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

question 60

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

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Definitions:

Moral Hazard

The risk that a party insulated from risk may behave differently than if they were fully exposed to the risk.

Walk-Throughs

Detailed guides or inspections usually performed to assess, explain, or demonstrate procedures or how a series of steps is to be followed.

Adverse Selection

A situation where asymmetric information results in high-risk individuals being more likely to participate in an exchange, leading to a market failure.

Health Insurance

A type of insurance coverage that pays for medical and surgical expenses incurred by the insured, often including preventive care, and sometimes dental and vision benefits.