Question

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 owners believe they will gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:

Y =

Answer 1

The quadratic model proposed to explain the demand for the rare gem by its price is expressed as Y = a
`x^2` + bx + c.

Step-by-step explanation:

The quadratic model Y = a
`x^2` + bx + c suggests that the relationship between the demand for the rare gem and its price is not linear but follows a quadratic function. In this model, 'Y' represents the demand, and 'x' represents the price of the gem. The coefficients 'a,' 'b,' and 'c' determine the shape of the quadratic curve.

The hypothesis that the demand for the gem increases with very high prices aligns with a quadratic function where the coefficient 'a' is positive, indicating an upward-opening parabola. This implies that as the price of the gem rises, the demand initially decreases (as suggested by the negative coefficient 'b') but then starts increasing at higher prices.

Understanding the quadratic model is crucial for predicting how changes in the price of the gem may impact its demand, especially considering the unique dynamics associated with status symbol goods. It provides a nuanced perspective that goes beyond simple linear relationships, capturing the complex interplay between price and demand for this particular gem.

For a deeper understanding of quadratic models in economics and their applications, particularly in analyzing demand and pricing dynamics, refer to relevant academic literature and research in the field of econometrics.