Question

Problem 1. Suppose the market demand is given by D(P) = 10 – 2p and the market supply is given by S(p) = 3p - 5. 1. Draw the supply and demand curves. Determine the equilibrium price p* and the equilibrium output x*. Determine CS, PS, and TS. 2. Explain why TS is maximized at the equilibrium price p*. 3. Suppose government imposed a $0.5 quantity tax. Determine the equilibrium price and the equilibrium output after the tax. Also, determine CS, PS, the tax revenue, and the deadweight loss. 4. Is the tax revenue from the consumers greater than the tax revenue from the producers? Explain why.

Answer 1

(1)

Demand: D(p) = Q = 10 - 2p

Supply: S(p) = Q = 3p - 5

From demand curve, When Q = 0, p = 10/2 = 5 (Vertical intercept) & when P = 0, Q = 10 (Horizontal intercept).

From supply curve, when Q = 0, p = 5/3 = 1.67 (Vertical intercept).

In following graph, D0 & S0 are initial demand & cupply curves intersecting at point A with price p* and quantity x*.

1.67 O X

In equilibrium, D(p) = S(p)

10 - 2p = 3p - 5

5p = 15

p* = 3

x* = 10 - (2 x 3) = 10 - 6 = 4

CS = Area between demand curve and market price = (1/2) x (5 - 3) x 4 = 2 x 2 = 4

PS = Area between supply curve and market price = (1/2) x (3 - 1.67) x 4 = 2 x 1.33 = 2.66

TS = CS + PS = 4 + 2.66 = 6.66

(2)

At price of p*, quantity demanded equals quantity supplied at a common price, therefore CS is maximized and TS is maximized, as a result TS is maximized.

(3)

The tax will lower effective price received by sellers by $0.5 at every output level, shifting supply curve leftward. New supply function is

Q = 3(p - 0.5) - 5 = 3p - 1.5 - 5 = 3p - 6.5

Equating with D(p),

10 - 2p = 3p - 6.5

5p = 16.5

p = 3.3 (Price paid by buyers)

Price received by sellers = 3.3 - 0.5 = 2.8

Q = 10 - (2 x 3.3) = 10 - 6.6 = 3.4

New CS = (1/2) x (5 - 3.3) x 3.4 = 1.7 x 1.7 = 2.89

New PS = (1/2) x (2.8 - 1.67) x 3.4 = 1.7 x 1.13 = 1.92

Tax revenue = 0.5 x (4 - 3.4) = 0.5 x 0.6 = 0.3

Deadweight loss = (1/2) x Unit tax x Difference in quantity = (1/2) x 0.5 x (4 - 3.4) = 0.25 x 0.6 = 0.15

(4)

Tax borne by consumers = Price paid by consumers after tax - Pre-tax price = 3.3 - 3 = 0.3

Tax revenue from consumers = 0.3 x 3.4 = 1.02

Tax borne by producers = Unit tax - Tax borne by consumers = 0.5 - 0.3 = 0.2

Tax revenue from producers = 0.2 x 3.4 = 0.68

Since consumers bear higher tax burden than producers, tax revenue from consumers is higher than tax revenue from producers.