Answer:
b. a 13.33 percent increase in the price of the good
Explanation:
We can write the price elasticity of demand as:
[tex]\frac{dQ/Q}{dP/P} =-0.75[/tex]
We have to guess which event produces a 10% drop in the quantity demanded (dQ/Q=-0.10).
Knowing the concept of elasticity, this can be produced by a price increase.
The amount of this increase can be estimated knowing the value of the PED (price elasticity of the demand).
[tex]dQ/Q=-0.10\\\\dQ/Q=\epsilon*dP/P\\\\dP/P=dQ/Q/\epsilon\\\\dP/P=(-0.10)/(-0.75)=0.1333[/tex]
Then, what causes the 10% drop in the demanded quantity is a 13.33% price increase.
Answer: The correct option is B. a 13.33 percent increase in the price of the good
Explanation: This is a simple problem of elasticity of demand. The formula for calculating elasticity of demand is given as:
Elasticity of demand = percentage change in quantity divided by the percentage change in price.
Elasticity of demand = ∆Q/∆P
From the question above, we have the following parameters:
Elasticity of demand = 0.75
Percentage change in quantity = 10%
Percentage change in price = x
Therefore, we substitute the values into the formula above, we have:
0.75 = 10/x
0.75x = 10
x = 10/0.75
x = 13.33 %.
Therefore an elasticity of 0.75 and a 10% change in quantity are consistent with a 13.33% change in price. Hence, the answer is option B.
