Using the Model $\boldsymbol { Y } = \boldsymbol { X } \boldsymbol { \beta } + \boldsymbol { U }$

question 13

Essay

Using the model $\boldsymbol { Y } = \boldsymbol { X } \boldsymbol { \beta } + \boldsymbol { U }$ and the extended least squares assumptions, derive the OLS estimator $\hat { \beta }$ . Discuss the conditions under which $\boldsymbol { X } ^ { \prime } \boldsymbol { X }$ is invertible.

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Definitions:

Tariffs

Taxes imposed by a government on imported or exported goods.

Economies of Scale

Economies of scale refer to the reduction in the cost per unit that companies experience as they increase their production volume.

Aggregate Factor Costs

The total cost of all inputs used in the production of goods or services, such as labor, capital, and materials.

Total Demand

The complete quantity of a product or service that all consumers in a market wish to purchase at a given price and time.