Do we have our priorities in order? We trust our school aged children to be taught by dedicated teachers in our schools, but we pay those teachers only about $50,000 per year. At the same time, we watch pro-basketball games as entertainment —and we pay some of the players 400 times as much!
A: When confronted with these facts, many people throw their hands up in the air and conclude we are just hopelessly messed up as a society—that we place more value on our entertainment than on the future of our children.
(a) Suppose we treat our society as a single individual. What is our marginal willingness to pay for a teacher? What is our marginal willingness to pay for a star basketball player?
(b) There are about 4million teachers that work in primary and secondary schools in the United States. What is the smallest dollar figure that could represent our total willingness to pay for teachers?
(d) For purposes of this problem, assume there are 10 star basketball players at any given time. What is the least our total willingness to pay for star basketball players could be?
(e) Is our actual total willingness to pay for basketball players likely to be much higher than this minimum?
(f) Do the facts cited at the beginning of this question really warrant the conclusion that we place more value on our entertainment than on the future of our children?
(g) Adam Smith puzzled over an analogous dilemma: He observed that people were willing to pay exorbitant amounts for diamonds but virtually nothing for water. With water essential for sustaining life and diamonds just an item that appeals to our vanity, how could we value diamonds so much more than water? This became known as the diamond-water paradox. Can you explain the paradox to Smith?
B: Suppose our marginal willingness to pay for teachers (x1) is given by MWTP = A−αx1 and our marginal willingness to pay for star basketball players (x2) is given by MWTP = B −βx2.
(a) Given the facts cited above, what is the lowest that A and B could be?
(b) If A and B were as you just concluded, what would α and β be?
(c) What would be our marginal and total willingness to pay for teachers and star basketball players?
(d) Suppose A = B = $100 million. Can you tell what α and β must be?
(e) Using the parameter values you just derived (with A = B = $100 million), what is our total willingness to pay for teachers and star basketball players?