The Ohio State University
Department of Economics
Econ 808–Problem Set #1
Due Thursday, April 11
Spring 2002
Levin and Peck
(1) In the following economy, there are two consumers, two …rms, and two
goods (labor/leisure and food). For i = 1,2, consumer i is endowed with zero
units of food and 1 unit of leisure,
!
i
=(0
;
1)
.L
e
t
t
i
n
g
x
i
denote consumer
i’s consumption of food and
`
i
denote consumer i’s consumption of leisure, the
utility function is:
log(
x
i
) + log(
`
i
)
.
Let
y
1
denote …rm 1’s output of food and
L
1
denote …rm 1’s labor input (so
that
L
1
must be nonnegative). Then …rm 1’s production function, the frontier
of its production set, is given by:
y
1
=
AL
1
, where the parameter A is a positive
real number. Firm 1 is owned by consumer 1.
Let
y
2
denote …rm 2’s output of food and
L
2
denote …rm 2’s labor input (so
that
L
2
must be nonnegative). Then …rm 2’s production function, the frontier
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 Spring '02
 PECK
 Economics, Utility, competitive equilibrium, following economy, Economics Econ 808Problem

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