Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
Assume that the depreciation rate is 5 percent per 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. Round your answers to two decimal places. (You might find it easiest to use a computer spreadsheet then transfer your answers to this table.)
|Steady State Values for Various Saving Rates|
What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
A saving rate of percent maximizes output per worker. A saving rate of percent maximizes consumption per worker.
Y = K0.3L0.7
Output per worker (y) = Y / L = (K/L)0.3 = k0.3 where k = K/L
When s: Savings rate, in steady state,
s / = k / y
s / = k / k0.3
s / = k0.7
Capital per worker (k*) = [s / ](1/0.7) = [s / ]1.43
Output per worker (y*) = k0.3 = [s / ](0.3/0.7) = [s / ]0.43
Consmption per worker (c*) = yY - sy* = y* x (1 - s) = [s / ]0.43 x (1 - s)
When = 0.05,
k* = (s / 0.05)1.43
y* = (s / 0.05)0.43
c* = (s / 0.05)0.43 x (1 - s)
A savings rate of 100% maximizes output per worker.
A savings rate of 30% maximizes consumption per worker.
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