TIME CONSISTENT
MACROECONOMIC POLICY
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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OUTLINE
INFLATION
 MACROECONOMIC MODEL
 A SIMPLE MACROECONOMIC MODEL
 MATHEMATICAL IDENTITIES
 ORDER OF PLAY AND EQUILIBRIUM
 PAYOFFS
 EXAMPLES AND
 PRECOMMITMENT

Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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INFLATION
 Inflation
is a persistent increase in the
general price level.

Continuous increase in general price
level and large amount of goods are
subjects for inflation.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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A SIMPLE MACROECONOMIC MODEL

Interdependency among 3 groups:
 Workers
 Central
Bank
 Employers
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Wage contracts are indexed to prices but the
indexation of wages to prices is not complete.
 Indexation has 2 important implications:

1-)The money wage that clears the labor market
will depend on the rate of inflation expected
over the period covered by the contract.
2-)If the inflation rate actually differs from what
was expected when the money wage was
negotiated,then workers will be forced by their
contracts to supply either more or less labor
than they would have supplied had the inflation
rate been correctly foreseen.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Mathematical Identities
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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ORDER OF PLAY

There are 2 time periods.

At the first time period,the workers choose
the money wage.

At the beginning of the second period,the
central bank chooses the rate of inflation.

The employers then choose the level of
employment.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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PAYOFFS

Workers are utility maximizers who value
both real income and leisure.
 Is(rt)
= α * rt
rt = wt-пt
 rt is real wage
 wt is nominal wage
 пt
is inflation ratio
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Payoff function for workers:
 Vw = -(I2-α *(w2-п2))2

Payoff function for Central Bank:
 WCB = -(I2-I-2)2-ч*(п2-п-2)2

Payoff function for employers:
 Ld(rt)=-n*rt
Ld(r2) = n*(п2-w2)


VE =-(I2-n*(п2-w2))2
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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
The labor market is in equlibrium when
the labor supply equals to labor
demand.At this equilibrium,the level of
employment is the natural level of
employment.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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EQUILIBRIUM

In this dynamic game,employers move
last.

Given the money wage chosen by the
workers and the rate of inflation chosen
by the central bank, the employer’s profit
maximizing strategy maximizes pay-off
function for employers.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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 I*2

=n*(п2-w2)
This equation shows aggregate
employment function.
 I*2 shows

the optimal level of employment.
The workers move first.Their choice
depends on their forecasts about
employment and inflation rates.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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
The inflation forecasts are called as
inflationary expectations.

Vw =-(I*2(w2,п*2(w2))- α*(w2-п*2(w2))2
=-(n+α)2 *(п* (w )-w )2
2
2
2

w*2=п-2 +n/ ч *I-2
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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
П*2(w*2)=п-2 +n/ ч *I-2

Since п*2(w*2) =w*2 ; Ld=Ls

Finally, the central bank can reach
inflation and employment targets if
I-2=0
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Reasons for higher target level of
employment

Taxes on income

Unemployment compensation

Monopolistic unions

Monoponistic employers pay wages below
the competitive level,thereby reducing the
quantity of labor supplied.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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
Whenever the target level of employment
is positive,the central bank misses its
employment target and its inflation target.
Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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Assoc. Prof. Yeşim Kuştepeli, ECN 4015 Game Theory
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