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) \(\beta 1 > 0\)

Recognize the importance of private ownership for economic decision-making and resource management.

Appreciate the balance between technological advancement and its impact on employment and economic growth.

Understand the principles of supply and demand as they apply to the conservation efforts of certain species and products.

Comprehend the concept of voluntary exchange and how mutual benefits are derived from such exchanges.

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Definitions:

Monetary Policy

The process by which the monetary authority of a country, like the central bank, controls the supply of money, often targeting an inflation rate or interest rate to ensure economic stability and growth.

Investments Abroad

Financial allocations by individuals or companies in business interests or assets in foreign countries.

Return

The profit or loss derived from an investment.

Free Floating Exchange Rate System

A currency system where the value of a country's currency is determined by the supply and demand for the currency in the foreign exchange market, without direct government control.