If y = k^1/2, the country saves 10 percent of its output each year, and the steady-state level of capital per worker is 4, then the steady-state levels of output per worker and consumption per worker are:

Question

Quizplus · Accepted Answer

We can use the steady-state equation to find the steady-state levels of output per worker and consumption per worker:

y = kS1U1P11/2S1S1P0

In the steady state, output per worker (y) is equal to consumption per worker (c), so we can write:

c = kS1U1P11/2S1S1P0

We are given that the country saves 10 percent of its output each year, so the investment per worker (i) is:

i = 0.1y

We can use the production function to write:

y = f(k)

where f(k) = kS1U1P11/2S1S1P0 is the production function. In the steady state, output per worker does not change, so we have:

f(k) = 0.1f(k) + c

Solving for c, we get:

c = 0.9f(k)

We know that the steady-state level of capital per worker (k*) is 4, so we can use the production function to find the steady-state level of output per worker:

y* = f(k*) = k*S1U1P11/2*S1S1P0 = 4*S1U1P11/2*S1S1P0

Substituting this into the expression for consumption per worker, we get:

c* = 0.9*y* = 0.9*4*S1U1P11/2*S1S1P0 = 3.6*S1U1P11/2*S1S1P0

Finally, we can use the definition of the Solow residual (U1) to rewrite the expression for consumption per worker:

c* = 3.6*S1U1P11/2*S1S1P0 = 3.6*S11/2*U1P11/2*S1S1P0 = 3.2

Therefore, the steady-state levels of output per worker and consumption per worker are 4 and 3.2, respectively, and the best choice is C) 4 and 3.2, respectively.

If Y = K1/2, the Country Saves 10 Percent of Its

If Y = K^1/2, the Country Saves 10 Percent of Its