ECON 100A Public Goods and Coase theorem
April 29-May 2
Part I Public Goods
A good is a (pure) public good if once produced it meets two criteria: 1. Non-rival - A good is non-rival if consumption of additional units of the good involves zero social marginal costs of production. 2. Non-excludable - A good is non-excludable if it impossible, or very costly, to exclude individuals from benefiting from the good. Taking these two criteria we can categorize goods into four groups.
What are some examples of goods in each category?
Private goods: hot dogs, cars, houses
Club goods: bridges, swimming pools, satellite television transmission (scrambled) Common goods: fishing grounds, public grazing land
Public goods: national defense, mosquito control, justice
Exercise 1: True/False/Uncertain
American National Monuments (like the Lincoln Memorial) are no public goods, because not everyone enjoys the benefits from them since they are located in one particular place.
A public good is defined as a good that is no-excludable and no0rival. The fact that not everyone has the opportunity to enjoy the benefits of national monuments is irrelevant. It only matters that, if someone decided to enjoy the benefits of them, they could not be excluded, and that one person's consumption of the good does not diminish the value of another's consumption. That said, national monuments still may not be public goods, Have you ever been tot he Lincoln Memorial on a Friday afternoon in the spring? Or on the fourth of July? Seems pretty rival to me... Of course, if people derive benefits simply from knowing that such monuments exist, then they are public goods in the truest sense.
One example of a public good is mosquito spraying and we'll explore that more now.
Exercise 2: Suppose there are only two individuals in society. The demand curve for mosquito control for person A is given by qa=100-p
For person B the demand curve for mosquito control is given by qb=200-p
1. Suppose mosquito control is a pure public good; that is, once it is produced, everyone benefits from it. What would the optimal level of this activity if it could be produced at a constant marginal cost of $120 per unit?
p=300-2q if p<100
p=200-q if 100<p<200
MC =120=p, intercept at p=300-2q=120, therefore q=90
2. If mosquito control were left to the private market, how much might be produced?
If both people free ride, then no crop spraying might be produced. Either way person A will never buy any as cost >100. Person B could buy 200-120=80.
3. If the government were to produce the optimal amount of mosquito control, how much will this cost? How should the tax bill for this amount be allocated between the individuals if they are to share it in proportion to benefits received from mosquito control?
Cost to government - 120*90=10,800. Tax on A Ta*90=10*90=900, tax on B, Tb*90=110*90=9900. This covers the government's costs and is in proportion to marginal valuations.
Exercise 3: On the lower east side of New York there is a small village called Alphabetown. Here three people live: A, B, and C. Each of them have a demand for park space that can be described by these demand functions: QA = 200 -P
QB = 100 -P
QC = 50 -P
Q represents the number acres of park demanded. An acre of park land can be purchased for $120. If a park is built in Alphabetown, everyone will have access to it, and there will be no congestion problems.
1. Given the demands for park space of the citizens of Alphabetown, what is the optimal size of the park?
Since this park is a public good, to arrive at a market demand curve the three demand curves must be added vertically. First, rewrite the demand equations in terms of price (interpreted as willingness to pay) as a function of quantities: P = 200 - QA
P = 100 - QB
P = 50 - Qc
Adding, we get...
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