Kieran’s kindergarten class listens to books read by their teacher during readin

Question

Kieran’s kindergarten class listens to books read by their teacher during reading time. Books that are read aloud are a collective consumption good (public good) for the class, as once the teacher starts reading all students are able to listen and none are able to prevent others from listening. An important problem facing the class is number of books that should be obtained. Suppose there are 5 children in the class and each of the five has the following utility schedules:

Books:         1      2     3      4      5

Isaac:           20   18   15   14    13

Kieran:        14   11    8      5      3

Harmony:    5      4     3      2      1

JJ:                   4       3    1       0    -1

Gwyneth:     3      2     0     -1    -2

Suppose that the marginal cost of a book is a constant $20 so that each student has to pay $4 each for each book.

Given that all of the students have different preferences for books, how do you suggest they decide how many books to obtain? Explain.

Given your suggestion in a), how many books will the class choose to obtain? Explain.

What is the socially optimal number of books obtained? Explain.

Assuming there are several different classes choosing several different quantities of books, suggest a way that the students can reconcile b) and c). Explain your answer.

Explanation / Answer

we will see the cost i.e $4 per book which student has to pay and compare it with the utility.

till the utility is more than the cost student will prefer reading book

Isaac -

for 1 book - utility is 20 and cost is 4

for 2 books- utility is 18 and cost is 8

for 3 books utility is 15 and cost is 12

for 4 books utility is 14 and cost is 16

Now in case of 4 books cost> utility so he will not prefer reading 4 books.Hence he prefer reading 3 books.

Similarly for others

Isaac: Prefers obtaining 3 books

Kieran: prefers obtaining 2 books

Harmony: prefers obtaining 1 book

JJ: prefers obtaining 1 book

Gwyneth: does not prefer obtaining even a single book.

Class will obtain 7 books in total by students as per the utility and cost comparision done earlier.

socially optimal number of books obtained will be 1 because except Gwyneth every other student wants to obtain 1 book minimum,

If there are several different classes choosing several different quantities of books, then there will be different total quanties which students are willing to obtain. then in order to reconcile b) and c) we will find the total number of books that the students are willing to obtain by the utility and cost comparision and the take the average of it eg- in case of one class 7 total books to be obtained and average is 7/5 i.e 1 book

similarly if there are many other classes we will obtain the total and take the average for socially optimal number of books.

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