Write down the equation of adaptive expectations hypothesis. Illustrate it with an example.

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The adaptive expectations hypothesis is a theory that suggests that people form their expectations about the future based on their past experiences. The equation of the adaptive expectations hypothesis is:

Et+1 = Et + α (Yt - Et)

Where:

Et+1 is the expected value of a variable in the next period

Et is the expected value of the variable in the current period

Yt is the actual value of the variable in the current period

α is the rate of adjustment or the degree to which expectations adjust to changes in the actual variable value

This equation shows that the expected value of a variable in the next period (Et+1) is equal to the expected value in the current period (Et) plus a fraction of the difference between the actual value of the variable in the current period (Yt) and the expected value in the current period (Et). The rate of adjustment (α) determines how quickly expectations adjust to changes in the actual variable value.

For example, let’s consider inflation. Suppose that the inflation rate last year was 2%, and people expected the same rate of inflation this year. However, this year the inflation rate turns out to be 3%. According to the adaptive expectations hypothesis, people will adjust their expectations for next year’s inflation based on this year’s actual inflation rate. If we assume that the rate of adjustment (α) is 0.5, then the equation would look like this:

Et+1 = 2 + 0.5 (3 - 2)

Et+1 = 2.5

This means that people will expect next year’s inflation rate to be 2.5%, which is an adjustment from their previous expectation of 2%.

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