Question

Shire is a small country that currently trades freely in the world barley market. Demand and supply for barley in Shire are as follows. Demand: P = 40−Q Supply: P = Q The world price of barley is $30 per bushel.

(a) What is the domestic equilibrium price and quantity when this is a closed economy. Calculate consumer surplus and producer surplus. (Draw the graph.)

(b) Now they trade freely in the world barley market. What would be amount of domestic demand, domestic supply, and export? What would be consumer surplus, and producer surplus in this case? (Draw the graph.)

(c) Assume that Shire imposes export tariff which is 5$ per bushel of barley. What would be domestic demand, domestic supply, export, and government revenue? Calculate the dead-weight loss caused by export tariff. (Draw the graph.)

(d) Consider two policies: tariff and import quota. In general, which policy generates more distortion in the market in terms of dead weight loss?

Answer 1

Solution:

Demand function: P = 40 - Q or Q = 40 - P, supply function: P = Q; world price of barley, pw = $30 per bushel

a) Finding domestic equilibrium levels: equilibrium occurs where quantity demanded equals the quantity supplied. So,

40 - P = P

2*P = 40

P = 40/2 = 20

So, equilibrium level of quantity = 20 bushels of barley, and equilibrium price = $20 per bushel

Calculating consumer surplus and producer surplus: refer to the below diagram

Consumer surplus = (1/2)*Qd*(40 - P) = (1/2)*20*(40 - 20) = $200

Producer surplus = (1/2)*Qs*P = (1/2)*20*20 = $200

b) On trading freely in the barley market, at world price of $30:

Quantity demanded, Qd = 40 - 30 = 10 bushels

Quantity supplied, Qs = 30 bushels

And thus, exports (which equals excess domestic production over domestic demand) = Qs - Qd

Exports = 30 - 10 = 20 bushels

Calculating consumer surplus and producer surplus: refer to the below diagram

Consumer surplus = (1/2)*Qd*(40 - Pw) = (1/2)*10*(40 - 30) = $50

Producer surplus = (1/2)*Qs*Pw = (1/2)*30*30 = $450

c) With export tariff of $5 per bushel of barley, world price charged = 30 - 5 = $25

So, quantity demanded, Qd = 40 - 25 = 15 bushels

Quantity supplied, Qs = 25 bushels

Exports = Qs - Qd = 25 - 15 = 10 bushels

With exports of 10 bushels, total government revenue earned with export tariff of $5 = 5*10 = $50

Dead weight loss due to export tariff = (1/2)*difference in Qd*tariff + (1/2)*difference in Qs*tariff

DWL = (1/2)*(15 - 10)*5 + (1/2)*(30 - 25)*5 = 2*(1/2)*5*5 = $25

Refer to the figure below: