Question

Q5. Consider 3 consumers, Al, Bo and Cass, who are living in a suburb in western Sydney. The consumers’ demand curves for fireworks displays are given by the following equations, where Q is the quantity measured as the number of shows and P is the price (in dollars) per show.

?^D_A =5−3?

?^D_B =10−2?

?^Dc =5−?

Where ?^D_Ais the demand curve for Al, ?^D_B is the demand curve for Bo, and ?^Dc is the demand curve for Cass.

a. Explain why fireworks displays would be considered a public good.

b.If fireworks displays could be put on my individuals and the cost of putting on a fireworks display was $4 per show (i.e. MC is constant at $4)– how many fireworks displays would be put on? Explain.

c. Explain why 4 fireworks displays is the socially optimal number of displays (assuming we can only have whole numbers of displays). How could this be achieved?

Answer 1

a)

This is a public good, as it is for the benefit of the society as a whole. There is fun element in this which makes people feel good and thus adds on to their well being.

b)

	Qa	Qb	Qc
P	5 - 3P	10 - 2P	5 - P
0	5	10	5
1	2	8	4
2	0	6	3
3	0	4	2
4	0	2	1
5	0	0	0

Above table provides different quantities demanded as per different prices.

If MC = 4, then price should be set as 4

If P = 4, total demand = 0+2+1 = 3

As per the demand 3 fireworks display should be put on.

c)

Socially optimal number is when social benefit equals social costs

	(5 - Qa)/3
Qa	P
1	1.33
2	1.00
3	0.67
4	0.33
5	-

	(5 - Qc)
Qc	P
1	4
2	3
3	2
4	1
5	-

	(10-Qb)/2
Qb	P
1	4.5
2	4
3	3.5
4	3
5	2.5

As per the tables above, and as we can take only whole numbers 4 fireworks display is the optimal number. Taking 5 as the number will reduce the P to zero in two cases Qa and Qc.