Consider a production function
Yt = F(Kt,Lt) = ¯AKα
t L1−α
t
(1)
and the resource constraint
Yt = Ct + It + Gt
and the capital accumulation equation
Kt+1 = It + (1 − ¯d)Kt
Consumers consume a certain fraction of the output so the consumption equation is
Ct = (1 − ¯s)Yt
The government spending Gt is a fraction of capital stock, so with the higher capital stock, there
is more government spending.
Gt = ¯gKt
Assume there is no population growth, so Lt = Lt+1 = ¯L
a. Derive a Solow-Growth model and describe the intuition of the equation.
b. What is the key assumption in this model
c. Find the steady state per-worker quantities of capital, output, and consumption
d. Draw the Solow model (the x-axis is Capital stock, the y-axis is output)
e. Suppose there was a big government spending. Therefore, ¯g increased. What is the new steady state per-worker quantities of capital, output, and consumption?
