2. Consider an economy consisting of a constant population of infinitely lived individu-

als. The representative individual maximises:

{(1+p)* u(04+3)].

-

with p≥ 0 and u(c₁) = ₁0c², 0 > 0. Assume that is in the range where u'(c)

is positive. The representative individual owns the capital stock k and rents it to

firms for the production of the consumption good.

Ut

=

a. State the problem of this representative individual and find the first-order con-

dition (Euler Equation) associated to this problem. Interpret your result.

Suppose that the technology of the representative firm is linear in capital and is given

by Y₁ = AKt + et with A >0 and there is no depreciation of the capital stock, such

that 8 = 0.

b. State the problem of this representative firm and find the first-order condition

associated with this problem. Interpret your result.

c. State the market clearing conditions and the system of equations describing the

equilibrium dynamics of this economy.

d. Assume that A = p. Guess that consumption takes the form of ct = a+nkt+yet.

Given this guess find the equilibrium function of K++1 as a function of K and

et.

e. What values must the parameters a, 7 and y be for the first-order condition of

the individual be satisfied for all values of K, and e?

f. Suppose that et = pet-1+€, with o € (0, 1). What are the effects of a one-time

shock to € on the paths of Y, K and c?