Problem Set 1: OLG Models
Econ720. Fall 2009. Prof. Lutz Hendricks
1 An Economy with Land
Consider a twoperiod OLG model in which production requires land and labor. Agents hold land as their
M
units per young household.
The cohort size is constant and normalized to one. Each household supplies one unit of labor when young.
(a)
Write down the household±s budget constraints. Note that the household sells his land holdings
at price
q
t
+1
when old. Denote the purchase price of land by
q
t
and its rental price by
r
t
+1
.
(b)
Derive the household±s FOCs and Euler equation. Utility is
u
(
c
y
t
) +
(
c
o
t
+1
)
(c)
has constant returns in land and labor:
F
(
M;L
)
(d)
(e)
Derive an implicit solution for
q
in steady state.
2 OLG Model with Assets
Consider a twoperiod OLG model. There are two types of households, indexed by
h
. In each period,
a mass of 0.5 households is born of each type. Households receive endowments
(
e
y
;e
o
)
when young and
old, respectively. Households issue or purchase one period bonds when young. Preferences are given by
ln
c
y
h;t
±
+
h
ln
c
o
h;t
+1
±
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 '09
 LUTZHENDRICKS
 Supply And Demand, #, Economic equilibrium, Market clearing, Prof. Lutz Hendricks

Click to edit the document details