Final answer:
The visual appearance of the campus is a public good that is nonexcludable and non-rival. The benefit of the beautification initiative, as revealed by the survey, is $8,330. Based on the estimated benefit being greater than the cost, the college administrators should undertake the initiative.
Step-by-step explanation:
A public good has two key characteristics: it is nonexcludable and non-rival. Nonexcludable means that it is costly or impossible for one user to exclude others from using the good. Non-rival means that when one person uses the good, it does not prevent others from using it.
In this case, the visual appearance of the campus is nonexcludable because it is difficult to prevent students from enjoying the beautification projects, and it is non-rival because one student's enjoyment of the campus does not reduce the enjoyment for other students.
To determine the benefit of the beautification initiative, the administrators conducted a survey of the students' willingness-to-pay. The average willingness-to-pay, as revealed by the survey, is $17. Since there are 490 students, the total benefit of the initiative can be calculated by multiplying the average willingness-to-pay by the number of students: $17 * 490 = $8,330.
The estimated benefit of $8,330 is greater than the cost of $8,160, so the college administrators should undertake the beautification initiative.