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Technical notes on public goods in environmental economics by prof. Gaudin. Public goods are classified based on their degree of excludability and subtractibility. The characteristics of public goods, their production and demand, and the challenges in providing them efficiently in the market. The document also discusses the role of the government in providing public goods.
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Public goods
Goods can be classified according to their degree of “excludability” and “subtractibility”. All goods are not pure public goods or pure private goods.
Subtractibility (Rivalry)
LOW HIGH
Excludability
DIFFICULT (^) Public goods Common Property Resources EASY Toll goods (or Club goods)
Private goods
Pure public goods have 2 characteristics that separate them from private good:
Most public goods may have a some degree of subtractibility and there could be ways to exclude people. But the cost of excluding is usually very high compared to the MC of use. [Examples of public goods are numerous: Defense and security, parks, infrastructure, air, basic research...]
Pure public goods are extreme examples of positive externalities because there is no marginal cost of having more people to enjoy the good.
Society’s demands for public goods are found by vertically summing all individual demand curves. [Note that this is quite different from private goods for which market demand was found by adding the quantities demanded at each price - i.e. by horizontally summing individuals demand curves].
Why? Since each person will be able to consume the same quantity of the public good without reducing other’s possibilities, we should add up each person’s willingness to pay to get total demand. The efficient amount of public good to be provided is determined given the marginal cost of producing the public good and the marginal benefit to the people (the sum of each individual’s marginal benefits).
Example: Suppose we have two individuals with the following demand for a park in terms of acres:
P1=200-10Q (=MB1) P2=100-10Q (=MB2)
Suppose MC is $150 per acre and constant.
To find the MBsociety, we add up each individual’s willingness to pay. Careful: with only two individuals, the total demand will have a kink since only individual 1 will ever want more than 10 acres of park. The easiest is to graph it:
Q. What is the efficient number of acres for the park? For Q<10 MBsociety=MB1+MB2=300-20Q. MC= MC=MB1+MB2 ⇒ 300-20Q=150 ⇒ Q=150/20 = 7.5 acres. (Q*) [Check if less than 10]
Why is a public good undersupplied by the private sector?
If P=MC of production (competitive market→ lowest possible private provision price), assuming that individuals would reveal their demand, individual 1 would demand 150=200-10Q ⇒Q=50/10= Individual 2 would not be willing to oay the $150 per acre for ANY size park since 150=100-10Q ⇒Q must be negative.
Therefore, if the good were to be supplied in the market, only individual 1 would pay. Individual 2 would take advantage of whatever size park without paying since she cannot be excluded...In this case, only 5 acres would be reserved for the park, causing a dead weight loss. – See graph.
It gets worse: Often, public goods have large costs associated with them so no single individual is willing to pay enough to have the good provided. Even if one entity would be willing to pay the cost for some positive amount, knowing that they could take advantage of a park that others pay for, they would not be willing to pay. I Here, individual 1 may not even want to pay the $150. Especially if there is imperfect information and she cannot tell whether someone else is willing to pay for the park. Since there is no way to exclude people from using the public good and more individuals can enjoy the public good at no extra cost (if there is no congestion), most people would rather be free
Q (acres)
MBsociety
DWL of private provision to individual 1