Consider the canonical OLG model with log preferences,

for each individual. Suppose that there is population growth at the rate n. Individuals work only when they are young and supply one unit of labor inelastically. Production technology is given by

where A(t + 1) = (1+ g) A(t), with A (0) > 0 and g > 0.

(a) Define a competitive equilibrium and the steady-state equilibrium.

(b) Characterize the steady-state equilibrium, and show that it is globally stable.

(c) What is the effect of an increase in g on the equilibrium?

(d) What is the effect of an increase in β on the equilibrium? Provide an intuition for this result.