The modeling expectations of finance, Keynesian macroeconomics and new classical macroeconomics are of immense importance in economics. Let us take an example to explain the concept of rational expectations. The expected level of inflation will influence the decision of a firm on its wage level in the coming year.
The share value of a stock is also influenced by the future income that is expected from that stock. The theory of rational expectations describes the expectations as the best future guess or the optimal forecast. Such a forecast is made by using all the information that is available.
However, the theory of expectations does not take part in predicting the human behavior. While making a rational expectation, it is assumed that the predicted outcome is not systematically different from the result that would have been earned if the market were at its equilibrium state.
The theory of rational expectations also assumes that while predicting the future, people do not commit systematic errors and the deviations seen from the perfect foresight are random in nature. Thus, it can be said that the rational expectations are not different predictably or systematically from the equilibrium results. The economic models thus are designed with two assumptions - a random variable carries the role of mistakes and ignorance and the value of variable is same as the predicted value.
Let us suppose that P represents the equilibrium price in a market that is calculated by demand and supply. According to the theory of rational expectations, we can say that the actual value of the variable P will deviate from the expected value only if an 'information shock' occurs in the expectation.
This theory can be represented by the following mathematical formulation:
P = P* + e
P* stands for the rational expectation
e stands for the random error term. The value of e is expected to be zero and it is independent of P*.