If the per-worker production function is given by y = k^1/2, the saving ratio is 0.2, and the depreciation rate is 0.1, then the steady-state ratio of output per worker (y) is:

Question

Quizplus · Accepted Answer

To find the steady-state ratio of output per worker (y), we set the change in capital per worker (k') and the change in output per worker (y') to zero and solve for y:

k' = sy - (n+δ)k = 0      (where s is the saving rate, n is the population growth rate (assumed to be zero in this case), and δ is the depreciation rate)
y' = f(k', L)/L - δ = 0

Substituting the given production function, we have:

y' = (kS^1u^1P^1/2)/(S+P^0.5k) - δ = 0

Solving for k, we get:

k = [(S/δ)P^-0.5u^-1y]^2

Substituting this into the production function, we get:

y = (S/δ)y^2P^-1u^-1

Rearranging, we get:

y = (δS/Pu)^0.5

Substituting the given values, we get:

y = (0.1*0.2/1)^0.5 = 0.1

Therefore, the steady-state ratio of output per worker (y) is 2.

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