Lets assume that equation (1) depicts the aggregate production function underlying the basic Solow

growth model in a closed economy in absence of an active government sector.

Yt=BKtLt1- ..(1), where Yt = real GDP of the economy in current year, B = state of

technology, Kt = amount of real capital goods in current year, and Lt = labor hours available in

current year.

a) Derive expressions for marginal products of labor and capital from the given production function.

Assume that wt = real wage rate per hour and rt = real rental rate or real price of capital. Now

derive an expression, which shows firms earn only normal profit given the perfectly competitive

product and resource markets (labor and capital).

b) Write down an equation for capital accumulation assuming that Kt = amount of real capital goods

in current year, Kt+1 = amount of real capital goods next year, It = gross investment in current

year, = depreciation cost of capital goods per year, St= gross savings in current year, and s =

savings rate per year. Derive the transition equation from this equation by utilizing the labor

growth equation and per capita production function.

c) Derive the Solow equation from capital accumulation equation by subtracting capital-labor ratio

in current year from both sides of this equation.

d) Derive an expression for the steady state condition from Solow equation using the information

that the economy comes to a standstill in long run when capital-labor ratio ceases to grow from the

current to the next year. Give an interpretation of the steady state condition.