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Consider an economy that lasts for T = ∞ periods

#### Consider an economy that lasts for T = ∞ periods

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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.