Topic 3: Two Region HOS Model

Question 1

Draw a diagram showing the following endowments.

L_H + L_* = L_W

K_H + K_* = K_W

ρ_H=L_H/K_H, ρ_*=L_*/K_*, ρ_W = L_W/K_W

ρ_X = L_X/K_X, ρ_Y = L_Y/L_K

Answer 1

Where the point E represents the subdivision of the global endowments between the two regions.

Question 2

What are the four HOS Theorems?

Answer 2

• 1. Heckscher-Ohlin Theorem.
• 2. Factor Price Equalisation Theorem (of Samuelson).
• 3. Stolper-Samuelson Theorem.
• 4. Rybczynski Thoerem.

Question 3

Heckscher-Ohlin Theorem

Answer 3

H has a product bias towards the good intensive in its relatively abundant factor.

Question 4

What is the Factor Price Equalisation Theorem (of Samuelson)

Answer 4

Free trade in goods between H & * causes factor prices to equalise so long as neither region specialises in either good.

Question 5

What is Stolper-Samuelson Theorem:

Answer 5

If industry X is labour-intensive, a rise in the price of X raises the wage and lowers the rental rate relative to both product prices.

Question 6

What is the Rybczynski Thoerem

Answer 6

At constant pX/pY, an increase in LH causes a more than proportionate increase in X (the labour intensive good) and a fall in Y.

Question 7

Explain why when the home region has a production bias towards the good intensive in it’s relatively abundant factor.

Answer 7

The endowment can be diagramed as below:

Y_H and X_H represent the resources used to produce X & Y respectively, and so sum to E.

If there is free trade and consumption preferences are shared, then the consumption of X and Y will be near equal in both places - while production will have a bias. As a result, regions trade the good they can produce better.

Question 8

Explain why free trade in goods between H and * causes factor prices to equalise, so long as neither region specialises.

Answer 8

When there is specialization, it is impossible for the world to produce as it would if there as only one region. This is because the two regions seperately cannot efficiently produce both goods on the edge of their production possiblity frontier- they are too scarse in one resource. As a result each region will produce only one good - and will do so at an inefficient ratio. If the regions specialise in different goods, then were they able to share factors, they may be able to eliminate each others scaresity.

The region that endowments must be in to avoid specialisation is shown below.

Question 9

Explain why if industry X is labour intensive, a rise in the price of X raises w and decreases r.

Answer 9

The rise in p_X induses a rise in X and an absorption by X of L & K, from industry Y.

But they are desired at ρ_X.

Industry Y is contracting, and if it did so at ρ_Y, then there would be constant returns to scale, and no change in r, or w.

However, as Y loses more L then K, it’s MP_L must rise and MP_K fall.

And so, w increases and r falls.

Question 10

Explain why at P=p_X/p_Y an increase in L_H causes a more then proportionate increase in X (the labour intensive good) and a fall in Y.

Answer 10

We can consider that there is a reallocation of some labour from country * to H.

In our diagram, this is a vertical endowment shift.

It is obvious then that the production of X must increase and Y decrease.