Question

Consider the following demand and supply equations for cell-phones in the do- mestic country: Supply: Qs = -60/2 + 3/2 P Demand: Qd = 300/2 - 3/2 P where the price is measure in $/cell-phone and the quantity is measure in thou- sands of cell-phones.

1. Graph the supply and demand schedules for the domestic economy. Clearly label the y-intercepts for both the supply and demand equations.

2. Suppose the world price of cell-phones is $40/cell-phone (denoted by Pw). What is the domestic demand and domestic supply at the world price? How many cell-phones will be imported into the domestic economy at this price? Clearly show all calculations, and illustrate your answer using a well-labeled graph.

3. Calculate the consumer surplus (CS1) and the producer surplus (PS1) for the domestic economy. Clearly show all calculations.

4. Suppose the domestic government levies a tari of $5/cell-phone (denoted by ). (a) What would happen to domestic demand and domestic supply once the tari is imposed? What is the corresponding level of imports? Clearly show all calculations, and illustrate your answer using a well labeled graph. (b) Calculate the consumer surplus (CS2) and the producer surplus (PS2) for the domestic economy after the tari is imposed. Clearly show all your calculations.

Answer 1

Qd = (300/2) - (3/2)P = 150 - 1.5P

Qs = - (60/2) + (3/2)P = - 30 + 1.5P

(1)

From demand function we get

When Qd = 0, P = 150/1.5 = 100 (Vertical intercept of demand curve)

From Supply function we get

When Qs = 0, P = 30/1.5 = 20 (Vertical intercept of supply curve).

In following graph, AB & CD are the demand & supply curves with vertical intercepts obtained above, which intersect at point E with price P0 and quantity Q0.

(2) At world price (Pw) = $40,

Qd = 150 - (1.5 x 40) = 150 - 60 = 90 (Point Q1 in above graph)

Qs = - 30 + (1.5 x 40) = - 30 + 60 = 30 (Point Q2 in above graph)

Import = Qd - Qs = 90 - 30 = 60 [= (Q1 - Q2) in above graph]

(3) At world price (Pw) = $40,

CS1 = Area lying between demand curve and Pw = Area AFPw = (1/2) x $(100 - 40) x 90 = 45 x $60 = $2,700

PS1 = Area ling between supply curve and Pw = Area CGPw = (1/2) x $(40 - 20) x 30 = 15 x $20 = $300

(4) After tariff of $5, domestic price rises from Pw to Pt = $45 (= Pw + T = $40 + $5). At this price,

(a)

Qd = 150 - (1.5 x 45) = 150 - 67.5 = 82.5 (Point Q3 in above graph), so Qd decreased by 7.5 (= 90 - 82.5).

Qs = - 30 + (1.5 x 45) = - 30 + 67.5 = 37.5 (Point Q4 in above graph), so Qs increase by 7.5 (= 37.5 - 30).

Import Qd - Qs = 82.5 - 37.5 = 45 [= (Q3 - Q4) in graph], so imports decreased by 15 (= 60 - 45).

(b) At after-tariff price Pt = $45,

CS2 = Area of triangle AHPt = (1/2) x $(100 - 45) x 82.5 = (1/2) x $55 x 82.5 = $2,268.75

PS2 = Area of triangle CJPt = (1/2) x $(45 - 20) x 37.5 = (1/2) x $25 x 37.5 = $468.75