Question

1. For the following, assuming that there is no population growth or technological progress.

a) What is the equation that defines the steady-state level of capital per worker?

b) How would you determine the steady state level or output per worker (i.e., real GDP per capita) from (a).

c) Explain, in words, how an economy that starts with too much capita per worker gets to its steady state.

2.Suppose the following represents the economy:

Y = F(K,L)=√ KL

s = 0.3

δ = 0.1

k0 = 4
a) Write out the per-worker production function.

b) Illustrate the per-worker production function, the investment function, and the depreciation function on the appropriately labeled graph.

c) Fill in the following table for years (1) to (4). See the note below about the economic growth rate g_y.

Year

k

y

gy

i

δk

∆k

1

4.0

N/A

2

3

4

…

SS

N/A

SS + 1

SS + 2

Note: Economic growth is

gY = Yt − Yt−1 / Yt−1

Since, in this model there is no population change, this is the same as

gY = (Yt /L − Yt−1/L) / (Yt−1/L)

= yt − yt−1/ yt−1 = gy

d) What do you notice happens to economic growth, gy, as k becomes larger? Why does this happen?

e) Suppose that the steady-state occurs in year “SS” above. Calculate the steady-state level of capital per worker, and fill in the remaining rows, (SS) to (SS+2).

f) What do you notice happens to economic growth, gy, once steady state is reached (and beyond the steady state)? Why does this happen?