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Consider an economy described by the production function: Y = F (K, L ) = K^(2/3)L^(1/3).
a) Find the per worker production function.
b) Find the steady-state capital stock per worker as a function of the savings, population growth, rate of technological change and depreciation rate.
c) Now assume the depreciation rate is 3% a year, population growth is 2% and technological change is 2% and the savings rate is 28%. Find the steady-state level of capital per worker and the corresponding levels of output per worker.
d) Now using the Marginal Product of Capital (per worker) find the level of capital that maximizes consumption per worker in the steady state. Depreciation is still 3% (.03), population growth is still 2% (.02) and technological change is still 2% (.02) e) What savings rate is necessary for the economy to reach this consumption maximizing steady state? (Hint use the answer from the first part of question
e) How does this compare to the current savings rate (28%)?
f) How much is steady state per capita GDP growth?