Topic 2: Open Economy HOS Model

Question 1

Explain how the HOS model is solved when the terms of trade is given.

Answer 1

We know p_X/p_Y, so firms can maximise their profits, production and GDP is then solved for.

Given GDP, we have income, and so consumers can pick their consumption bundle along the line Y = M/p_Y-Xp_X/p_Y

Question 2

Solve through equations, the producer problem, given

w = VMPL = 3p_XX/4L_X=p_YY/4L_Y

r = VMPK = p_XX/4K_X=3p_YY/4K_Y

Answer 2

We want to get X/Y by combining those initial equations

We then get

¹/₃^p_Y/_PX^L_X/_KY = 3^p_Y/_PX^K_X/_KY

Defining ρ_X = L_X/K_X and so for Y

we get ρ_X = 9ρ_Y

Going back to our production functions,

X/Y = (ρ_Xρ_Y)^3/4K_X/L_Y

Which is also equal to the given equations. Solving those, we get

^ρ_X/_3P= (ρ_Xρ_Y)^3/4 where P = p_x/p_Y

Now we can eliminate ρ_X & ρ_Y seperatly to get

ρ_X = 3/P²ρ_Y = 1/3P₂

Adding to this our factor constraints and we get factor usage and so production.

Question 3

Solve the consumer problem in the open HOS model.

Answer 3

We still have that p_XC_X = P_YC_Y

Now our budget constraint is that GDP = M = p_XC_X+P_YC_Y

So then M/2=p_XC_X=P_YC_Y which solves simply for marshellian demand functions, which are fully solvable.So we are done.

Question 4

In the open HOS model, what is w/r dependent on?

Answer 4

w/r = 3/ρ_X = 1/3ρ

From the solved example, we get:

^w/_r=P²

So the ratio o funit factor reward depends on the terms of trade.

This are proporties of production functions and assumptions about firms (price takers that minimise cost/max profits)

Not to do with factor endowments or consumer preferences.

Question 5

Draw and explain the Samuelson diagram

Answer 5

On the left side, w/r is determined by P.

On the right side, we have the relationship between w/r and K/L by industry. As we assume wage & rent arbitrage, we know we can then get ρ_X and ρ_Y

Question 6

In our sovled example, if there is a rise in p_X, what happens to real factor rewards?

Answer 6

Ther eis a relative rise in w relative to p_X, and a fall in r relative to P_X. This is the essence of the Stolper-Samuelson Thoerum.

Question 7

When does the Stolper-Samuelson theorum hold?

Answer 7

Only when the country endowment ratio ρ_H = L/K lies between factor proportions in industries. ie

ρ_X >= ρ_H >= ρ_Y

Or graphically:

This is called the diversification ratio. P determines w/r, which determines ρ_X & ρ_Y. If the countries endowment ratio is not inbetween these, then onyl one good will be produced. Ie, say that the country is very labour heavy in endowment, more so the ratio of labour required in the labour intensive industry. It follows that the labour intensive industry will be the only industry used.