Find the per worker production function

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Reference no: EM131103614

Consider an economy described by the production function: Y = F (K, L ) = K1/2L1/2.

a) Find the per worker production function.

b) Find the steady-state capital stock per worker as a function of the savings (s) and depreciation rate (δ). (Hint: your answer will be in the form k*=f(s, δ))

c) Now assume the depreciation rate is 4% (.04) a year and the savings rate is 24% (.24). Find the steady-state level of capital per worker and the corresponding levels of output per worker and consumption per worker.

d) Now using the Marginal Product of Capital (per worker) and δ find the level of capital that maximizes consumption per worker in the steady state. (Assume depreciation is still 4%).

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 b).

How does this compare to the current savings rate (24%)?

Reference no: EM131103614

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