An economy has a per worker production function y=k^1/4, a marginal propensity to save of 24%, a population growth rate of 4%, and capital depreciates at a rate of 2% each period. what is the steady state capital/worker ratio?
y = k1/4
In steady state,
s / (d + n) = k / y, where s: Marginal propensity to save, d: Depreciation rate and n: Population growth rate
0.24 / (0.02 + 0.04) = k / (k1/4)
0.24 / 0.06 = k3/4
k3/4 = 4
Taking (4/3)rd root on each side,
k = 6.35
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