Question

16. The demand for ice cream is given by 20- 2P, measured in gallons of ice cream. The supply of ice cream is given by 4P- 10. a. Graph the supply and demand curves, and find the equilibrium price and quantity of ice cream. b. Suppose that the government legislates a SI tax on a gallon of ice cream, to be collected from the buyer. Plot the new demand curve on your graph. Does demand increase or decrease as a result of the tax? c. As a result of the tax, what happens to the price paid by buyers? What happens to the price received by sellers? How many gallons of ice cream are sold? d. Who bears the greater burden of the tax? Can you explain why this is so? e. Calculate consumer surplus both before and after the tax f. Calculate producer surplus both before and after the tax. g. How much tax revenue did the government raise? h. How much deadweight loss does the tax create?

Answer 1

(a)

From demand function,

When QD = 0, P = 20/2 = $10 (Vertical intercept) and when P = 0, QD = 20 (Horizontal intercept).

From supply function,

When QD = 0, P = 10.4 = $2.5 (Vertical intercept).

In equilibrium, QD = QS.

20 - 2P = 4P - 10

6P = 30

P = $5

Q = 20 - (2 x 5) = 20 - 10 = 10

In following graph, D0 & S0 are demand and supply curves intersecting at point A with equilibrium price P0 (= $5) and quantity Q0 (= 10).

(b)

The $1 tax will increase the effective price paid by buyer, which will decrease demand and shift demand curve leftward by $1 at every output. New demand function is

QD = 20 - 2(P + 1) = 20 - 2P - 2 = 18 - 2P

When QD = 0, P = 18/2 = $9 (Vertical intercept) and when P = 0, QD = 18 (Horizontal intercept).

In above graph, D1 is new demand function. Since demand curve has shifted leftward, there is a decrease in demand.

(c)

Equating new QD with QS,

18 - 2P = 4P - 10

6P = 28

P = $4.67 (Price received by sellers = P1)

Price paid by buyers (P2) = $4.67 + $1 = $5.67

Q (Q1) = 18 - (2 x 4.67) = 18 - 9.34 = 8.66

(d)

Tax burden of buyers = After-tax price paid - Pre-tax price = $5.67 - $5 = $0.67

Tax burden of sellers = Pre-tax price - After-tax price received = $5 - $4.67 = $0.33 (= Unit tax - Tax burden of buyers).

Buyers share higher tax burden. The reason is demand is more inelastic than supply.

NOTE: As per Answering Policy, 1st 4 parts are answered.