Mathematics for Economists

Cake eating problem

Observe that the partial derivative is by the parameter of the goal function

so with

g(p,x) = βT^2 u(x)+βT^1 u(px)

∂g

∂p(p,x(p)) = β

T (^1) u (^0) (px(p))
that is
dVT 1 (w)
dw (w)=β
T (^1) u (^0) (wc(w)).
Which gives the Euler equation.