UCLA
ECONOMICS 102
E. McDEVITT
SQ set #3:
SOLOW GROWTH MODEL
1. What is a steady state? What is investment in a steady state? What is the intuition behind
this equation?
Assume the following initial values:
K
t
= 500 ,
L
t
=100,
δ
= 8%, and n = 2%. The
capitaltoworker ratio is k = 500/100 = 5. What would happen to the capitaltolabor
ratio if actual investment was 20? How much investment is required to maintain the
capitaltolabor ratio at 5? Verify by calculating the levels of K & L and the ratio k.
2. Convert the following production function into the perworker production function: Y =
AK
0.1
L
0.9
. Find k
gold
. Show steps. Assume that the population growth rate is 5%, the
depreciation rate is 5%, and that A = 100. Show outcome on
a graph.
3. True or false? The higher the steadystate capitallabor ratio (k) is, the more consumption
each worker can enjoy in the long run. Explain.
4. What equation do we use to determine the steady state level of k? How do you interpret
each side of the equation? Explain why k increases when its initial level is below the steady
state level. ...when its initial level is above the steady state level. Write out the equation that
gives us the
change
in k. Show these cases on graphs. Label each curve. Suppose an
economy initially in a steadystate experiences an event (such as a war) that moves k below
the steadystate level. What is the impact of this event on y? What is the impact on MPK
(relate this to the graph)?...impact on MPL?
5. a. Using the information from question (2) find the steady state level of k when the
savings rate is 5%. Show all steps.
b. What is output per worker and consumption per worker in this steady state?
c. What savings rate is required to bring about k
gold
?
6. Using the shortcut formula, indicate how a change in A, s, or n affects the steadystate
value of k in the Solow growth model. Shows these results on graphs and also show the
impact on steady state y and c.
7. Assume
s = 10%,
δ
= 3%, n = 2%, Y
t
= A*K
t
1/3
L
t
2/3
and A is constant at 1.
a. Find k
steadysstate
, y
steadystate
and c
steadystate
using the “short cut” formulas.
b. Suppose the initial value of k was k
0
= 9. What is required investment per worker at this
initial value? In what sense, do we mean “required investment”? What is actual investment
per worker at this initial value? What is k in the next period?
8. Suppose the current savings rate is below the savings rate that brings about
k
gold
. Does it
follow that policies designed to increase the savings rate are desirable? Explain.
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 Spring '09
 EDWARDMCDEVITT
 Economics, Steady State, MPK

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