3 An economy described by the Solow growth model has the fol

3. An economy described by the Solow growth model has the following production function: a. Solve for the steady-state value of y as a function of s, n, g, and ?. b. A developed country has a saving rate of 28 percent and a population growth rate of 1 percent per year. A less-developed country has a saving rate of 10 percent and a population growth rate of 4 percent per year. In both countries, g-0.02 and 60.04. Find the steady-state value of y for each country. c. What policies might the less-developed country pursue to raise its level of income?

Solution

Y = (K)^1/2, This can be converted to a per capita equation by dividing both sides by L

y = k^1/2

Since per capita capital directly affects per capita output, the key factor behind economic growth is capital accumulation.

The capital accumulation equation for the economy looks like:

dk = sy - ( [\\delta] +n+g)k, i.e. change in capital stock is determined by aggregate savings less capital stock depreciation, labor growth and technical growth

Now dividing both sides by k

dk/k = sy/k - ( [\\delta] +n+g)

Or.  dk/k = s/(k)^1/2 - ( [\\delta] +n+g)

A steady state will be where dk = 0

s/(k)^1/2  = [\\delta] +n+g

Thus, k* = [s/( [\\delta] +n+g)]^2 i.e. the steady state level of capital

Thus steady state level of output, y* = s/( [\\delta] +n+g)

b. For the developed country, y* = 28/(4+1+2) = 28/7 = $4 per capita income

For developing country, y* = 10/(4+4+2)= 10/10 = $1 per capita income

c. A less developed country must- (i) Ramp up its savings rate (ii) Curb its population growth rate