Mathematics for Economists

Cake eating problem

Example

Solve the cake eating problem for theu(x)$lnxfunction.

IfT=2 then the Euler equation is

1

c 1

=β^1

c 2

.

By the constraint

c 1 +c 2 =w 1.

Solving the equation

c 1 =

1

1 +βw^1 ,c^2 =

β

1 +βw^1.