Mathematics for Economists

Calculus of variations

Again introduceu=y^0 .(It is always working whenyis missing.) Then

0 = u+xu^0.

^1

x

dx =^1

u

du

lnjxj = lnjuj+c

c

x

= u=y^0

y = c 1 lnx+c 2

Using the initial conditions the extremal solution isy=lnx.