5 . Consider an economy described by the production function: Y = F(K; L) = K^.32^.68 : a) What is the per-worker production function? b) Find the steady-state capital stock per worker, and consumption per worker as a function of the saving rate and the depreciation rate. (In other words, instead of using numbers for s and , you just keep them as part of the expression.) c) Assume that the depreciation rate is 7.5 percent a year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent and so on until 100 percent. (You will need a calculator with an exponent key for this, you can also use Excel.) Which saving rate maximizes output per worker? Which saving rate maximizes consumption per worker?
5 . Consider an economy described by the production function: Y = F(K; L) = K^.32^.68 : a) What is the per-worker production function? b) Find the steady-state capital stock per worker, and consumption per worker as a function of the saving rate and the depreciation rate. (In other words, instead of using numbers for s and , you just keep them as part of the expression.) c) Assume that the depreciation rate is 7.5 percent a year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent and so on until 100 percent. (You will need a calculator with an exponent key for this, you can also use Excel.) Which saving rate maximizes output per worker? Which saving rate maximizes consumption per worker?
