Question

In the Solow​ model, suppose the per worker production function is y = 3 k^0.5. Suppose s ​=0.11​,n ​=0.03​,and d​ =0.10.

Calculate the​ steady-state equilibrium​ capital-labor ratio.

k​ = ​(Round to two decimal places​.)

Answer 1

Given:

y = 3k^0.5

n = 0.03

s = 0.11

d = 0.10

At the steady-state level, the breakeven investment is equal to the investment.

That is,

Investment is the savings rate times the income = sy

And breakeven investment = (n+d)k

where s = saving rate

y = income per labor

k = capital per labor or capital labor ratio, or k = K/L

n = population growth rate

d = depreciation rate

Steady-state level

Therefore putting values into the formula, we get the capital-labor ratio or the capital per labor.

Since,

therefore, putting y = 3k^0.5

Solving,

k = 6.44

Therefore the steady state-level equilibrium capital-labor ratio is 6.44