The current price for a good is $20, and 100 units are demanded at that price. The price elasticity of demand for the good is negative 2.
When the price of the good drops by 10 percent to $18, consumer surplus
A. Increases
B. Decreases
by _ ? (Enter your response to the nearest penny.)
To determine how a change in price affects the consumer surplus, we need to calculate the change in quantity demanded and then multiply it by the difference in price.
Given that the price elasticity of demand is -2, we know that a 10% change in price will result in a 20% change in quantity demanded (since the elasticity is the percentage change in quantity demanded divided by the percentage change in price).
So, when the price drops by 10% to $18, the new quantity demanded can be calculated by multiplying the original quantity demanded (100 units) by (1 + 0.2), resulting in 120 units.
To calculate the change in consumer surplus, we need to find the area between the demand curve and the new price line. Since the demand curve is a straight line, we can use the formula for the area of a triangle, which is 0.5 * base * height.
The base of the triangle is the change in quantity demanded, which is 120 - 100 = 20 units. The height of the triangle is the change in price, which is $20 - $18 = $2.
Plugging these values into the formula, we get:
Consumer Surplus = 0.5 * base * height
= 0.5 * 20 * $2
= $20
Therefore, when the price of the good drops by 10% to $18, consumer surplus increases by $20.
So, the correct answer is:
A. Increases