# Heckscher-Ohlin Theory

**Question description**

Consider two countries whose representative consumers have the same preferences given by U(CC;CF ) = CC CF

and U^{*} (CC*;CF*_)
= CC*CF*_
.
The two countries share the same production technologies which are given by

QC
=
L_{c}^{2/3 }K_{c}^{1/3} , Q_{F}=
L_{F}^{1/3 }K_{F}^{2/3}

The home country is endowed with 400 units of capital and 300 units of labor, while the foreign country is

endowed with 100
units of capital and 50 units of labor.

1. Answer the following questions for the home country, then for the foreign country:

(a) It turns out that in autarky equilibrium the wage-rent ratio is 1.333 for
the home country and 2 for the foreign country. Find the capital-labor ratio
used in each industry.

(b) Calculate the number of workers employed and the amount
of capital used in each industry in autarky equilibrium (find L_{c}^{A}
;L_{F}^{A} ;K_{c}^{A} ;K_{F}^{A}
) where ^{A} means under Autarky.

(c) Calculate the autarky production (= consumption) for
each industry (Q_{c}^{A} and Q_{F}^{A}).

(d) Derive the autarky price ratio, (P_{c}/ P_{F})^{A},
and the real value of production in autarky.

(e) Calculate the real wage rate ( w/P_{F}) and the real rate of return
oncapital ( r/P_{F}) in autarky.

(f) Calculate real total factor income. Is it equal to the real value of production that you derived in question 2d?

2. It turns out that in the free-trade equilibrium the wage-rent ratio for both countries is 1.4287. Find the capital-labor ratio used in each industry.

3. Calculate the number of workers employed and the amount of capital used in each industry in free trade for each country.

4. What are the quantities produced of clothing and food in the home and in the foreign country?

5. Calculate the price ratio in free
trade as well as free trade consumption in each country (Find (P_{c}/ P_{F
})^{T }, C_{c}^{T}, C_{F}^{T}, C_{C*}^{T},
C_{F*}^{T}).

6. Determine real GDP in each country.

7. Determine the real interest rate and real wage rate in each country.

8. Calculate real total factor income
for each country.

9. Calculate each country's exports and imports.

10. Calculate the autarky and free trade utility for each country.

11. Has each country benefited from trade?

12. Does the Heckscher-Ohlin theorem hold? Explain briefly

13. Does the Factor-Price Equalization Theorem hold? Explain briefly

14. Does the Stolper-Samuelson Theorem hold? Explain briefly

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