The use of formal education in Denmark 1980-1992

12 Vanek’s chain rule

(11) and (12) are called Vanek’s chain rule. As it rest on Heckscher-Ohlin (7) they together
constitutes the Heckscher-Ohlin-Vanek or HOV model. Even though there are no information
about all factors of production in Denmark the models makes it possible to analyse the
relationship between different types of education and total labour input.

No factor price equalisation

In cases with no factor price equalisation trade patterns will still reveal important information
about production factors and factor remuneration in Denmark. This is shown by Leamer 1984.

Let Denmark’s export of j different goods to a country (say Germany) be X_j^dg .The factor
content of this export depends on production technology in Denmark P_d . The factor content
of Denmark’s export to Germany thus is: P_dX_j^dg . Let the international determinated price of
tradeable goods be γj. and factor remuneration in Denmark w_dand we have the value of
Denmark’s export to Germany:

χ.X^dg ' wPX^dg                          13

Jj J          d d J

The same goods could also be produced in Germany with German technology and German
factor remuneration. In the extreme case factor prices are equalized and equilibrium on the
productions function will be the same. However if factor prices are not equalized then
production in Germany would cost:

w P X ^dg # wP X ^dg
ggJ   gdJ

since the Germans will use production technologyP_g if and only if it is not more expensive
than the Danish technologyP_d. A similar argument goes for the ability of Danish export to

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