A Certain Type of Rare Gem Serves as a Status $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$

question 70

Multiple Choice

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$$
where $y =$ Demand (in thousands) and $x =$ Retail price per carat (dollars) .
This model was fit to data collected for a sample of 12 rare gems.
If the experts are correct in their assumptions about the relationship between price and demand, which of the following should be true?

• A) \(\beta 1 < 0\)
• B) \(\beta _ { 2 } < 0\)
• C) \(\beta _ { 2 } > 0\)
• D) \(\beta 1 > 0\)

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Definitions:

Adaptive Organizations

Entities that have the ability to adapt and transform in reaction to shifts in market environments, obstacles, and prospects.

Tall Structures

An organizational structure characterized by many levels of hierarchy, with a large number of management levels between the top executives and the lower-level employees.

Authority-And-Responsibility Principle

The principle that authority should equal responsibility when work is delegated.

Supervisor

An individual in a position of authority who oversees and directs the work of others to ensure tasks and objectives are completed effectively.