Question

Home’s demand curve for wheat is: D = 100 - 20P. Its supply curve is: S = 20 + 20P.

a) Derive and graph Home’s import demand schedule. What would be the price of wheat and quantity sold in Home in the absence of trade?

Now add Foreign, which has a demand curve: D* = 80 -20P and a supply curve S* = 40 + 20P.

b) Derive and graph Foreign’s export supply curve and find the price of wheat and quantity sold in Foreign in the absence of trade.

c) Now allow Foreign and Home to trade with each other. Find and graph the equilibrium under free trade. What is the world price of wheat? What is the volume of trade?

Answer 1

(a) For Home,

Demand Curve for wheat is: D = 100 - 20P

Supply Curve for wheat is : S = 20 + 20P

The Import Demand schedule is the difference between the Demand of customers and Supply of producers of the country.

Hence, Import Demand schedule for Home is

M = D - S

or, M = (100 - 20P) - (20 + 20P)

or, M = 80 - 40P..........(1)

This is Home's import demand schedule. The schedule is drawn in a diagram below.

In absence of trade, the equilibrum would be at that point where Demand and Supply are equal. Hence, ar equilibrum,

D = S

or, 100 - 20P = 20 + 20P

or, P = $2

Let the equilibrum quantity is Q.

Hence, Q = D = S at equilibrum.

Hence, Q = S = 20 + 20P = 20 + 20×2

or, Q = 60

​​​​​​At Home, in absence of trade, the price of wheat is $2 and quantity sold is 60 units.

(b) For Foreign,

Demand for wheat is: D* = 80 - 20P

Supply of whear is: S* = 40 + 20P

Hence, Export Supply schedule for Foreign is the difference between Supply of peoducers and Demand of customers. Hence, Export Supply schedule is

X = S* - D*

or, X = (40 + 20P) - (80 - 20P)

or, X = -40 + 40P..........(2)

This is the export supply schedule for Foreign. The schedule is drawn in the following diagram.

In absence of trade, the equilibrum is at that point where the Foreign Demand and Supply of wheat are equal. Hence, at equilibrum,

D* = S*

or, 80 - 20P = 40 + 20P

or, P* = $1

Let the equilibrum quantity is Q*. Hence at equilibrum,

Q* = D* = S*

From, Q* = S* = 40 + 20P* = 40 + 20×1

or, Q* = 60

At Foreign, in absence of trade, the price of wheat is $1 and the quantity sold is 60 units.

(c) Now, Home and Foreign are allowed to trade with each other. Hence, the Import Demand and Export Supply curves are the following.

Import Demand curve is: M = 80 - 40P

Export Supply curve is : X = -40 + 40P

At equilibrum, the Import Demand must be equal to Export Supply. Hence, at world free trade equilibrum,

M = X

or, 80 - 40P = -40 + 40P

or, 80P = 120

or, P° = $1.5

P° is the world price of wheat.

Let, equilibrum volume of trade is Q°. Hence, at free trade equilibrum,

Q° = M = S

Hence, Q° = S = -40 + 40P° = -40 + 40×1.5

or, Q° = 20

The equilibrum under free trade is at P° = $1.5 and Q° = 20 units. The equilibrum is drawn in the following diagram.

The world free trade is marked at point E in the diagram.

The world price of wheat is $1.5.

The volume of trade is 20 units.

Hope the solutions are clear to you my friend.