Question

a. On the basis of the three individual demand schedules below, and assuming these three people are the only ones in the society determine the collective demand schedule on the assumption that the good is a public good. 

b. Use the public demand schedule above and the following supply schedule to ascertain the optimal quantity of this public good

Answer 1

Private demand is obtained by horizontal summation of individual demand curves but public demand is obtained by vertical summation of individual demand curves. Therefore:

At Qd= 1

price of individual 1 is $12

price of individual 2 is $16

price of individual 3 is $14

so at Qd =1, P= 12+16+14 = $42

similarly, at Qd =2,

price of individual 1 is $10

price of individual 2 is $14

price of individual 3 is $12

so at Qd =2, p = 10 + 14 + 12 = $36

And so on

Price	Qd
42	1
36	2
8 +12 + 10 = 30	3
6 + 10 + 8 = 24	4
4 + 8 + 6 = 18	5
2 + 6 +4 = 12	6
0 + 4 + 2 = 6	7
0 + 2+ 0 = 2	8

Optimal quantity is where Qd =Qs

So according to the tables, at price P = 24, Qd=Qs = 4

optimal quantity is 4