Question

What is the key equation that determines capital per worker in the steady state of the...

What is the key equation that determines capital per worker in the steady state of the Solow model?

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Answer #1

The key equation is given by the fact that at the steady state, there is no change in capital per worker. Here y = f(k) is the per worker production function, d is the rate of depreciation, n is the population growth rate, g is the growth rate of technology, a is the capital share in income, A is the total factor productivity and s is the saving rate. Thus we have investment = saving at steady state

k(d + n + g) = sy

k/y = s/(d + n + g)

k/Ak^a = s/(d + n + g)

k^(1 - a) = sA/(d + n + g)

k* = [sA/(d + n + g)]^(1/1 - a)

Hence the  key equation that determines capital per worker in the steady state of the Solow model is given by k(d + n + g) = sy and results in k* = [sA/(d + n + g)]^(1/1 - a)

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