Someone please explain how the \"Willingness to pay\" is 42,36,30,24,18,12,8,4 A

Question

Someone please explain how the "Willingness to pay" is 42,36,30,24,18,12,8,4

Also how is optimal quantity: 2

I would like to see the math involved and not just through text.

Individual #1 Individual #2 Individual #3 Public Demand Amount Society is 42 36 30 24 18 12 8 Price Qd Price Qd Price Qd Qd Willing to Pay $16 $16 $16 12 12 12 10 10 10 6 6 6 6 6 Use the public demand schedule above and the following supply schedule to ascertain the optimal quantity of this public good. Quantity Supplied 10 Price $44 42 40 38 36 34 0 Instructions: Enter your answer as a whole number. Optimal quantity

Explanation / Answer

If one analyze the individual demand schedule then it can be seen that for 1 unit individual 1 can pay $16 while individual 2 can pay $10 while individual 3 can pay $16.

These three individuals constitute the society.

So,

Maximum willingness to pay of society for 1 unit = Maximum willingness to pay of individual 1 for 1 unit + Maximum willingness to pay of individual 2 for 1 unit + Maximum willingness to pay of individual 3 for 1 unit

Maximum willingness to pay of society for 1 unit = $16 + $10 + $16 = $42

So, society is willing to pay $42 for 1 unit.

Similarly,

If one analyze the individual demand schedule then it can be seen that for 2 units individual 1 can pay $14 while individual 2 can pay $8 while individual 3 can pay $14.

These three individuals constitute the society.

So,

Maximum willingness to pay of society for 2 units = Maximum willingness to pay of individual 1 for 2 units + Maximum willingness to pay of individual 2 for 2 units + Maximum willingness to pay of individual 3 for 2 units

Maximum willingness to pay of society for 2 units = $14 + $8 + $14 = $36

So, society is willing to pay $36 for 2 units.

In similar fashion other willingness to pay can be ascertained.

Case II

How to calculate optimal quantity?

Optimal quantity is that quantity at which society's willingness to pay is equal to supply price.

If we analyze public demand schedule, we can see that society's willingness to pay is $36 for 2 units of public good.

Now, if we analyze supply schedule, we can see that 2 units can be supplied at $36.

Thus, at 2 units of public good, society's willingness to pay ($36) is equal to supply price ($36).

Hence, the optimal quantity is 2 units.

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