Question

Suppose the cost to build the park is $24 per acre and that the residents have agreed to split the cost of building the park equally. If the residents vote to determine the size of park to build, basing their decision solely on their own willingness to pay (and trying to maximize their own surplus), what is the largest park size for which the majority of residents would vote "yes?"

Answer 1

Answer: 2 Acres

Explanation:

All 3 residents of the town have agreed to split the cost of building the park equally. The cost is $24 so equally would be,

= 24/3

= $8

Each of them would have to pay $8.

If the cost per person is $8, how much will each person vote for.

Referring to the table;

Cedric will vote No for all acres because the $8 passes the amount Cedric is willing to pay for any size of Acre.

The majority vote can still be carried if the other 2 vote yes.

Sophia will not vote yes for anything more than 2 acres because Sophia's willingness to pay at $8 is for 2 acres alone.

At 2 acres, Amber's willingness to pay is $18 so Amber will vote yes as well.

Therefore if the majority vote is to be carried then the amount of acres should be 2.

Answer 2

Following are the calculation to the given question:

• If the inhabitants decide to split the bill evenly, each owner's share of the cost is $\frac{\ 24}{3}=\ 8$.
• Cedric's readiness to pay less than $\ 8$ per acre means that he'd never vote in favor of establishing a park.
• The other two residents should vote in support of establishing the park in order for the majority to vote yes.
• It will only happen for two acres of land since Sophia would not vote yes beyond that.
• As a result, the largest size whereby a majority of the voters could vote yes is 2 acres of property.

Therefore, the final answer is "2 acres".

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