Consider an economy that lasts for T = ∞ periods

Consider an economy that lasts for T = ∞ periods. The parameters of the
economy are gA = 0.02, gL = 0, s = 0.12, δ = 0.1, α = 0.5. Also, A1 = L1 = 1.
When we refer to steady-states, we always refer to positive ones. That is, we
never look at the uninteresting steady-state in which ?k∗= 0.

1) Compute the steady-state value of capital per unit of effective labor, ?k∗,
where capital per unit of effective labor at any time t is ?kt = Kt
AtLt. You
do not need to derive the formula for it, but it could be good practice to
do so.

2) Show that if ?kt > ?k∗, then ?kt+1 < ?kt, and vice versa that if ?kt < ?k∗, then ?kt+1 > ?kt. How do we call this property? To answer this question only,
do not replace the model parameters with the values provided above. You
can choose whether to answer with question analytically (that is, using
formulas) or graphically.

3) Assume the economy in period t = 2 is at the steady-state (the same
steady state you computed in question 1.). Compute the value of capital,
K2. Then, assume that in period t = 2 the growth rate of technology gA
increases to 0.04. Keep in mind that when the change happens, K2 has
been already determined from savings in period t = 1. Compute ?k3 and
K3. How are they different from ?k2 and K2? Provide intuition.