Question

Assume that f(k) = Ak^α , and that the saving rate is s. Solve for the steady state level of capital, and for the golden rule level of capital. What is the condition on s that would imply that they are the same?

Answer 1

Savings rate = s

At the steady state, investment is just enough to cover depreciation i.e. capital per worker will remain constant, ∆k = 0

To find the golden rule level of capital, planner wants to maximize consumption

At the steady state, capital is k* and

To maximize consumption and find golden rule level of capital

Condition on s so that

Hence needs to be satisfied for .