Economics Course in International Trade: General Equilibrium Model

Factor Growth and Trade

(All the assumptions of H-O-S are sustained.)

At constant commodity prices, an increase in the endowment of one factor (say L) will increase the output of the commodity intensively using that factor (say X), and will reduce the output of the other commodity (say Y).

Proof

Consider H: L-abundant country and X is L-intensive. PPF is biased toward X, and H produces at A where the world commodity price is the tangent of PPF.

If L increases, H's PPF shifts outward, being more oriented toward X. With the same world price P_X/P_Y, H will produce at A'.

Result: As L increases, the output of X (L-intensive) increases, and the output of Y (K-intensive) decreases.

Rybczynski Line

We can derive a country's growth path by connecting all optimal output points as a factor increases.

General Equilibrium Approach

Consider an Edgeworth Box explaining H's production. At equilibrium A, Isoquants for X and Y must be tangent, and the tangent line represents the relative factor price (W/r).

X employs L_X labour and K_X capital, and produces a certain amount of X at A. Factor intensity of X (=k_X) is the slope of the straight ray O_XA (=K_X/L_X). The distance O_XA represents the amount of X produced. Y employs L_Y labour and K_Y capital, and produces a certain amount of Y at A. Factor intensity of Y (=k_Y) is the slope of the straight ray O_YA (=K_Y/L_Y). The distance O_YA represents the amount of Y produced.

Now, if H's labour endowment increases for some reason (with fixed K), the box will expand horizontally (as much as new L) while the height will still be the same (as K does not change).

At constant commodity prices, factor prices will be constant. As factor prices are constant, factor intensities k_X and k_Y will be the same as before. Therefore, the new equilibrium A' should satisfy the following conditions:

I_X and I_Y must be tangent.
The tangent is the factor price, which should be the same as before.
Each sector must keep the same factor intensities, k_X and k_Y

We can find A' satisfying all the conditions. A' is found to be further than A from O_X and closer than A to O_Y. This result suggests that, as L increases, sector X expands and sector Y shrinks.

Another Graphical Exposition of Rybczynski

Total endowment of labour and capital in this economy is E¹= (L¹,K¹)

Sectors X and Y use factor intensities k_X and k_Y for producing outputs.

Optimal allocation of L and K to each sector with given E, K_X and K_Y should be A¹= (L¹_X, K¹_X) for sector X and B¹= (L¹_Y, K¹_Y) for sector Y.

Remember that L¹= L¹_X+L¹_Y and K¹= K¹_X+K¹_Y.

Suppose labour endowment in this economy increases while capital is unchanged. Then the economy will have a new endowment E². With given E, K_X and K_Y, the new equilibrium in this economy should be A² and B².

Remember that L²= L²_X+L²_Y and K²= K²_X+K²_Y.

It is obvious from the above analyis that, as labour endowment increases, sector X employs more L (from L¹_X to L²_X) and K (from K¹_X to K²_X) and sector Y employs less L (from L¹_Y to L²_Y) and K (from K¹_Y to K²_Y).

Conclusively, sector X (labour-intensive) expands and sector Y (capital-intensive) shrinks as labour increases.

Remember that this result is drawn because K_X and K_Y are not changed as endowment changes (small country assumption).

General Equilibrium Model - Trade

Ricardo Model

General Equilibrium Model

Web site created by
First Step Communications