Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Contract models

Contract models are based on the observation that labor contracts often forbid firms
from changing wages in the short run

The existence of long term relationships between firms and workers implies that
wage does not have to adjust to clear the labor market in each period.

Workers are content to stay in their current jobs as long as the income streams they
expect to obtain are preferable to their outside opportunities. Because of their longterm relationships with their employers, their current wages may be relatively
unimportant to this comparison.

Workers are risk averse while the firm is assumed to be risk neutral.
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Firms offer implicit insurance to workers in the form of contracts that reduce
sensitivity of workers’ incomes in response to fluctuation in labor demand.
In exchange, workers accept lower wages than they would otherwise demand.
There is a mutual gain since the firm (who does not care about risk) raises its
expected profit but incurs more risk, and the workers reduce risk enough to more
than offset the utility lost from lower expected incomes.
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Basic Model
Firm’s profits
where L is the quantity of labor employed and w is the wage. A reflects technology and
shifts the profit function.
Consider a world with a finite set of possible states of the Ai where A is random. The firm’s
expected profits are:
where pi is the probability that A= Ai with i =1,…,K and Li, wi is the realization if A is Ai
Each worker is assumed to work the same amount. The worker’s utility is:
where U() is the utility from consumption and V() is the disutility from working. Workers
are risk averse with U’’()<0.
Worker’s expected utility is:
with some reservation level of expected utility u0 that workers must obtain to work for the
firm.
To solve the problem, firms maximize expected profits subject to worker’s expected utility
exceeding their reservation level of utility u0 that they get from not working. We also
assume that the worker’s consumption C is equal to their labor income wL.
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Set up the Lagrangian:
Solving the model:

The model implies strong real wage rigidity since workers real incomes are constant
under efficient contracts
 firms supply workers with insurance against income uncertainty thereby producing a
relatively stable real wage
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Minimum wages


Walrasian wage is w* with full employment L*
If minimum wage is employed above the market clearing level, there will be
unemployment of

The magnitude of unemployment arising from the minimum wage law depends on
the elasticity of the labor supply and labor demand curves. If both are inelastic, the
unemployment gap is small.

Typically, minimum wages are set well below the average wage in the economy. If
wages are set at w2, the minimum wage has no effect as it is non-binding


Empirically, minimum wages have relatively minor employment effects
However, they have significant impacts during certain time periods and on certain
group of workers, especially unskilled and teenager workers

We need a segmented model for skilled and young workers better study the effects
of minimum wage laws and spillovers between markets
Two sector labor market
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke


In the skilled labor market, the equilibrium wage exceeds the minimum wage, so
there is no direct effect of the minimum wage law on unskilled labor, while the
wage floor is effective in the market for unskilled market.
There may be demand or supply spillovers on either the demand or supply side, or
both.
Supply side: In the short run, there would be no immediate spillover of workers from one
market to the other. Unskilled workers cannot, presumably, become skilled immediately,
while skilled workers earn a higher wage in the skilled market and have no incentive to
move.
In the longer run, supply flows in either direction are possible.
Demand side: firms’ demand for skilled workers may be affected by the increase in the
wage for unskilled labor. If skilled and unskilled workers are substitutes, the firm will
increase its demand for skilled workers, which will tend to push skilled wages upward. If
they are complements, this will reduce skilled-labor demand and lower skilled wages.
Although the substitute-complement relationship between skilled and unskilled labor is
likely to vary across industries, the most common assumption is that they tend to be
substitutes. If that assumption is true, then an increase in the minimum wage will raise the
wages of skilled workers.
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Unions and bargaining

The presence of a labor union that engages in collective bargaining on behalf of
workers can leads to a different pattern of real wages and employment than would
be observed under competition.

How wages and unemployment is determined can be analyzed in a two sector model
with a union and nonunion sector. Spillovers between models can be analyzed
similar to the minimum wage case above.

Blanchard proposes a simple bargaining model to explain the high levels of
unemployment in the 1970s in Europe. He uses it to argue that the rise in
unemployment is due to adverse supply shocks due to technological growth and oil
price shocks.
Blanchard bargaining model (wage setting/ price setting model)

The wage setting curve (WS), reflects the bargaining power of unions (or workers)

the price setting curve (PS) reflects the market power of firms over prices.
Price setting equation:

Firms are assumed to act as price-setting monopolists. They have market power and
set prices as a markup (µ>0) over cost.

Firms produce goods using only labor with production function Y=AN. This leads
to prices being set as a constant mark up over nominal unit labor costs.
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Wage setting equation:

Wages are assumed to be determined through bargaining between workers and
firms, which is referred to as the bargained wage:

Unemployment has a negative relationship with real wage

z measures other factors that have a positive effect on wages given the price level
and unemployment rate

The level of unemployment that makes the wage and price curves intersect is
labeled the natural rate or the NAIRU (these terms are often used interchangeably).

The NAIRU changes if either PS or WS shift.
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke

The NAIRU is a long run equilibrium rate of unemployment which only depends on
structural supply factors.

In the short run the unemployment rate may diverge from the NAIRU due to
demand (macroeconmic policies), but in the medium/long term the economy returns
to the NAIRU as inflation stabilizes.

Note: When ω=1 (or close to 1)
 Add two sources of frictions (real and nominal wage rigidities) to see how a can
affect NAIRU and explain the slow adjustment in unemployment
Real rigidities
Change the wage bargaining equation into:
Assume it is updated as
While the actual process follows a random walk
What is the equilibrium level of employment?
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Econ 701-Survey of Macroeconomics
Spring 2015/ Manopimoke
Suppose there is a one period adverse supply shock ∆a=ɛ<0, what will happen?

In the previous model with at= ate we get an immediate shift in the real wage but no
change in the unemployment rate/NAIRU since ω=1

This type of real rigidity can explain why adverse supply shocks in the 70s had
effects on unemployment for a long period

Real wage rigidities are frictions that prevent the real wage from adjusting to its
long run equilibrium value.
Nominal rigidities
This is when nominal prices slowly adjust. The bargaining model becomes:
So it is not just productivity that the workers have to form expectations over, but also the
price level. This gives us nominal wage stickiness. Equilibrium level of unemployment is
now:

Shows that monetary policy can counteract real wage rigidities using monetary
policy to change the rate of inflation.
But unemployment in Europe continued to rise during the 1980s. Hard to argue that this
was the effect of shocks more than 10 years ago. Furthermore, inflation stabilized while
unemployment was high. Why?
Next time: Two new elements to explain this: (i) Responses of capital accumulation, (ii)
Hysteresis.
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