Using the midpoint method,the price elasticity of demand for a good is computed to be approximately 2.Which of the following events is consistent with a 0.1 percent increase in the price of the good?
A)The quantity of the good demanded decreases from 250 to 150.
B)The quantity of the good demanded decreases from 200 to 100.
C)The quantity of the good demanded decreases by 0.05 percent.
D)The quantity of the good demanded decreases by 0.2 percent.

Question

Quizplus · Accepted Answer

Using the midpoint method, the formula for calculating price elasticity of demand is:
E = [(Q2-Q1)/((Q2+Q1)/2)] / [(P2-P1)/((P2+P1)/2)]

We are told that E = 2. Let's assume that the initial price was $100.

For a 0.1% increase in price, P1 = $100 and P2 = $100.1.

Using the formula, we can rearrange it to solve for the change in quantity demanded (Q2-Q1):

(Q2-Q1) = E * [(Q2+Q1)/2] * (P2-P1)/[(P2+P1)/2]

(Q2-Q1) = 2 * [(250+150)/2] * (0.1)/[(100.1+100)/2] = 25

This means that quantity demanded will decrease by 25 units. To find the percentage change, we can use the midpoint method again:

% change in quantity demanded = (Q2-Q1)/[(Q2+Q1)/2] * 100%

% change in quantity demanded = (-25)/[(250+150)/2] * 100% = -8.33%

However, we are looking for a decrease of only 0.1%. Therefore, the answer is D: The quantity of the good demanded decreases by 0.2%.

Using the Midpoint Method,the Price Elasticity of Demand for a Good