The Model
The model contains a group of N islands, with one individual on each. Each individual produces some quantity Y, which can be bought for some amount of money M. Individuals use money a given number of times to buy a certain quantity of goods which cost a certain price. In the quantity theory of money, this is expressed as MV = PY, where money supply times velocity equals price times output.
Lucas then introduced variation in the price level. This can occur through changes in the local price level of individual islands due to increased or decreased demand (i.e. asymmetric preferences, z) or through stochastic processes (randomness) that cannot be predicted (e). However, the island dweller only observes the OLG model price change, not the component price changes. Essentially, all prices can be rising, in which case the islander wants to produce the same, as his real income is the same, which is shown by (e). Or the price of his product is rising and others are not, which is z, in which case he wants to increase supply due to a higher price. The islander wishes to respond to z but not to e, but since he can only see the total price change p, (p = z + e) he makes errors. Due to this, if the money supply is expanded, causing general inflation, he will increase production even though he is not receiving as high of a price as he thinks (he confuses some of the price as an increase in z). This exhibits a Phillips curve relationship, as inflation is positively related with output (i.e. inflation is negatively related with unemployment).
The twist is that due to the rational expectations included in the model, the islander isn't tricked by long-run inflation, as he incorporates this into his predictions and correctly identifies this as pi(long-run trend inflation) and not z. This is essentially the Policy Ineffectiveness Proposition. This means in the long-run, inflation cannot induce increases in output, which means the Phillips curve is vertical.
An important consequence of the Lucas island model is that it requires that we distinguish between anticipated and unanticipated changes in monetary policy. If changes in monetary policy and the resulting changes in inflation are anticipated, then the islanders are not mislead by any price changes that they observe. This implies that the islanders learn from their past experience and form their expectations accordingly. Consequently, they will not adjust production and the neutrality of money occurs even in the short-run. With unanticipated changes in inflation, the islanders face the imperfect information problem and will adjust production. Therefore, monetary policy can stabilize output only if policymakers have more information than agents.
Read more about this topic: Lucas Island Model
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