Question

On the basis of the three individual demand schedules in the following table, and assuming these are the only three people in the society, determine (a) the market demand schedule on the assumption that the good is a private good and (b) the collective demand schedule on the assumption that the good is a public good.

P($)	$Q_d\left(D_1\right)$	$Q_d\left(D_2\right)$	$Q_d\left(D_3\right)$
8	0	1	0
7	0	2	0
6	0	3	1
5	1	4	2
4	2	5	3
3	3	6	4
2	4	7	5
1	5	8	6

Short answer

a. Market demand schedule for the private good.

Price($)	Market Demand for the private good
8	1
7	2
6	4
5	7
4	10
3	13
2	16
1	19

b. Collective demand schedule for the public good

Price($)	Collective demand for the public good
19	1
16	2
13	3
10	4
7	5
4	6
2	7
1	8

Step-by-step solution

Explanation for part ‘a’ 

In the case of a private good, the market demand schedule is calculated by adding the individual demands for the private good at each level of price. For example, At an $8 price, the sum of individual demands (D1, D2, and D3) gives the market demand at the said price; that is, the market demand equals 1 unit of the private good (=0+1+0).

Similarly, the market demand at each price level can be calculated to form the whole schedule as shown below:

P($)	QdD1	QdD2	QdD3	Market Demand (MD=$D_1+D_2+D_3$
8	0	1	0	1(=0+1+0)
7	0	2	0	2(=0+2+0)
6	0	3	1	4(=0+3+1)
5	1	4	2	7(=1+4+2)
4	2	5	3	10(=2+5+3)
3	3	6	4	13(=3+6+4)
2	4	7	5	16(=4+7+5)
1	5	8	6	19(=5+8+6)

Explanation for part ‘b’

In the case of a public good, the collective demand schedule is calculated by estimating the total worth of a unit of the good for the consumers; that is, by adding up the willingness to pay of different individuals for different quantities of the public good, we get the demand.

For example, using the given table, we will find the prices at which the three consumers are demanding the 1st unit of the good; that is, the 1st consumer demands 1st unit at $5 price, 2nd consumer demands at $8, and 3rd consumer demands at $6. The total price willingness gives the worth of the good, which is equal to $19 (=5+8+6).

Similarly, we can find the worth of the two units and so on, as shown below.

1st consumer’s willingness to pay($)	2nd consumer’s willingness to pay($)	3rd consumer’s willingness to pay($)	Total price willingness ($)	Demand for the public good
5	8	6	19(=5+8+6)	1
4	7	5	16(=4+7+5)	2
3	6	4	13(=3+6+4 )	3
2	5	3	10(=2+5+3 )	4
1	4	2	7(=1+4+2)	5
0	3	1	4(=0+3+1)	6
0	2	0	2(=0+2+0)	7
0	1	0	1(=0+1+0)	8