Question

Using the midpoint method, the price elasticity of demand for a good is computed to be approximately 0.75. Which of the following events is consistent with a 10 percent decrease in the quantity of the good demandeda. a 7.5 increase in the price of the good
b. a 13.33 percent increase in the price of the good
c. an increase in the price of the good from $7.50 to $10
d. an increase in the price of the good from $10 to $17.50

Answer 1

Answer:

b. a 13.33 percent increase in the price of the good

Explanation:

We can write the price elasticity of demand as:

$\frac{dQ/Q}{dP/P} =-0.75$

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).

$dQ/Q=-0.10\\\\dQ/Q=\epsilon*dP/P\\\\dP/P=dQ/Q/\epsilon\\\\dP/P=(-0.10)/(-0.75)=0.1333$

Then, what causes the 10% drop in the demanded quantity is a 13.33% price increase.

Answer 2

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.