#### Summary

There is a relationship between inflation and unemployment that can be easily analysed. Governments around the world take this relationship very seriously, since there will always be a trade-off when implementing economic policies. Even though this relationship was first analysed by Alban William Housego Phillips in 1958, it has since evolved, taking into consideration adaptive and rational expectations.Rational expectation models are those where an agent’s future predictions affect the value they assign to a variable in their current time period. In this sort of self-fulfilling prophecy, expectations become truths, and errors in forecasting future variables become random. This makes those forecasts valid, because present expectations about the future become dependent variables of future values. This model was developed and put forwards by John Muthin two articles: “Optimal Properties of Exponentially Weighted Forecasts”,1960, and “Rational Expectations and the Theory of Price Movements”, 1961 and later summarised by Peter Whittle in 1963, before becoming influential in *Robert Lucas*’ work in the 1970s. Particularly, Lucas developed the use of rational expectations in his article “Expectations and the Neutrality of Money”, 1972, in which he used *Edmund Phelps*’ island parable, though applying rational expectations, instead of *adaptive expectations*.

Mathematically, rational expectations can be represented as:

Which simply means that the value of *x* today will be the value that we expected it to be plus a random error.

Essential to this hypothesis is the fact that individuals have perfect information and markets are perfect and tend towards equilibrium. This places us firmly back in the realm of *neoclassical economics*, whose main ideas where retaken by *New Classical Macroeconomics*.