Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. A perfectly inelastic demand means that the quantity demanded does not change at all regardless of the price.
If students *must* live in dorms, then the quantity demanded of dorm space remains the same even if the price increases. Students have no alternative; they are required to live in the provided housing. Therefore, the price elasticity of demand is 0.
However, this is only true in the short run. In the long run, several factors could affect elasticity:
* Students might choose different universities: If the dorm prices are excessively high, prospective students might choose universities with more affordable housing options (even if those universities might not be their first choice). This increases the elasticity of demand for a *specific* university's dorm space.
* Students might find alternative accommodations: While prohibited by the rule in the short term, students might seek illegal off-campus housing, or the university might eventually be forced to relax the rule due to student pressure.
* Universities might build more dorms: If the university observes high demand despite high prices, they might respond by increasing the supply of dorm space in the long run, thus impacting the elasticity of demand.
In conclusion, the rule would create a perfectly inelastic demand in the short run, but the long-run elasticity would depend on the flexibility of students' choices and the university's response to student needs and potentially the rule's legal viability.