problem set 4 -heckscher-ohlin model. - sweetsweet.ua.pt/afreitas/aulas/int/ps4_2012-13_with...

International economics – Problem sets

[email protected] Miguel Lebre de Freitas 16

Problem set 4 -Heckscher-Ohlin model. Exercise 1

Home can produce two goods: x which is capital-intensive and y which is labor-intensive. As a result of opening up for trade with the rest of the world we see that Px/Py at Home increases.

a) What good does Home export and what good does it import? Is Home capital or labor abundant?

b) What should happen to: i) the wage-rental ratio; ii) capital intensity in each sector; iii) capital employed in each sector.

c) Plot the changes resulting from opening up for trade in the Harrod-Johnson diagram. As a result of trade, what happens to the real price of labor and capital? Which group benefits from trade: capital-owners or workers?

Exercise 2

B is a small economy where two goods are produced, scarfs (X ) and flags (Y ), according to the following production functions:

43

41

5.0 XX LKX = and 21

21

YY LKY = .

The labor and capital endowments in this economy are respectively, 40=L and 150=K . It is known that in B the preferences are homothetic and the autarky relative

wage is 9== rwω . a) Draw the diagram that relates capital intensity with the relative wage. Identify the

capital intensive good and the points of full specialization.

b) Examine the effects of opening to international trade, assuming that in the rest of the world 8=ω and 4== LKk :

(i) Which of the countries is relatively abundant in capital? Explain your answer, specifying the concept of abundance;

(ii) Describe the passage from autarky to free trade and show graphically the gains from trade in B. Quantify when possible;

(iii) Explain the evolution of the factors returns after opening to trade.

c) Assume that, in the short run, capital cannot move between sectors. Describe the short-run effects from opening to trade on production, consumption and factors returns, compare it with the long run solution from b).



Exercise 3

Consider a world with two countries (N and R), two goods and two factors. The technologies are CRS and identical in both countries and the substitution elasticity between factors in both industries is constant and equal. Allow y to be the capital-intensive good. Determine the specialization pattern when both countries are identical in everything except in the fact that:

a) The consumers of N have a larger relative preference for good x.

b) Country N has more capital and labor than country R, but with the same proportion of both factors.

c) County N has more capital than country R, being the labor endowments equal.

d) Country N has a larger relative labor endowment and the consumers of N have a larger relative preference for good x.

Exercise 4

Consider a small open economy where 2 goods, X and Y, are produced using labor and capital according to the following expressions:

21

21

XX LKX = and 41

43

4 YY LKY = .

a) Complete the following figure:

ω

3?

? k

y

x

Suppose that this economy is open to international trade and that the relative wage in the rest of the world is equal to 4.

b) Determine the relative return of factors in this country. Justify it.

c) Check which of the following conditions are compatible with this exercise:

(i) This country has comparative advantage in the production of x; (ii) This country has the same preferences as the rest of the world but a smaller

endowment of labor; (iii) This country has the same endowments and technology as the rest of the

world but its consumers have a larger relative preference for good x.



Exercise 5

Comment the accuracy of the following statements: “If, after opening to international trade, the capital intensive sector has contracted and the labor intensive sector has expanded, then…”

a) "... it is because the country had a larger labor endowment than the rest of the world”;

b) "... workers are worse with trade and capital owners are better with trade";

c) "... the national product, measured at autarky prices, has decreased, so the gains from specialization are negative”.

Exercise 6

Consider a small open economy, described by the following equations:

X K LX X= 434

14

Y K LY Y= 414

34

U XY= L = 100 e K = 10

a) Show that in both industries the average and marginal productivity of labor and capital depends only on the factors proportion and not on the absolute production levels. Why does this occur?

b) Use the Pareto efficiency conditions in the factors market to determine the relation between: rw=ω and jjj LKk = .

c) Find out the relationship between ω and XY PPp = as well as the maximum range of ω . Draw the Harrod-Johnson diagram.

d) Determine the expression for the production contract curve. Represent it graphically.

e) Compute the expression for the relative supply curve of y.

Hint:

(i) Based on the Harrod-Johnson diagram, compute the relation between p and

Yk ;

(ii) Use the contract curve expression in (i) to obtain a relationship between YL and p;

(iii) Use the productivity of labor in both sectors obtained in (a) and the expressions obtained in (a) to compute the relative supply of Y in terms of YL and p;

(iv) Use (ii) and (iii) to eliminate YL ;

(v) If you reached 3

2

103130pp

pXY

S −−

=⎟⎠

⎞⎜⎝

⎛ you are correct!



f) Determine the relative demand curve of Y.

g) Define the autarky equilibrium, finding the:

(i) Relative price and relative wage; (ii) Capital intensity in both sectors; (iii) Absolute levels of labor and capital usage; (iv) Absolute production levels of X and Y. Check that the results are compatible

with the relative demand expression; (v) Autarky utility level.

h) Suppose now that the country opens to international trade. Assuming that, in the

world economy, 2.0=p , find:

(i) The relative wage under free trade. Were you expecting a change in this direction?

(ii) The capital intensity in both sectors; (iii) Absolute levels of labor and capital usage; (iv) Absolute production levels of X and Y. Check that the results are compatible

with the relative supply. (v) The national income in units of X; (vi) The optimal consumption quantities; (vii) Exchanged quantities of both goods. Show it graphically; (viii) The utility level with trade.

i) Suppose that the country experiences a strong immigration wave increasing the

labor endowment to 150.

(i) Compute the new contract curve; (ii) Using the information about capital intensity, compute the employment level

in both industries; (iii) Compute the new production optimum. Which important theorem have you

just confirmed? Show it graphically; (iv) Using the fact that the ‘Engel Curve’ in this exercise is a straight line,

discuss whether the trade triangle has increased or decreased. If the labor endowment were larger, would it be possible to invert the specialization pattern? Why?

Exercise 7

Consider a small open economy where 2 goods, X and Y, are produced using labor and capital according to the following expressions:



XX LKX 2= YY LKY = 64.036.0 YXU =

100=L 100=K

a) Find out the expression of the PPF assuming that both factors are perfectly mobile across industries. Compute the MRT.

b) Explain why in this economy endowments of labour and capital are not relevant to explain the specialization pattern.

c) Find out the equilibrium allocation under autarky.

Suppose that in the rest of the world, the production functions are:

XX LKX 75.0= YY LKY =

d) Compute the equilibrium price under free trade.

e) Under free trade, will there be convergence of real incomes?

f) Find out the specialization pattern of the home country under free trade.

g) Suppose that in the short term, capital was immobile. Departing from the autarky equilibrium, find out the expression for the short term PPF. Confirm the optimality of the allocation found in (c).

h) Examine again the move from autarky to free trade, but disentangling the short term and the long term effects on production, welfare and real incomes.



Solutions – PS 4

Exercise 1

Solved in class.

Exercise 2

a) y is capital intensive.

b) !!! As explained in class, due to a mistake, I solved the exercise with 4=ω (and not with 8=ω 4== LKk ). These solutions are for 4=ω .

b.i) Country B is capital abundant.

b.ii) Production points will be (23.03 , 15) in autarky and (2.01 , 72.5) under free trade.

b.iii) Real returns of capital increase in country B; real wages decrease.

c) We are back in the Specific factors model; ( )xpr and ( )ypw decrease; ( )ypr and

( )xpw increase.

Exercise 3

a) Country R: exports x, imports y. b) No trade.

c) Country R: exports x, imports y. d) Ambiguous.

Exercise 4

a) k = 3; 1== rwω .

b) Relative return in B: 4== rwω ; Real returns: ( ) 1=xpw , ( ) 45.6≈ypw ,

( ) 25.0=xpr , ( ) 61.1≈ypr .

c) (i) Yes; (ii) No (if ‘smaller labor endowment’ is meant in relative terms); (iii) No.

Exercise 5

a) True (large labor endowment in relative terms). b) Wrong. c) Wrong.

Exercise 6



a) Due to CRS. b) ω=3xk , ω=yk3 . c) ω=p d)

x

xx L

LK8100

90+

=

e) Additional hint: manipulate the expression used in c) to write it as a function of X and Y.

f) 1−= pXY

g) (i) 1.0=p , 1.0=ω ; (ii) 3.0=xk , 30/1=yk ; (iii) 25=xL , 5.7=xK ; (iv)

536.40≈X , 186.128≈Y ; (v) 115.5196≈U .

h) (i) 04.0=ω ; (ii) 12.0=xk , 75/1=yk ; (iii) 25.81=xL , 75.9=xK ; (iv)

2627.66≈X , 48566.25≈Y ; (v) National income = 71.3598; (vi) 6799.35≈X , 3995.178≈Y .

i) (i) x

xx L

LK8150

90+

= ; (ii) 75=xL , 9=xK ; (iii) 1656.61≈X , 94.101≈Y .

Rybczynski theorem. (iv) Trade triangle decreases; Yes, pattern may change if labor endowment increases further.

Exercise 7

a) xy 5.0100−= .

b) Both sectors use the same factor intensities. This is does not correspond to the HO model.

c) ( ) ( )64,72, =yx .

d) 34== YX PPp .

e) There will be no convergence of real incomes.

f) The small open economy exports x and imports y.

g) The short-run PPF is: 10064144

22

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛ yx .

h) New production point will be ( ) ( )40,92.103, =yx .

problem set 4 -heckscher-ohlin model. - sweetsweet.ua.pt/afreitas/aulas/int/ps4_2012-13_with...

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