Question

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.

Individual #1 Individual #2 Individual #3 Demand Curve- Public Good
Price Qd Price Qd Price Qd Amount Society is Willing to Pay Qd
$16 0 $16 1 $16 1 $ 1
14 1 14 2 14 2 2
12 2 12 3 12 3 3
10 3 10 4 10 4 4
8 4 8 5 8 5 5
6 5 6 6 6 6 6
4 6 4 7 4 7 7
2 7 2 8 2 8 8
Use this public demand schedule above and the following supply schedule to ascertain the optimal quantity of this public good.

P Qs
$20 10
18 8
16 6
14 4
12 2
10 0
The Optimal quantity = _____

Answer 1

The optimal quantity of a public good is found where the collective demand equals the supply. Societal demand is determined by summing the quantities demanded at each price by all individuals. The point of equilibrium represents the ideal amount that balances cost and societal willingness to pay.

Step-by-step explanation:

To determine the optimal quantity of a public good from a collective demand schedule and a supply schedule, we look for the point where the collective willingness to pay (demand) equals the cost of supplying that good (supply). The collective demand merges the quantities demanded at each price level by all individuals in the society. Since each individual's demand for a public good could be entirely satisfied without affecting the satisfaction of others, we sum the quantities that each individual is willing to pay for at each price point to find the societal demand.

For instance, at the price of $16, individuals #2 and #3 are willing to pay for 1 unit each, hence the societal demand at $16 is 2 units. At the price of $14, since individual #1 is willing to pay for 1 unit, and individuals #2 and #3 are willing to pay for 2 units each, the total societal demand is 5 units.

This process is continued until all price points are calculated. Comparing the final collective demand schedule with the supply schedule, the optimal quantity of the public good occurs where the societal willingness to pay matches the quantity supplied. We determine this by looking for the closest price where the quantity demanded equals or exceeds the quantity supplied without going over the cost to provide those units.