Appendix: Properties of Linear
Letf(k,e) be a linear homogeneous function, i.e.
f(βk,βe) = βf(k,e). (2.A1)
This function satisfies the Euler equation (subscripts denoting partial derivatives):
fk(k,e)k + fe(k,e)e = f(k,e). (2.A2)
Differentiation with respect to k and e yields
fkkk + fkee = 0. (2.A3)
fkek + feee = 0, (2.A4)
where the arguments have been dropped for convenience. Combining these two equations gives:
fkkfee - fke2 = 0. (2.A5)
Combining equations (2.A2),(2.A3), and (2.A4) yields. (2.A6) (2.A7)
Questia, a part of Gale, Cengage Learning. www.questia.com
Book title: International Trade, Factor Movements, and the Environment.
Contributors: Michael Rauscher - Author.
Publisher: Clarendon Press.
Place of publication: Oxford.
Publication year: 1997.
Page number: 38.
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