Question

Suppose a university raises its tuition from $3,000 to $3500. As a result, student enrollment falls from 5,000

to 4,500. Calculate the price elasticity of demand using the mid-point formula. (Round to three decimal places). Is the demand elastic, unitary elastic or inelastic?

For full credit please tell me the following:

1. What is the numerator
2. What is the denominator?
3. What is the numerator divided by the denominator?
4. Is the demand is elastic, unit elastic or inelastic.


Hint: When calculating the midpoint formula start by determining the starting quantity Q1 and the starting
price P1. Next, determine the ending quantity Q2 and the ending price P2.

Answer 1

Answer: The numerator is the percentage change in quantity demanded, which is (Q2 - Q1)/[(Q2 + Q1)/2] = (4500 - 5000)/[(4500 + 5000)/2] = -0.1818

The denominator is the percentage change in price, which is (P2 - P1)/[(P2 + P1)/2] = (3500 - 3000)/[(3500 + 3000)/2] = 0.1429

The numerator divided by the denominator is -0.1818/0.1429 = -1.2727

The price elasticity of demand is greater than 1 in absolute value, which means the demand is elastic.

Using the midpoint formula, we can calculate the price elasticity of demand as:

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

Substituting the given values, we get:

[(-500)/((5000 + 4500)/2)] / [(3500 - 3000)/((3500 + 3000)/2)]

Simplifying, we get:

-0.1818 / 0.1429 = -1.2727

Since the price elasticity of demand is greater than 1 in absolute value, the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price, and the university can expect a relatively large decrease in enrollment due to the tuition increase.

Explanation: