Question

Find steady-state output per worker: plug the expression for steady state capital into the production function and simplify

EQUATIONS

steady state capital per worker: kt = (sA/δ + n)^1/1-α

0 = sAkt^α - (δ + n)kt (at steady state)

production function: Yt= AKt^αNt^(1−α)

Answer #1

Your answer:- Y_{t}/K_{t}
=AK_{t}^-(1-α).N^1-α simply dividing the production
function by K_{t}.

Now as everything is function of t so I write K instead of
K_{t,}Also N instead of N_{t.} and Y instead of
Yt.

so the equation becomes Y/K =A(K/N)^-(1-α)

THEREFORE, (Y/N)/(K/N) =A(K/N)^-(1-α)

Y/N =A(K/N)^α

Now substitute for steady state capital per worker: kt = (sA/δ +
n)^1/1-α where kt=(K/N) or (K_{t}/N_{t})

THEREFORE, Y/N =steady-state output per worker = A(sA/δ + n)α^/1-α

Hence the result.

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