Consider a basic Solow–Swan model with constant labour force L and constant total factor productivity A. Suppose the saving rate is 𝑠=0.4 and the depreciation rate is 𝛿=0.1 . Suppose also that steady-state output per worker is 100. Steady state capital per worker is?
Question
Consider a basic Solow–Swan model with constant labour force L and constant total factor productivity A. Suppose the saving rate is 𝑠=0.4 and the depreciation rate is 𝛿=0.1 . Suppose also that steady-state output per worker is 100. Steady state capital per worker is?
Solution
In the Solow-Swan model, the steady-state condition is when investment equals depreciation. In per worker terms, this is written as:
s * Y/L = δ * K/L
where: s = saving rate Y/L = output per worker δ = depreciation rate K/L = capital per worker
We are given that s = 0.4, Y/L = 100, and δ = 0.1. We are asked to find K/L.
Substituting the given values into the equation, we get:
0.4 * 100 = 0.1 * K/L
Solving for K/L, we get:
K/L = (0.4 * 100) / 0.1 = 400
So, the steady-state capital per worker is 400.
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