Intermediate
Macroeconomics
Tutorial 6
Chapter 5: Rational Expectations
- From Adaptive to Rational Expectations
- Stochastic Equilibrium
,T6 5.1, 5.2, 5.3, 5.5
Adaptive Expectations
If the monetary authority increases the money supply (to stimulate the economy), aggregate demand
is boosted. The price level rises. However, in this process there is a discrepancy between the expected
price level and the actual price level. This gap slowly narrows by an upward revision of the expected
price level. This indicates that agents make systematic mistakes along this path. The initial shock
causes an expectational error that is slowly eliminated. All along the adjustment path, the error is
negative and stays that way such that agents keep guessing wrongly.
Perfect Foresight
Agents’ expectations coincide with the actual path. Under perfect foresight the aggregate supply curve
is vertical because there is no discrepancy in the price level. Suppose the money supply is increased
by the central bank. Since there is no uncertainty in the model, forecasting is not difficult for the
agents. They realise that a higher money supply induces a higher price level and adjust their wages
upwards. As a result, the real wage, employment, and output are unaffected (PIP).
Rational Expectations
In reality all kinds of change occurrences play an important role. In a macroeconomic context one
could think of stochastic events such as fluctuation in the climate, natural disasters, shocks to world
trade. Then forecasting is much more difficult. The REH incorporates such stochastic elements. The
basic proposition is that
- Information is scarce and the economic system does not waste it
- The way in which expectations are formed depends in a well-specified way on the structure
of the system describing the economy.
1
, T6 5.1, 5.2, 5.3, 5.5
5.1 Short Questions
Suppose you tossed a fair Dutch euro coin 100 times. Suppose that heads probability is 0.45 and tails
0.55. Each time heads comes up you gain 1 euro and when tails come up you lose one euro. What is
your rational expectation regarding your total gains after 100 rounds of tossing?
Expected pay-off 0.45 × 1 − 0.55 × 1 = −$0.10
Hundred times −0.10 × 100 = −$10
It is your rational expectation to expect a negative payoff of $10.
“The hypothesis of rational expectations assumes that everybody is a brilliant economist. Since brilliant
economists are rather scarce, the assumption of rational expectations is absurd.” Explain and evaluate
this proposition.
False. All that the REH states is that the subjective expectation coincides with the objective
expectation. Not everybody needs to be a brilliant economist. As long as there are no systematic
mistakes, the REH is fine as an operating assumption.
The Rational Expectations Hypothesis (REH) doesn't assume everyone is an economic genius—it
simply means people learn from experience and don't consistently make predictable mistakes. Over
time, even ordinary individuals and businesses adjust their behaviour based on observed patterns (like
noticing that money printing leads to inflation), eliminating systematic errors. While not perfectly
realistic (since people do make short-term errors), REH works as a useful benchmark because markets
tend to correct persistent irrationality—smart actors exploit mistakes, and repeated patterns get
incorporated into expectations. It's not about perfect foresight, but rather the idea that people aren't
forever fooled by the same policies. This makes REH a reasonable starting point for modelling how
economies adapt to predictable rules, even if real-world behaviour includes some frictions and delays.
2
Macroeconomics
Tutorial 6
Chapter 5: Rational Expectations
- From Adaptive to Rational Expectations
- Stochastic Equilibrium
,T6 5.1, 5.2, 5.3, 5.5
Adaptive Expectations
If the monetary authority increases the money supply (to stimulate the economy), aggregate demand
is boosted. The price level rises. However, in this process there is a discrepancy between the expected
price level and the actual price level. This gap slowly narrows by an upward revision of the expected
price level. This indicates that agents make systematic mistakes along this path. The initial shock
causes an expectational error that is slowly eliminated. All along the adjustment path, the error is
negative and stays that way such that agents keep guessing wrongly.
Perfect Foresight
Agents’ expectations coincide with the actual path. Under perfect foresight the aggregate supply curve
is vertical because there is no discrepancy in the price level. Suppose the money supply is increased
by the central bank. Since there is no uncertainty in the model, forecasting is not difficult for the
agents. They realise that a higher money supply induces a higher price level and adjust their wages
upwards. As a result, the real wage, employment, and output are unaffected (PIP).
Rational Expectations
In reality all kinds of change occurrences play an important role. In a macroeconomic context one
could think of stochastic events such as fluctuation in the climate, natural disasters, shocks to world
trade. Then forecasting is much more difficult. The REH incorporates such stochastic elements. The
basic proposition is that
- Information is scarce and the economic system does not waste it
- The way in which expectations are formed depends in a well-specified way on the structure
of the system describing the economy.
1
, T6 5.1, 5.2, 5.3, 5.5
5.1 Short Questions
Suppose you tossed a fair Dutch euro coin 100 times. Suppose that heads probability is 0.45 and tails
0.55. Each time heads comes up you gain 1 euro and when tails come up you lose one euro. What is
your rational expectation regarding your total gains after 100 rounds of tossing?
Expected pay-off 0.45 × 1 − 0.55 × 1 = −$0.10
Hundred times −0.10 × 100 = −$10
It is your rational expectation to expect a negative payoff of $10.
“The hypothesis of rational expectations assumes that everybody is a brilliant economist. Since brilliant
economists are rather scarce, the assumption of rational expectations is absurd.” Explain and evaluate
this proposition.
False. All that the REH states is that the subjective expectation coincides with the objective
expectation. Not everybody needs to be a brilliant economist. As long as there are no systematic
mistakes, the REH is fine as an operating assumption.
The Rational Expectations Hypothesis (REH) doesn't assume everyone is an economic genius—it
simply means people learn from experience and don't consistently make predictable mistakes. Over
time, even ordinary individuals and businesses adjust their behaviour based on observed patterns (like
noticing that money printing leads to inflation), eliminating systematic errors. While not perfectly
realistic (since people do make short-term errors), REH works as a useful benchmark because markets
tend to correct persistent irrationality—smart actors exploit mistakes, and repeated patterns get
incorporated into expectations. It's not about perfect foresight, but rather the idea that people aren't
forever fooled by the same policies. This makes REH a reasonable starting point for modelling how
economies adapt to predictable rules, even if real-world behaviour includes some frictions and delays.
2
