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Rationing a limited quantity of parking spaces

Many "on-ground" university campuses sell parking permits to their students allowing them to park on campus in designated areas. Although most students complain about the relatively high cost of these permits, what annoys many of these students even more is that after having paid for their permits, vacant parking spaces in the designated lots are very difficult to find during much of the day. Many end up having to park off campus anyway, where permits are not required. Assuming the university is unable to build new parking facilities on campus due to insufficient funds, what recommendation might you propose that would remedy the problem of students with permits being unable to find places to park on campus?"

(Hint: Think in terms of demand and supply analysis and how a market functions.)

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The issue the students face here is a limited supply. At the current price, too many students are buying them, while the number of slots isn't sufficient to accommodate them. There is no equilibrium in this market - it is a classic shortage. This occurs when ...