Assume that an economy described by the Solow model has the production functionY=K^1/3(LE)^2/3, where all the variables are defined as in class. The saving rate is 36%, the capital depreciation rate is 1%, the population growth rate is 1%, and the rate of change in efficiency (E) is 2%.

1. Derive the per-effective worker production functiony=f(k). All derivations are required.
2. Write down the equation that represents the dynamics of lower-case k.
3. Suppose in the current year, capital per effective worker k is 1. Calculate what the level of k is in the next year.
4. Solve for the steady state levels of k*, y*, and c*
5. Does this economy always converge to the steady state? Why or why not?