Question

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

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)