Mathematics for Economists

Cake eating problem

It is easy to see that

c 1 =

w 1

1 +β+.. .+βT^1

,

c 2 = βw^1

1 +β+.. .+βT^1

,

..

.

cT = β

T (^1) w 1
1 +β+.. .+βT^1
is a stationary point. As the problem is convex, it is the optimal solution.