ECON 302: Problem Set #2
Lecturer: Santiago Acosta Ormaechea, Social Science 6460
Due on Wednesday, October 22, 2008 (4pm CDT).
You may work in groups of 2,3 or 4 students. You must submit you work individually. You must
also indicate the name/s of your collaborators.
1. Unemployment
Recall that the natural or steady-state rate of unemployment is de๎ned as (U
L)n=s
s+f.
Assume that the law of motion for unemployment is given by ๎U=sE ๎fU: Also assume
that Lis constant over time.
(a) Express the change in the unemployment rate as a function of s; f; and U=L:
(b) Show that if the unemployment rate is above the natural rate, the unemployment rate
falls and that if the unemployment rate is below the natural rate the opposite happens.
What determines the speed of adjustment to the natural rate?
2. Basic Solow Model
Consider an economy described by the following production function:
Y=F(K; L) = K1=3L2=3
(a) What is the per-worker production function f(k)? Assuming no population growth or tech-
nological progress, ๎nd the steady state capital stock, output, and consumption (all in per-
worker terms), as functions of the saving rate sand the depreciation rate ๎:
(b) Find the golden-rule saving rate, sGR:
3. Fiscal Policy in the Solow Model
The model is as follows:
Y=AK๎L1๎๎(Technology)
๎K=I๎๎K (Ktal law of motion)
S(= I) = sY (Saving rule)
๎L
L=n(Labor growth rate)
Assume that the government imposes an investment tax. In such a case investment becomes
I=s(1 ๎๎)Y: Assume also that government consumption is equal to its tax revenue ๎Y .
(a) Calculate the steady-state capital per-worker without taxes (k๎) and with taxes (k๎๎). Plot
investment and depreciation as functions of kboth without and with taxes.
(b) Calculate the golden-rule steady-state capital per worker without (k๎
GR) and with taxes (k๎๎
GR).
(c) The government decides now to use all tax revenues (๎Y ) for investment instead of consump-
tion. That is, I=s(1 ๎๎)Y+๎Y: Obtain the steady-state capital per worker (k๎๎
i). What is
the value of ๎that the government must impose to have k๎๎
i=k๎
GR.
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