Final answer:
The price elasticity of demand for college tuition is calculated at − 1.2, indicating that demand is somewhat elastic. This means that a 1% increase in tuition results in a 1.2% decrease in enrollment, reflecting a sensitive response to price changes in college tuition.
Step-by-step explanation:
The student is asked to calculate the price elasticity of demand for college tuition. The price elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. The formula for price elasticity of demand (E_d) is given as:
E_d = (dQ/dP) × (P/Q)
Where:
- dQ/dP is the derivative of the demand function with respect to price
- P is the price level
- Q is the quantity demanded at price level P
For the given demand equation q = 9,900 − 2p:
- dQ/dP = − 2
- P = $2,700 (the average tuition fee)
- Q = 9,900 − 2×2700 = 9,900 − 5400 = 4,500
Now, plugging these values into the formula:
E_d = (− 2) × (2700 / 4500) = − 2700 / 2250 = − 1.2
The negative sign indicates that the demand is inversely related to the price, which is typical for price elasticity of demand. The magnitude of the elasticity is 1.2, which means that a 1% increase in price will result in a 1.2% decrease in enrollment, indicating that the demand is somewhat elastic.
It's important to note that in the context of higher education, the increasing cost of tuition and fees significantly outpaces the increase in household income, making college affordability a growing concern for many students and families.