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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.

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  • $\begingroup$ 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? $\endgroup$
    – Michael Greinecker
    May 22 at 10:05
  • $\begingroup$ @MichaelGreinecker Lindahl pricing? $\endgroup$
    – Casio
    May 22 at 12:58
  • $\begingroup$ 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 $c_2<25$). $\endgroup$
    – Michael Greinecker
    May 22 at 13:34
  • $\begingroup$ @MichaelGreinecker thanks. If you post this as an answer I will mark this resolved. $\endgroup$
    – Casio
    May 22 at 15:14

1 Answer 1

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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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