InÖnite cake eating problem
If
α =
1 β^1 /σ
σ
λ = 1 β^1 /σ
then
1 β^1 /σ
σ
=
1 β^1 /σ
( 1 σ)
+β
1 β^1 /σ
σ
β(^1 σ)/σ=
=
1 β^1 /σ
( 1 σ)
+
1 β^1 /σ
σ
β^1 /σ=
=
1 β^1 /σ
σ
1 β^1 /σ+β^1 /σ
hence(α,λ)solves the equation.
If
α =
1 β^1 /σ
σ
λ = 1 β^1 /σ
then
1 β^1 /σ
σ
=
1 β^1 /σ
( 1 σ)
+β
1 β^1 /σ
σ
β(^1 σ)/σ=
=
1 β^1 /σ
( 1 σ)
+
1 β^1 /σ
σ
β^1 /σ=
=
1 β^1 /σ
σ
1 β^1 /σ+β^1 /σ
hence(α,λ)solves the equation.