Consider the Following Model $$Y _ { t } = \alpha _ { 0 } + \alpha _ { 1 } X _ { t } ^ { e } + u _ { t }$$

question 7

Essay

Consider the following model $$Y _ { t } = \alpha _ { 0 } + \alpha _ { 1 } X _ { t } ^ { e } + u _ { t }$$ t
where the superscript "e" indicates expected values.This may represent an example
where consumption depended on expected, or "permanent," income.Furthermore, let
expected income be formed as follows: $$X _ { t } ^ { e } = X _ { t - 1 } ^ { e } + \lambda \left( X _ { t - 1 } - X _ { t - 1 } ^ { e } \right) ; 0 < \lambda < 1$$ 1
This particular type of expectation formation is called the "adaptive expectations
hypothesis."
(a) In the above expectation formation hypothesis, expectations are formed at the beginning of the period, say the $1 ^ { \text {st } }$ of January if you had annual data. Give an intuitive explanation for this process.

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Definitions:

Unit Of Input

A measurement of the amount of resources (labor, materials, etc.) used in the production of goods and services.

Average Product

The output per unit of input, calculated by dividing the total product by the quantity of input.

Marginal Product

Marginal product is the increase in output that results from adding one more unit of a specific input, holding all other inputs constant.

Fixed Costs

Expenses that do not change with the level of production or sales, such as rent, salaries, and insurance premiums.