If a university faces a downward sloping, linear demand curve for the undergraduate education that it provides and is able to engage in perfect, first degree price discrimination(through obtaining detailed financial information from each prospective student and offering different levels of financial aid), then the university’s marginal and average revenue curves will be identical.” Explain why this statement is true, false or uncertain.
Tough question. I believe the statement is false. For a perfect price-discriminating monopolist, the demand curve is also the MR curve. This monopolist does not get the same from each person. For the first person, the U gets the highest willingness to pay (P1). For the second the second highest willingness to pay (P2), and so on. However, for n students, the average revenue is (P1+P2+...Pn)/n. The MR for n students is simply Pn. and these two are not the same.
This statement is true. Under perfect, first-degree price discrimination, a firm is able to charge each customer the maximum price they are willing to pay, resulting in capturing the entire consumer surplus. In the case of the university, it can obtain detailed financial information from each prospective student and offer different levels of financial aid, effectively charging students different prices based on their ability to pay.
In this context, the university can determine the precise willingness to pay of each student and set the price accordingly. Since the demand curve is downward-sloping, the price charged to each individual student will decrease as the number of students increases.
Under perfect price discrimination, the marginal revenue for each additional student is equal to their willingness to pay, as the university charges them the maximum price they are willing to pay. Therefore, the marginal revenue curve in this scenario will coincide with the demand curve.
Additionally, the average revenue is simply the total revenue divided by the number of units sold. In perfect price discrimination, since the university charges the maximum price to each customer, the average revenue will also coincide with the demand curve.
Hence, the statement is true as in perfect, first-degree price discrimination, the marginal and average revenue curves for the university will be identical, and both curves will coincide with the demand curve.