Question

Economic Growth II-End of Chapter Problem Suppose an economy described by the Solow model has the following production function: Y-K (LE a. For this economy, what is f(k)? f(k) b. Use your answer in part a to solve for the steady-state value of y as a function of s, n, g, and 6. y Suppose two neighboring economies have the above production function, but they have different parameter values. Atlantis has a saving rate of 28% per year and a population growth rate of 1% per year. Xanadu has a saving rate of 10% per year and a population growth rate of 4% per year. In both countries. g = for each country 0.02 and 5-0.04. Solve for the steady-state value of y C. y Alanis

Answer 1

(a)

f(k) = (Y/LE) = (K/LE)^1/2 = k^1/2 where k = K/LE

(b)

In steady state,

k / y = s / ($\dpi{80} \delta$ + n + g)

k / (k^1/2) = s / ($\dpi{80} \delta$ + n + g)

k^1/2 = s / ($\dpi{80} \delta$ + n + g)

y* = s / ($\dpi{80} \delta$ + n + g) [since y* = f(k) = k^1/2]

(c)

y*_atlantis = 0.28 / (0.04 + 0.01 + 0.02) = 0.28 / 0.07 = 4

(d)

y*_xanadu = 0.10 / (0.04 + 0.04 + 0.02) = 0.10 / 0.10 = 1