Question

Suppose the market demand curve for a good is represented by the linear equation Q = 100 - 0.5P. If the market price were to decrease from P = 40 to P = 30, then holding all other factors constant, what would be the change in quantity demanded?

1) 10 units
2) 15 units
3) 20 units
4) 25 units

Answer 1

The change in quantity demanded would be 5 units when the price decreases from P = 40 to P = 30 according to the given linear demand equation Q = 100 - 0.5P.

Step-by-step explanation:

The change in quantity demanded when the market price decreases from P = 40 to P = 30 can be calculated using the given market demand curve equation Q = 100 - 0.5P. The direct answer to determining the change is to apply the equation for both price points and identify the difference in quantity.

First, for P = 40:
Q = 100 - 0.5(40) = 100 - 20 = 80 units.
Second, for P = 30:
Q = 100 - 0.5(30) = 100 - 15 = 85 units.
Therefore, the change in quantity demanded is 85 units - 80 units = 5 units.
This is an application of basic algebra to a linear demand function, illustrating a fundamental concept in economics known as the law of demand, which states that there is an inverse relationship between price and quantity demanded, ceteris paribus (all other factors being constant).