5) Solow Model Growing Population problem: A country's production function is Y =
K<sup>1/2</sup>L<sup>1/2</sup>, capital depreciates at the rate of 6% (? = 0.06) each year, the population grows at
the rate of 2% (n = 0.02) each year, and the savings rate is 36% (? = 0.36). Solve for the
steady-state values of capital per worker (k), output per worker (y), and consumption per
worker (c):
k* = 20.25
y* = 4.5
c* = 2.88
If this economy has achieved its steady-state equilibrium with a labor force (L) of 80
workers in year 1, how much is the aggregate capital stock (K) and aggregate output (Y) in
year 1? Calculate the labor force, aggregate capital stock, and aggregate output in year 2.
K = kL ? 20.25(80) = 1620
Y = yL = 4.5(80) = 360
Year 1: L = 80
K = 1620
Y = 360
L = 80 + nL = 80 + 0.02(80)
= 80 + 1.6 = 81.6
Year 2: L = 81.6
K = 1652.4
Y = 367.2
K = kL = 20.25(81.6)
y = yL ? 4.5(81.6) = 367.2
