Question

Home's Domestic Demand and supply curves for shoes are D = 500-10P and S = 300+20P. Foreign's domestic demand and supply curves for the same type of shoes are D = 1000-10P and S = 200 + 40P. Problem 2.1 (3 points each). (a) Find the autarky price and quantity for each country. If the countries trade, which country will export shoes? (b) Derive algebraically the import demand and export supply functions. Find the price and volume of trade with free trade. (c) Show graphically the world equilibrium, equilibrium at Home, and at Foreign under free trade

Answer 1

Home's Domestic Demand and supply curves for shoes are:

D = 500-10P

S = 300+20P

Foreign's domestic demand and supply curves for the same type of shoes are:

D = 1000-10P

S = 200 + 40P

a)

Autarky means no trade.

Equilibrium arises where Demand = Supply

In home:

500-10P=300+20P

200= 30P

Ph= 20/3 Autarky price in home

Put Ph=20/3 in demand equation:

Qh=500-10P= 500-10(20/3)= (1500-200)/3= 1300/3 Autarky quantity in home

In Foreign:

1000-10P=200+40P

1000-200= 50P

Pf= 16 Autarky price in foreign

Put Pf=16 in demand function :

Qf= 1000-10(16)= 840 Autarky Quantity in foreign

Here as shoes are cheaper in home market and expensive in foreign market. So people in foreign will demand from home and home producers wants to sell in foreign market at a higher prices. This implies that Home will export and foreign will import.

b)

Import demand function:

Imports(M)= D(in foreign)-S(in foreign)

M= 1000-10P-(200 + 40P)

M= 800-50P Import demand function

Export supply function:

X= S(in foreign) - D(in foreign)

X= 300+20P-500+10P

X= 30P-200 Export supply function

To determine price in free trade:

M=X

30P-200 = 800-50P

80P = 1000

P= 1000/80= 12.5 Price in free trade

Put P=12.5 in export function:

Volume of trade= 30P-200= 375-200= 175

c)