Question

Suppose that the world price for a good is 120 and the domestic demand-and-supply curves are given by the following equations:

Demand: P = 200 – 8Q

Supply: P = 20 + 10Q

a. How much is domestic consumption?

b. How much is domestic production?

c. Calculate the values of consumer and producer surplus.

d. If a tariff of 30% is imposed, how much do consumption and domestic production change?

e. What is the change in consumer and producer surplus?

f. How much revenue does the government earn from the tariff?

g. What is the net national cost of the tariff?

Answer #1

From demand: QD = (200 - P)/8 = 25 - 0.125P

From supply: QS = (P - 20)/10 = 0.1P - 2

(a)

When P = 120,

QD = 25 - 0.125 x 120 = 25 - 15 = 10

(b)

When P = 120,

QS = 0.1 x 120 - 2 = 12 - 2 = 10

(c)

When QD = 0, P = 200

Consumer surplus (CS) = (1/2) x (200 - 120) x 10 = 5 x 80 = 400

When QS = 0, P = 20

Producer surplus (PS) = (1/2) x (120 - 20) x 10 = 5 x 100 = 500

(d)

After tariff, P = 120 x 1.3 = 156

QD = 25 - 0.125 x 165 = 25 - 19.5 = 5.5

So QD decreases by (10 - 5.5) = 4.5

QS = 0.1 x 156 - 2 = 15.6 - 2 = 13.6

So QS incraeses by (13.6 - 10) = 3.6

(e)

When P = 156,

CS = (1/2) x (200 - 156) x 5.5 = 2.75 x 44 = 121

So CS decreases by (400 - 121) = 279

PS = (1/2) x (156 - 20) x 13.6 = 6.8 x 136 = 924.8

So PS increases by (924.8 - 500) = 424.8

(f)

After tariff,

Import = QD - QS = 5.5 - 3.6 = 1.9

Unit tariff = 120 x 30% = 36

Tariff revenue = 36 x 1.9 = 68.4

(g)

Net national cost = Increase in PS - Decrease in CS - Tariff revenue = 424.8 - 279 - 68.4 = 77.4

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