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Derive the per-capita-worker production function

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1.) Consider an economy described by the following Cobb-Douglas, constant returns to scale, aggregate production function: Y (K, L) = ^.4 ^.6:

i.) Derive the per-capita/worker production function

ii.) Assume the depreciation rate is 2 percent, the population growth is 5 percent, and the savings rate is 8 percent; derive the discrete fundamental Solow Growth equation, and finally find the steady-state capital stock per-capita/worker and output per-capita/worker.

iii.) Assume the savings rate rises to 12 percent, all else equal, recalculate steady-state per-capita/worker stock and output per-capita/worker. Then explain the positive implications of an increase in the savings rate on the economy in the long-run.

Reference no: EM132655659

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