Find out an economy described by the production function: Y = F (K, L ) = K2/3L1/3.
1. Identify per worker production function.
2. assuming no population growth or technological change, estimate the steady-state capital stock per worker as a function of the savings and depreciation rate.
3. Find out the steady-state level of capital per worker and the corresponding levels of output per worker. Now assume the depreciation rate is 6% a year and the savings rate is 24%.
4. Now using the Marginal Product of Capital, calculate the level of capital that maximizes consumption per worker in the steady state. Depreciation is still 6%.
5. Explain what savings rate is necessary for the economy to reach this consumption maximizing steady state and how does this compare to the current savings rate (24%)?