In a production model where the production function is $Y = \bar{A}K^{1/3}L^{2/3}$ the equilibrium wage rate is equal to 2, labor supply is 27 workers and the productivity parameter is equal to 3.
What is the equilibrium level of capital? (Hint: Use the fact that the wage rate equals the marginal product of labor and, in addition, that the marginal product of labor is proportional to $\frac{Y}{L}$, the average product of labor.)