7. a. Suppose that the demand for packs of cigarettes is given by D(P)=180-40P,

Question

7. 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) At equilibrium, quantity supply is equal to quantity demanded

180-40P = 20+10P

160=50P

P=3.2

Q=180-40(3.2) = 52

Eqiuilibrium price = 3.2, Equilibrium quantity = 52

(B) Now price recieved by seller is P and price paid by buyer is P+T

As quantity demand and quantity supply are equal

180-40(P+T)=20+10P

160-40T=50P

P = 3.2-0.8T

So, the price recieved by seller is clearly less than the price recieved before tax was imposed.

Buyer pay price, recieved by seller plus tax which is (P+T=3.2-0.8T+T) = (P+T=3.2+0.2T)

Quantity sold now is 180-40P = 52-8T (put the value of P=3.2+0.2T)

The distribution of tax burden only depand on the elasticity of supply and demand

(C). tax revenue is T*Q. Here tax revenue is T(32+2T) = 52T-8T2

If the government want to maximize tax revenue they need to choose the tax rate which is the mid of highest and lowest tax rate. At both highest and lowest tax rate revenue is zero

(D). deadweight loss = 1/2 * (P2-P1) * (Q1-Q2)

=1/2 * (3.2+0.2T-3.2) * (52-52+8T)

=2T2/5

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