Write the Following Four Restrictions in the Form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$

question 2

Essay

Write the following four restrictions in the form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$ where the hypotheses are to be tested simultaneously.
$\begin{array} { l } \beta _ { 3 } = 2 \beta _ { 5 } , \\\beta _ { 1 } + \beta _ { 2 } = 1 , \\\beta _ { 4 } = 0 , \\\beta _ { 2 } = - \beta _ { 6 } .\end{array}$
Can you write the following restriction $\beta _ { 2 } = - \frac { \beta _ { 3 } } { \beta _ { 1 } }$ in the same format? Why not?

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Definitions:

Monopolistically Competitive

A marketplace configuration in which a wide variety of firms supply products that are analogous but not identical, thereby granting them a modicum of market influence.

Elastic

A characteristic of goods where their demand or supply changes significantly when the price changes.

Monopolistic Competitor

A market structure where many firms offer products or services that are similar but not perfect substitutes, allowing for some degree of market power.

Excess Capacity

describes a situation where a firm produces less than its total output capacity, usually resulting in inefficiencies and higher production costs.