3. (7 points) Consider a market in which the demand and supply curves are: QD 40

Question

3. (7 points) Consider a market in which the demand and supply curves are: QD 4000-2P Qs162.5+P/4 a) Calculate economic welfare in autarky with no government intervention b) Calculate economic welfare in autarky with a tax of S180/unit c) Calculate economic welfare with free trade with the rest of the world (and no tax) and PW of $800/unit. d) Calculate economic welfare with free trade with the rest of the world and PW of $800/unit and a tariff of $200/unit e) Calculate economic welfare with free trade with the rest of the world and world price of $800/unit and a tax on consumers of $200/unit (and no tariff

Explanation / Answer

From demand function, when QD = 0, P = 4,000/2 = $2,000 (Reservation price)

From supply function, when QS = 0, P = 162.5 x 4 = $650 (Minimum acceptable price)

Consumer surplus (CS) = Area between demand curve and market price

Producer surplus (PS) = Area between supply curve and market price

Total welfare (TW) = CS + PS

(a) In free-trde equilibrium, QD = QS

4,000 - 2P = - 162.5 + (P/4)

4,000 - 2P = - 162.5 + 0.25P

2.25P = 4,162.5

P = $1,850

Q = 4,000 - (2 x 1,850) = 4,000 - 3,700 = 300

CS = (1/2) x $(2,000 - 1,850) x 300 = 150 x $150 = $22,500

PS = (1/2) x $(1,850 - 650) x 300 = 150 x $1,200 = $180,000

TW = $(22,500 + 180,000) = $202,500

(b) The $180 tax will shift supply curve leftward by $180 per unit and new supply function will be

QS = - 162.5 + (P - 180) / 4 = - 162.5 + 0.25P - 45 = 0.25P - 207.5

Equating QD with new QS,

4,000 - 2P = 0.25P - 207.5

4,207.5 = 2.25P

P = $1,870 (Price paid by buyers)

Price received by sellers = $(1,870 - 180) = $1,690

Q = 4,000 - (2 x 1870) = 4,000 - 3,740 = 260

CS = (1/2) x $(2,000 - 1,870) x 260 = 130 x $130 = $16,900

PS = (1/2) x $(1,690 - 650) x 260 = 130 x $1,040 = $135,200

Tax revenue = $180 x 260 = $46,800

TW = CS + PS + Tax revenue = $(16,900 + 135,200 + 46,800) = $198,900

(c) When PW = $800,

QD = 4,000 - (2 x 800) = 4,000 - 1,600 = 2,400

CS = (1/2) x $(4,000 - 800) x 2,400 = 1,200 x $3,200 = $3,840,000

QS = - 162.5 + (800/4) = - 162.5 + 200 = 37.5

PS = (1/2) x $(800 - 650) x 37.5 = (1/2) x $150 x 37.5 = 2,812.5

TW = $(3,840,000 + 2,812.5) = $3,842,812.5

(d) The tariff will increase price by $200, to $(800 + 200) = $1,000. At this price,

QD = 4,000 - (2 x 1,000) = 4,000 - 2,000 = 2,000

CS = (1/2) x $(2,000 - 1,000) x 2,000 = 1,000 x $1,000 = $1,000,000

QS = - 162.5 + (1,000/4) = - 162.5 + 250 = 87.5

PS = (1/2) x $(1,000 - 650) x 87.5 = (1/2) x $350 x 87.5 = $15,312.5

Imports = QD - QS = 2,000 - 87.5 = 1,912.5

Tariff revenue = Unit tariff x Imports = $200 x 1,912.5 = $382,500

TW = CS + PS + tariff revenue = $(1,000,000 + 15,312.5 + 382,500) = $1,397,81.5

NOTE: As per Chegg Answering Policy, first 4 parts are answered.

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