Mathematics for Economists

Production saving model

Example

Solve the production saving model withU(c)=lnc,f(k)=kα.

Asf should be concave henceα 1 .Of courseβ 1 .The Euler equation

is

1

ct

=β^1

ct+ 1

f^0 (kt+ 1 )=βα

ktα+ 11

ct+ 1

Multiplying bykt+ 1

kt+ 1

ct

=βα

ktα+ 1

ct+ 1

=βαf(kt+^1 )

ct+ 1

.