1. 1 Public Goods

2. 2 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 you 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. Private goods have the properties of rivalry and exclusivity.

3. 3 Demand In the private good case we said the market demand was the horizontal summation of each individual’s demand. The logic there was that once a unit was made available for sale only 1 buyer could get a benefit from the good. This would lead each buyer to bid on the unit in hopes of getting the unit. Ultimately the bid would match their willingness to pay for the unit. For a public good if a unit can be made available all can enjoy the benefit of the good. Maybe we will have a free rider problem with a public good. This is the idea that some may not pay for the public good because if others pay, the non-payers can get the benefits for free.

4. 4 Public good Wow, with a free rider problem maybe no one buys the good because they think others will buy. Maybe the government makes the good available to the public. How many units should the government make available? If we use the willingness to pay as a proxy for the benefits consumers get from the good then we can calculate the marginal benefit of each unit of the good. This MB is the demand for the public good. Let’s next turn to a numerical example where we will think of both a private good case and a public good case from the same example. As we consider the example we will just be concerned with the demand side of things initially. Then we will build in the supply side.

5. 5 example Quantity of goodAdam’s willingness to pay(WTP) Ben’s WTP 145 234 323 412 501

6. 6 Example – private good From the example, if we consider the good to be a private good here is how we have to think of the demand: Sellers of the private good think about the price at which to sell the good. At a price of 5 they would see Adam wanting none and Ben wanting 1 unit. The market demand at a price of 5 would yield a quantity demanded of 1 unit. But, if the price is 4 Adam will want 1 unit and Ben will want 2 units. So we have P = 4 Q = 3. Will follow he same logic on down the line (Just look at all the willingness to pay values as possible prices and add the quantities demanded by each to get the market demand – the horizontal sum.) We have the following private good demand curve PQ 51The Q = 1 comes from Ben 43The Q = 3 is 1 from Adam and 2 from Ben 35The Q = 5 is 2 from Adam and 3 from Ben 27can you see the rest of the story? 19 010

7. 7 Example – public good While each person might like to be a free rider, we can see how much each is willing to pay for the first unit. Since the government is providing the good we see in the first unit has value of $4 to Adam and $5 to Ben. Thus, the first unit is valued by $9 to all members of society. Similarly, the second unit has value of $3 to Adam and $4 to Ben. Thus the second unit is valued at $7 to all members of society. (So, at each Q add up the $ values from each person) The demand for the public good is PQ 91At Q = 1 Adam will pay 4 and Ben 5 72At Q = 2 Adam will pay 3 and Ben 4 53do you see the rest of the story? 34 15

8. 8 MC = MB rule for public goods So, the demand curve for a public good shows the marginal benefit in society for each unit of the good. Now we bring in the cost side of things but in only the context of public goods. The government as a producer can not get past the law of diminishing returns any differently than can any other producer. Thus the supply curve of the government is just a marginal cost curve and as we saw in the past, when returns are diminishing marginal cost is rising. To use the resources of the world wisely the government should make units up to the point where the marginal cost is equal to the marginal benefit. This way all units with MC MB do NOT get made.

9. 9 How much government should make available The demand for the public good is shown in the first two columns, where remember the price is really a statement about marginal benefit. The MC has been added here (and made for example sake) P (MB)QMC 911.50 723.75 535.00 346.60 159.00 Here we see the government should make available three units of the good. Any additional unit would have MC greater than MB, and this is bad because if we let the resources go elsewhere they will be more valued there.