the supply curve is given by the equation P = 50 + 1/4 Q, where P represents the price of the good (measured in dollars per unit) and Q represents the quantity of the good (measured in units per week).
(i) Find the equilibrium price and quantity for this market.
(ii) Suppose the government imposes a sales tax of $9 per unit on this good. Find the new formula for the demand curve, the new equilibrium quantity, the post-tax price received by suppliers, and the post-tax price paid by demanders.
(iii) What fraction of the economic burden of this tax is borne by demanders and what fraction is borne by suppliers?
(i) Q = 200 units per week and P = $100 per unit.
(ii) The new demand curve is P = 191 - 1/2 Q. The new equilibrium quantity is Q = 188 units per week, and the new equilibrium price is P = $97 per unit. Since the legal incidence is on demanders, the post-tax price received by suppliers is $97 per unit and the post-tax price paid by demanders is $97 + $9 or $106 per unit.
(iii) Demanders bear 2/3 of the tax burden, while suppliers bear the other 1/3.
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