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(ECON525)fex01rak.pdf
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Final Exam
Econ 525 -Macroeconomic Theory
May 16, 2002

1 Wage Contracting
The production function of competitive . rms in the economy is
Y = L.
. rms pay the marginal product of labor. We can think of this as the labor demand curve:
.. 1 .. 1
W . 1 W 1 . 1 W .
= .L. 1 ) LD = ) Y =
P .P .P
Income will be split between goods and money at a constant level so we can write
MtV . = YtPt
We write these two equations as log deviations from steady state
yt = mt pbt
bb
yt = . [wbt pbt] . =
b. 1
Wages are set by contracts in which nominal wages are set by workers and . rms hire as many workers as they want at that wage. Workers have some constant level of the real wage they would like to target. Let I be the information set that the workers have available when they select their wage. Thus, the set their wage equal to
wt = E(pbt p I)
b
Money follows a . rst order auto regressive process
mt = mbt 1 + .t
b
a. Solve for output, ybt, as a function of mbt 1 and .t when workers sign contracts with full information, i.e. wbt pt.
= b
When workers have full information, there are no deviations from steady state.
yt = . [wbt pbt]= 0
b
1
b. Solve for output, ybt, as a function of mbt 1 and .t when workers sign contracts with only the information available at time t 1, i.e. wbt = Et 1(pbt).
By the law of iterated expectations
Et 1(wbt)= Et 1(Et 1(pbt)) = Et 1(pbt)
From the supply equation, expected output is zero.
Et 1 (ybt)= . [Et 1 (wbt) Et 1 (pbt)] = . [Et 1 (pbt) Et 1 (pbt)] = 0
From the demand equation
Et 1 (ybt)= Et 1 (mbt) Et 1 (pbt)=0 ) Et 1 (pbt)= Et 1 (mbt)= Et 1 (wbt)
yt = . [Et 1 (mbt) mt + ybt]= [mbt Et 1 (mbt)] = . . " t
bb. 1
c. Assume that workers are split into two unions. Each of these unions alternate in setting wages for that period and the next period. The unions are exible enough to negotiate dierent wages in dierent periods. The real wage paid by . rms is the average of the wages that they pay to each of their unions
wt = 1 wt;1 + 1 wt;2
b2 b2 b
where
wt;1 = Et 1(pbt) wt;2 = Et 2(pbt)
bb
Solve for output, ybt, as a function of mbt 2 and .t, .t 1. First examine the wage setting of type 2 union.
1
Et 2 (wbt)= 2Et 2 [wbt;1]+ 12Et 2 [wbt;2]
1

= Et 2 [Et 1(pbt)] + 1Et 2 [Et 2(pbt)] = Et 2(pbt)
22
From the supply equation,
Et 2 (ybt)= . [Et 2 (wbt) Et 2 (pbt)] = 0
From the demand equation
0= Et 2 (ybt)= Et 2 (mbt)Et 2 (pbt) ) Et 2 (pbt)= Et 2 (mbt)= Et 2 (wbt)= wt;2
b
Now examine the wage setting of the type 1 union
1
Et 1 (wbt)= Et 1 [wbt;1]+ 1Et 1 [wbt;2]=
22
11

2 [Et 1(pbt)] + 21 [Et 2(pbt)] = 2Et 1(pbt)+ 21Et 2(mbt)
From the supply equation
Et 1 (ybt)= . [Et 1 (wbt) Et 1 (pbt)] = . 1Et 1(pbt)+ 1Et 2(mbt) Et 1 (pbt)
22
=[Et 2(mbt) Et 1 (pbt)]
2
2
From the demand equation
[