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Solution:
The elasticity of demand is given by the formula:
Elasticity of demand = percentage change in quantity demanded / percentage change in price
Here, we are given that the price of good X falls from $8 to $2 per unit. This represents a 75% decrease in price.
Using the formula for elasticity of demand, we can calculate the percentage change in quantity demanded as:
Percentage change in quantity demanded = (Q2 - Q1) / ((Q1 + Q2) / 2) × 100%
where Q1 is the initial quantity demanded at a price of $8, and Q2 is the new quantity demanded at a price of $2.
Substituting the given equation for QX into this formula, we get:
Percentage change in quantity demanded = (1500/8 - 1500/2) / ((1500/8 + 1500/2) / 2) × 100%
Simplifying this expression, we get:
Percentage change in quantity demanded = -75%
Now we can use the formula for elasticity of demand to calculate the elasticity of demand when the price falls from $8 to $2 per unit:
Elasticity of demand = (-75% / 75%) / (-75% / 75%) = 1
Therefore, the elasticity of demand of the good X when its price falls from $8 to $2 per unit is equal to one. The answer is (c) equal to one.
Correct option is (c)