Consider the following modified Solow Growth model.

Economy wide production function is:

Y = f(L,K),

where Y is output (GDP), K is the stock of capital and L is labor input. Assume that the production function is characterized by constant returns to scale. Both the marginal products of labor and capital are diminishing.

Assume that population (L) is growing over time at the rate n.

The capital-labor ratio evolves over time according to:

(K/L) = I/L - ( + n) K/L

Where (K/L) in the change in the capital-labor ratio, I/L is investment per capita, and is the depreciation rate

Total savings in the economy is given by -> S= sY,

where s is the marginal propensity to save (or the savings rate). In equilibrium, total investment expenditures, I, equals total savings, S.

a) Using a diagram show the steady state level of the capital-labor ratio. What is the growth rate of GDP per capita (Y/L) in the steady state? What is t he growth rate of GDP (Y) in the long-run?

b) Suppose there is a permanent one-time increase in the savings rate (s). Show this effect in the context of the above Solow growth model. What happens to the current level of per capita GDP? What happens to the steady level of per capita GDP? What happens to the growth rate in per capita GDP in the long run? What happens to the growth rate in GDP in the long run?

c) Suppose that the marginal product of capital satisfies the following condition:

lim F(sub)k = A > ( + n)/s

as K/L -> infinity

Show this model in the context of the above Solow growth model. What does this imply about the existence of a steady state? Will growth in per-capita GDP be continual?