Problem 6: Continue with the demand and supply curves given in Problem 4: World

Question

Problem 6:

Continue with the demand and supply curves given in Problem 4:

World Price= 30$

QD = 200 – 4P (U.S. Demand)

QS = – 40 + 2P (U.S. Supply)

Now assume the government imposes a 10% tariff on all goods imported into the U.S.

(a) What are the new (i) price, (ii) quantity demanded, (iii) quantity supplied, and (iv)

imports/exports?

(b) With respect to the change from free trade to tariff-protected trade, calculate the changes in (i)

CS, (ii) PS, (iii) government spending/revenue, and (iv) TS (i.e., DWL/DWG.)

(c) Who would support a policy of moving to tariff-protected trade? Who would oppose it?

Explanation / Answer

(a)

(i) After tariff, Price = $30 x 1.1 = $33

(ii) QD = 200 - (4 x 33) = 200 - 132 = 68

(iii) QS = - 40 + (2 x 33) = - 40 + 66 = 26

(iv) Import = QD - QS = 68 - 26 = 42

(b)

(i) CS = Area between demand curve and market price

Before tariff, QD = 200 - (4 x 30) = 200 - 120 = 80

From demand function, when Q = 0, P = 200/4 = $50 (Reservation price)

CS before tariff = (1/2) x $(50 - 30) x 80 = 40 x $20 = $800

CS after tariff = (1/2) x $(50 - 33) x 68 = 34 x $17 = $578

Change in CS = $(578 - 800) = - $222 (Loss)

(ii) Before tariff, QS = - 40 + (2 x 30) = - 40 + 60 = 20

From supply function, when QS = 0, P = 40/2 = $20 (Minimum price)

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

PS before tariff = (1/2) x $(30 - 20) x 20 = 10 x $10 = $100

PS after tariff = (1/2) x $(33 - 20) x 26 = 13 x $13 = $169

Change in PS = $(169 - 100) = $69 (gain)

(iii) Tariff revenue = Import x Tariff per unit = 42 x $(33 - 30) = 42 x $3 = $126

(iv) DWL = Loss in CS - Gain in PS - Tariff revenue = $(222 - 69 - 126) = $27

(c) Producers and government will support the tariff since both of them will gain after tariff. But consumers will oppose the tariff since they will lose (as CS will fall).

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