8105-11Midterm - MACROECONOMIC THEORY ECON 8105 MIDTERM...

1
MACROECONOMIC THEORY T. J. KEHOE
ECON 8105 FALL 2011
MIDTERM EXAMINATION
Answer two of the following three questions.
1. Consider an economy with two infinitely lived consumers. There is one good in each period.
Consumer i , 1, 2 i  , has the utility function
0
log ti
t
t
c




.
Here , 01  , is the common discount factor. Each of the consumers is endowed with a
sequence of goods:
1111
0123
( , , , ,...) (2,1,2,1,. ..) wwww 
2222
01 23
(,,,, ...) (1,4,1,4,. ..)  .
There is no production or storage.
(a) Describe an Arrow-Debreu market structure for this economy, explaining when markets are
open, who trades with whom, and so on. Define an Arrow-Debreu equilibrium for this economy.
(b) Describe a sequential market structures for this economy, explaining when markets are open,
who trades with whom, and so on. Define a sequential markets equilibrium for this economy.
(c) Carefully state a proposition or propositions that establish the essential equivalence of the
equilibrium concept in part a with that in part b. Be sure to specify the relationships between the
objects in the Arrow-Debreu equilibrium and those in the sequential markets equilibrium.
(d) Calculate the Arrow-Debreu equilibrium for this economy. (This equilibrium is unique, but
you do not have to prove this fact.)