Question

Consider the following model of trade between Germany and China. Assume throughout this problem that these are the only two countries for which trade is possible. Assume there are two types of goods: cars and apparel. Consumers in both countries spend 1/3 of their income on apparel and the remaining on cars, and labor is the only factor of production. Each German worker can produce 6 cars or 3 units of apparel per unit of time, while each Chinese worker can produce 2 cars or 2 units of apparel per unit of time. Assume there are 30 million workers in China and 12 million workers in Germany.

A) Find the autarky relative price of apparel in both countries (price of apparel divided by price of cars).

B) Derive the relative demand curve relating the relative demand for apparel to the relative price of apparel. Solve algebraically, and then draw the curve in a diagram with the relative price of apparel on the vertical axis and the relative quantity of apparel on the horizontal axis. 


C) Derive and draw the world relative supply curve for apparel. 


D) Compute the equilibrium relative price of cars under free trade. Which country 
produces which good? Is there complete specialization? 


E) How does your answer from part C change if China experiences an exogenous 
decrease to its labor force leaving it half of its workers? Which country produces which good? Is there complete specialization?

Answer 1

A)

MPL	Cars	Apparel
Germany	6	3
China	2	2

The autarky relative price of apparel in both countries is equal to opportunity cost of producing apparels in both countries.

In Germany:  

3 apparels=6cars

1 apparel = 2cars

In China:

2 apparels = 2 cars

1 apparel = 1 car

Hence, we see that opportunity cost of producing an apparel in Germany is 2 and in China is 1. So the relative relative price of apparel (price of apparel divided by price of cars) in Germany is 2 and in China is 1 in autarky.

B) Assuming that both car and apparel are normal goods, relative demand for apparel is negatively related to relative price of apparel. It means that as price of apparel is increased, relative to car, with income remaining the same, the quantity demanded of apparel will fall relative to car. For example, let's assume a consumer in a country has income of $30. Out of which, he spends $10 on apparel. Let's assume that the relative price of apparel to be 1, this would buy him 10 units of apparel but if the relative price rises to 2, with the same income of $10, consumer can only buy 5 units of apparel. So, the relative demand will be a downward sloping curve in quantity-output space.

C) No country will produce apparel if its relative price is less than 1 because price will be less than opprtunity cost of produing an apparel in both countries. At relative price=1, China will be indifferent in producing either apparel or car because workers in china earn the same amount of real wage producing either of the good while Germany produces all cars (since relative price of apparel is less than cost of producing an apparel in Germany which is 2).

At relative price>1 but less than 2, workers in China earn more from producing apparel than car (as price is more than the cost of producing apparel and it is also more than price of car), so China produces cars only while Germany still produces cars only. This is the zone of complete specialisation where China produces apparels only and Germany produces only cars.

At relative price=2, Chinese workers specialise in apparel production only while German workers are equally well off in producing either apparel or cars because they are paid equal to the opportunity costs. Similarly, for relative price>2, both the countries produce apparel only.

The world relative supply curve for apparel is shown in the following image:

At relative price=1, 30 million chinese workers produce 60 million apparel at a point of time.

At relative price=2, 12 million german workers produce 36 million apparel and total world supply in the world will reach 60+36 million=96 million.

D)  The equilibrium relative price of cars under free trade depend on intersection of relative supply and relative demand of the car in international market. Relative supply of the car can be drawn in the same way as we have drawn relative supply of apparel in the previous part. Relative demand of car is negatively related to relative price and hence is downward sloping. The equilibrium in world market of car is shown below:

For relative demand curve RD, there is complete specialisation. Germany produces cars only and China produces apparel only. The relative price of car, then will be anything between 1/2 and 1.

Note that, for any relative demand curve like RD₁ or RD₂ it is not necessary that both countries necessarily specialise. They may or may not specialise.

E) China experiences an exogenous ?decrease to its labor force leaving it half of its workers to 15million workers. There will be no change in the shape of relative supply curve of apparel (as in the part C). However, there will be change in points on the X-axis. The point labelled as 60 will come down to 30 and the point 96 will become 66.

So, there will be a change in total production in apparel as chinese workforce is reduced. Everything else remains the same because there is no change in productivity of labor in either of the country. So, if countries specialise (depending on where the RD and RS intersect), China still specialise in apparel while Germany produces all the cars.