If the per-worker production function is given by y = k1/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady-state ratio of output per worker (y) is:

Question

Quizplus · Accepted Answer

In the steady state, output per worker (y) remains constant over time. Thus, we have:

investment per worker = depreciation per worker
s*y = δ*y
0.3*y = 0.1*y
y = k^(1/2)

At the steady state, capital per worker (k) is also constant over time. To find the steady-state value of k, we use the fact that in the steady state, the marginal product of capital (MPK) equals the depreciation rate (δ):

MPK = ∂(y)/∂(k) = 1/(2*k^(1/2))
δ = 0.1

Setting these equal to each other, we have:

1/(2*k^(1/2)) = 0.1
k = 25

Finally, we can use the steady-state value of k to find the steady-state value of y:

y = k^(1/2) = 5^(1/2) * 3^(1/2) = 3.87

So the steady-state ratio of output per worker (y) is approximately 3.87, which is closest to answer choice C) 3.

If the Per-Worker Production Function Is Given by Y =