a. Suppose that the demand for packs of cigarettes is given by D(P)=180-40P, whe
ID: 2428805 • Letter: A
Question
a. Suppose that the demand for packs of cigarettes is given by D(P)=180-40P, where p is the price of a pack of cigarettes. The supply of cigarettes is given by S(P)=-20+10P. Solve for the equilibrium price and quantity packs of cigarettes. b. Now suppose that the government adds a tax of $t per pack of cigarettes to by paid by consumers. What is the new equilibrium quantity of packs of cigarettes? What is the after-tax price paid by consumers? What is the price received by sellers? Does the proportion of the tax burden payed by consumers depend on the size of the tax? (Your answer may have t in it) c. Find an expression for tax revenue as a function of t. If the government wanted to maximize tax revenue, what tax would they choose? d. Find an expression for deadweight loss as a function of t.
Explanation / Answer
(a) In pre-tax equilibrium, D(P) = S(P)
180 - 40P = - 20 + 10P
50P = 200
P = $4
Q = 180 - (40 x 4) = 180 - 160 = 20
(b) The $t tax on consumers will shift demand curve leftward. New demand function will be
D(P) = 180 - 40(P + t) = 180 - 40P - 40t
Equating new D(P) with S(P),
180 - 40P - 40t = - 20 + 10P
50P = 200 - 40t
P = 4 - 0.8t (Price received by producers)
Price paid by consumers = 4 - 0.8t + t = 4 + 0.2t
Q = 180 - 40 x (4 + 0.2t) = 180 - 160 - 8t = 20 - 8t
Tax burden of consumers = Price paid by consumers after tax - Pre-tax equilibrium price
= 4 + 0.2t - 4 = 0.2t
Proportion of tax burden of consumers = 0.2t / t = 0.2 = 20%
Therefore, even though absolute (dollar) value of tax burden of consumers depend on size of tax, proportion of tax burden does not.
(c) Tax revenue = Unit tax x After-tax quantity = t x (20 - 8t) = 20t - 8t2
(d) Deadweight loss = (1/2) x Unit tax x Change in quantity = (1/2) x t x [20 - (20 - 8t) = 0.5t x 8t = 4t2
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.