<p>A situation in which the public good is not provided is inefficient; it is possible to make both consumers better off. To see this, let <span class="math-container">$c_1$</span> and <span class="math-container">$c_2$</span> be to numbers such that <span class="math-container">$c_1+c_2=100$</span>, <span class="math-container">$c_1&lt;80$</span> and <span class="math-container">$c_2&lt;25$</span>. Such numbers are necessarily positve, for <span class="math-container">$c_1=100-c_2&gt;100-25$</span> and <span class="math-container">$c_2=100-c_1&gt;100-80$</span>.</p>
<p>Now, provide the public good, let consumer <span class="math-container">$1$</span> pay <span class="math-container">$c_1$</span>, and let consumer <span class="math-container">$2$</span> play <span class="math-container">$c_2$</span>. Then the public good can be funded, since <span class="math-container">$c_1+c_2=100$</span>. Consumer <span class="math-container">$1$</span> is better off than before, because <span class="math-container">$80-c_1&gt;0$</span>; their personal benefit exceeds their personal cost. Consumer <span class="math-container">$2$</span> is better off than before, because <span class="math-container">$25-c_2&gt;0$</span>; their personal benefit exceeds their personal cost too.</p>

CC BY-SA 4.0
2022-05-22T18:05:29.160Z
2022-05-22T18:05:29.160Z
Michael Greinecker
<p>Suppose there are two consumers in the whole economy. If the cost of a public good is 100, and the maximum willingness to pay for a public good for consumers 1 and 2 is 80 and 25, would it still be efficient to provide public good?</p>
<p>Here is my confusion:</p>
<ul>
<li><p>Because total willingness is greater than the cost, the good should be efficient to provide.</p>
</li>
<li><p>If I think of max willingness to pay as benefit derived, then total benefit &gt; total cost, so it would be inefficient because they need to be equal.</p>
</li>
</ul>

CC BY-SA 4.0
2022-05-22T10:05:07.073Z
Can you think of a way to distribute the cost of producing the public good among the two consumers such that both are better off with the good being provided?
Michael Greinecker
CC BY-SA 4.0
2022-05-22T12:58:59.743Z
@MichaelGreinecker Lindahl pricing?
Casio
CC BY-SA 4.0
2022-05-22T13:34:49.050Z
Not that complicated. You just need to find two positive numbers $c_1$ and $c_2$ such that $c_1+c_2=100$, $c_1<80$, $c_2<25$. Then, if consumer $1$ pays $c_1$ and consumer $2$ plays $c_2$, then the public good is funded (since $c_1+c_2=100$) and both consumers get more benefit from the public good than the cost they have to bear (since $c_1<80$ and $c_2<25$).
Michael Greinecker
CC BY-SA 4.0
2022-05-22T15:14:36.007Z
@MichaelGreinecker thanks. If you post this as an answer I will mark this resolved.
Casio
<microeconomics><public-goods>
Efficiency Criteria to provide a public good?
Casio
# Efficiency Criteria to provide a public good?

(Asked by: username_0 on 2022-05-21)

Suppose there are two consumers in the whole economy. If the cost of a public good is 100, and the maximum willingness to pay for a public good for consumers 1 and 2 is 80 and 25, would it still be efficient to provide public good?

Here is my confusion:

* Because total willingness is greater than the cost, the good should be efficient to provide.
* If I think of max willingness to pay as benefit derived, then total benefit > total cost, so it would be inefficient because they need to be equal.

**Tags:** microeconomics, public-goods
> **Comments:**
> **username_1**: Can you think of a way to distribute the cost of producing the public good among the two consumers such that both are better off with the good being provided?  
> **username_0**: @MichaelGreinecker Lindahl pricing?  
> **username_1**: Not that complicated. You just need to find two positive numbers $c_1$ and $c_2$ such that $c_1+c_2=100$, $c_1<80$, $c_2<25$. Then, if consumer $1$ pays $c_1$ and consumer $2$ plays $c_2$, then the public good is funded (since $c_1+c_2=100$) and both consumers get more benefit from the public good than the cost they have to bear (since $c_1<80$ and $c_2<25$).  
> **username_0**: @MichaelGreinecker thanks. If you post this as an answer I will mark this resolved.  

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## 1 answers

### Answer by username_1 on 2022-05-22. Score: 3 | Accepted answer

A situation in which the public good is not provided is inefficient; it is possible to make both consumers better off. To see this, let $c\_1$ and $c\_2$ be to numbers such that $c\_1+c\_2=100$, $c\_1<80$ and $c\_2<25$. Such numbers are necessarily positve, for $c\_1=100-c\_2>100-25$ and $c\_2=100-c\_1>100-80$.

Now, provide the public good, let consumer $1$ pay $c\_1$, and let consumer $2$ play $c\_2$. Then the public good can be funded, since $c\_1+c\_2=100$. Consumer $1$ is better off than before, because $80-c\_1>0$; their personal benefit exceeds their personal cost. Consumer $2$ is better off than before, because $25-c\_2>0$; their personal benefit exceeds their personal cost too.


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