Public Goods

A public good is one that is nonrival and nonexclusionary in consumption. Nonrival means that when you consume the good it does not diminish the availability for me to consume the good. An example would be radio signals. When turn on your radio it does not stop me from doing the same and listening to the same station. Nonexclusionary means that when the good is provided no one can be excluded from consuming it. Once radio waves are out there they are out there for all. Most goods and services we have (implicitly) considered this term are private goods that do not have the characteristics mentioned here.

Demand In the private good case we said the market demand was the horizontal summation of each individuals demand. The logic there was that at a given price each consumer decided how much to consume on there own. For the public good, all consumers consume the same amount, although each may be willing to pay a different amount for additional units of the good. Constructing the demand for a public good then is NOT the horizontal sum. It is the vertical sum. This means that at each quantity we have to see how much in total consumers as a group are willing to pay.

Say the demand for each of three people is, respectively, p1 = 30 – q1,p2 = 30 – q2, p3 = 30 – q3(note we have identical demands, although this may not always be the case). As a private good you add the demands horizontally by first re- expressing the demands in Q form, like q1 = 30 – p1, q2 = 30 – p2, q3 = 30 – p3, and then total demand is Q = q1 + q2 + q3 = 90 – 3p. Note if p = 1 the total market demand is 87 and each individual will demand 29 units.

In the public good case the total demand is P = p1 + p2 + p3 = 90 – 3q. Note if q = 1 the total amount folks are willing to pay is 87 and each person is willing to pay 29. Q $ Each individuals demand Total demand

Say that each unit of the public good can be supplied at a MC = 54. Note that each individual alone does not value even 1 unit enough to cover the MC. But, as a group, the three have evaluations of the product above or equal to the MC up to 12 units. We see this by setting 90 – 3q = 54, or q = (90 – 54)/3= 12. Q $ MC = units is considered the socially optimal level of output. These units are valued as much or more as what it cost to make the units. Note each person would pay 18 for each of the 12 units, while they would be willing to pay more than 18 on some of those units so each person gets Consumer surplus =.5(30 – 18)12 = 72, for a total of 3(72) = 216.

A point I want to make clear here is that if each is identical and if on the last unit each is willing to pay $18 lets collect 18 from each as a tax on each unit. Then the surplus each gets is.5(30 – 18)12 = 72. Lets think about one of the three saying they have no value from the public good (which is untrue, but how can we know for sure?). The demand would then only be p = q and set equal to MC = 54 we would have solution q = (60 – 54)/2 = 3. So only 3 units of the public good would be provided. The two who pay would each pay 27 per unit ( p = 30 – 3) and each would have consumer surplus =.5(30 – 27)3 = 4.5 for a total from the 2 = 9.

Now, the one who said they have no need for the public good actually gets a benefit or consumer surplus =.5(30 – 27)3 + 27(3) = The individual has an incentive to be a free rider because they benefit more (85.5 to 72), while as a group the total consumer surplus is smaller (216 to 94.5). Each individual may chose to be a free rider and then no units of the good will be produced.

The logic of this lesson suggests that there is a legitimate reason for the government to tax to raise funds to provide some public goods. Of course, there will probably always be debate on which public goods the government should provide. By the way, Another context for this would be a professional sports league and the league doing national advertising. The national advertising is like a public good for each team. Each team might have an incentive to be a free rider. But, maybe the league charges each the same amount for the advertising campaign.