Question

2. Suppose an economy described by the Solow model has the following production function and capital law of motion, with the variables as defined in class:

Y =K^(1/2)(LE)^(1/2)

∆k = sy − (δ + n + g)k
The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, a population

growth rate of 2 percent, and a growth rate of labor productivity of 1 percent.

(a) At what rate do total output (Y ), output per worker ( Y/L ) and output per effective worker

(y = Y/LE ) grow in steady state?

Answer 1

Y = K^1/2(LE)^1/2

s = 24% = 0.24

d = 3% = 0.03

n = 2% = 0.02

g = 1% = 0.01

(a) Growth rate of Y in steady state is equal to the growth rate of population and labor productivity = (n+g) = (2+1)% = 3%.

Growth rate of Y/L in steady state is equal to growth rate of labor productivity = g = 1%

Growth rate of Y/LE in steady state is equal to 0.