Question

In Example A.2, quantity of compact discs was related to price and income by quantity = 120 - 9.8 price + .03 income. What is the demand for CDs if price = 15 and income = 200? What does this suggest about using linear functions to describe demand curves?

Answer 1

It is given that the demand function of the CD is dependent on its own price and income of the consumer. The demand function is as follows:

 

Quantity = 120 – 9.8Price + 0.03 income

Here,

Price = 15, and

Income = 200.

 

Substitute the value of P and Y in the demand equation to get the value of Q:

Q = 120 – 9.8P + 0.03Y

    = 120 – 9.8P + 0.03Y

    = 120 – 147 + 6

    = -21

 

Thus, the value of Q is -21 which is not possible. Thus, the quantity demanded is zero at price equals $15 per unit (keeping income equals 200).

 

From the demand equation, it is clear that there is an inverse relationship between price and demand. The sign (–) indicates that as the price of commodity increases, the quantity demanded decreases and vice-versa.

 

The relationship between income and quantity demand is positive. This sign (+) indicates that as income increases, the demand for commodity increases and vice-versa. This means, the good is a normal good.

The relationship between income and quantity demand is positive. This sign (+) indicates that as income increases, the demand for commodity increases and vice-versa. This means, the good is a normal good.