Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Practice Problem Set 6 Suggested Solutions
Professor Sanjay Chugh
Spring 2011
1.
Lags in Labor Hiring.
Rather than supposing that the representative firm at the
beginning of period t can decide how much labor it would like to hire for use in
period t, suppose that labor used in period t must be chosen in period t1.
(That is,
suppose n is a stock (aka state) variable.) As usual, capital for use in production in
period t must be purchased in period t1 because of the “time to build” surrounding
capital goods.
With this lag in labor hiring, construct the lifetime (in the twoperiod
model) profit function of the firm, and show that the real interest rate now is a
relevant price for labor as well as capital goods.
Provide brief economic intuition.
(
Hint:
Make as close an analogy with our model of firm ownership of capital as you
can – in particular, think of workers in this model as being “owned” (contractually
obligated to) firms.)
Solution:
With employees being contractually bound to (“owned by”) firms, the periodt nominal
profits of a firm are given by
1
1
(
,
)
t
t
t
t
t
t
t
t
t
t
t
t
t
t
PR
P f k n
Pk
Pw n
Pk
Pw n
±
±
±
±
²
²
,
in which labor used in production in period t,
t
n
, is chosen in period t1 (and thus labor
used in production in period t+1,
1
t
n
±
, is chosen in period t.
In analogy with our model
with only capital predetermined, the employees of a firm are a valuable “asset,” with
total market value
t
t
t
Pw n
 notice that this term enters
positively
in period t profits,
rather than negatively with nonpredetermined labor.
What enters negatively in period t
profits here is the “purchase” of period t+1 labor, namely the term
1
t
t
t
Pw n
±
²
.
In the two
period model, discounted nominal profits of the firm are therefore
2
2
2
2
2
2
2
2
2
3
2
2
3
1
1
1
1
1
1
1
1
1
2
1
1
2
(
,
)
(
,
)
1
1
1
1
1
i
i
i
i
i
P f k
n
P k
P w n
P k
P w n
PR
P f k
n
Pk
Pw n
Pk
Pw n
i
i
i
i
i
±
±
²
²
±
±
±
²
²
±
±
±
±
±
The usual zeroterminalassets condition in this case means that
3
0
k
and
3
0
n
(the
latter, again, because labor should be thought of as an “asset” here).
Focusing attention
on the choice of
2
n
(since
1
n
was chosen in period t1), the firstorder condition of the
lifetime profit function with respect to
2
n
is
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2
2
2
2
2
2
1
1
1
1
(
,
)
0
1
1
n
P f
k
n
P w
Pw
i
i
²
±
±
±
±
.
This expression can be rearranged to yield (using the exact Fisher equation)
1
1
2
2
2
(1
)
(
,
)
n
r w
f
k
n
w
±
±
.
If the real wage were equal to one in each period, this condition would reduce to
1
2
2
(
,
)
n
r
f
k
n
, which would be almost identical to the condition we derived in class
regarding capital demand (except of course in that case
k
f
is the relevant marginal
product rather than
n
f
).
The expression
1
2
2
(
,
)
n
r
f
k
n
shows that if firms must choose
labor for period 2 in period 1, the real interest rate between period 1 and period 2 is a
relevant price to consider – which makes sense because there is now an interest
opportunity cost associated with hiring labor (ie, “investment” in hiring).
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 Spring '08
 chugh
 Economics, Utility, Period, representative

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