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Lecture 5

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**Tragedy of the Commons Springfield Aquarium as common property**

The city has a park that never gets crowded. People can do activities inside. The city council is contemplating an aquarium. Let me ask you a simple question: assuming that all residents have identical tastes, how much will they be willing to pay for it?

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**Tragedy of the Commons Springfield Aquarium as common property**

The answer is zero! Why? This is exactly the problem of the elimination of social gains due to overuse of common property. The problem is also called “the dissipation of rents”.

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**Solution to Commons Problem**

So what’s exactly the problem? Market outcome is not socially optimal But why does the The First Fundamental Theorem of Welfare Economics not hold here? How went wrong in this example?

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**Compare with the monopoly**

You may say: wait a minute. The graph looks so much similar to the graph for a monopoly firm. Conflict: monopoly leads to a deadweight loss. So how come the intersection of MR and MC curves provides a socially optimal outcome in the case of aquarium?

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**Solution to Commons Problem**

Admission fees Graphical analysis Private ownership (in fact, all sorts of assignments of the property rights)

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Difference Pays We now assume that tastes differ across individuals. Specifically, people have different values on picnics. Dissipation of rents still occurs, but in a different way. Remedies can only reach sub-optimal outcomes. (see graph) Public versus private ownership

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**Some important common resources**

Clean air and water Congested roads Oil deposits Fish, whales and other wildlife

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**Collapse of Atlantic Cod Stocks Off the East Coast of Newfoundland in 1992**

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**Conclusion: The importance of property rights**

The market fails to allocate resources efficiently when property rights are not well established (i.e. some item of value does not have an owner with the legal authority to control it).

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**Conclusion: The importance of property rights**

When the absence of property rights causes a market failure, the government can potentially solve the problem.

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**Case study: tree poaching**

Can we privatize the trees? The incentive is the key to the problem.

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**Case study: Pricing rhinos?**

some economists have found that private ownership is a great way of conserving wildlife. But there's a problem. Property rights have to be enforced, and the cost could be high. Me, $10K only?

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**The Tragedy of the Commons**

Consider an agricultural village in which villagers graze their cows on a common field. Let p be the cost of a cow. The average value of the milk produced is AR(c)=100-c, where c refers to total number of cows. AR is decreasing because adding a cow reduces existing cows’ productivity. The total value will therefore be

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**The Tragedy of the Commons**

Now suppose a central planner makes the decision on how many cows to put on, and his/her goal is to maximise the profit. The profit maximising problem is: The FOC is

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**The Tragedy of the Commons**

This part, part (A), is negative, representing the loss due to reduced milk produced by existing cows This part, part (B), is positive, referring to the gain from the additional cow’s contribution

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**The Tragedy of the Commons**

Solving for the FOC:

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**The Tragedy of the Commons**

Now suppose there is no central planner, and every villager can access to the field and has to decide whether or not to use the common field. His/her consideration will reduce to: Only part (B) is considered for the additional joiner Part (A) is not a concern for the new joiner

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**The Tragedy of the Commons**

Solving for the new FOC: Which shows that the common field is overly exploited and not efficient.

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Section 14.2 Public goods

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Public Goods Good where one person’s consumption increases consumption available for others Nonexcludable Nonrivalrous

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**When to provide a public good? -- the case of fixed amount of G**

Suppose now the decision is for two roommates to decide to purchase a TV as a public good (G) or not. Settings: 2 roommates Incomes: w1 and w2 There is a private good, x, with market price = 1 There is only one public good G The 2 persons consume x1 and x2, respectively, and G together. They contribute g1 and g2 for the TV The cost of the TV is c

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**When to provide a public good? -- the case of fixed amount of G**

Their budgets are therefore: Assume that the utility function is Define that the reservation price (r1) of person 1 on G is the maximum amount that he/she is willing to pay to have the TV. So by definition, the following must be true:

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**When to provide a public good? -- the case of fixed amount of G**

The necessary condition for purchase of the TV to be a welfare improvement is that each person is making a contribution that is les than his maximum willingness to pay: The sufficient condition for purchase of the TV to be a welfare improvement is that the total amount that the roommates are willing to pay is at least as large as the cost of TV:

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**When to provide a public good? -- the case of fixed amount of G**

Note that the sufficient condition is for an welfare improvement, or a more efficient allocation of the goods, from the point of view of a central planner. It does not necessarily imply that they will purchase the TV. To see individual decisions, we need to conduct benefit-cost analysis at the individual level. That is, the sufficient condition carries a policy implication, but not a behavioural implication. The free-rider problem is an important consideration in an individual’s decision.

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**The free-rider problem**

A free-rider is a person who receives the benefit of a good but avoids paying for it. Since people cannot be excluded from enjoying the benefits of a public good, individuals may withhold paying for the good hoping that others will pay for it. The free-rider problem prevents private markets from supplying public goods.

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**The free-rider problem**

Let’s use the game theory to analyse the TV example: Suppose that each roommate’s wealth is $500, and each values the TV at $100 (ie, r1=r2=100), and the cost of the TV is $150. Check the sufficient condition: The game then looks like:

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**The free-rider problem**

Buy Buy not A 25 , 25 -50 , 100 100,-50 0 , 0 In each cell, the 1st number refers to the payoff of player A, and the 2nd number to B. From A’s point of view, the best strategy is always “buy not”, regardless of B’s decision. Same from B’s point of view. And they know each other’s point of view. They will end up with (0,0), which is not the most efficient outcome.

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**The free-rider problem**

So, what goes wrong? The answer is that they both like to be a free rider. However, if they can negotiate and ensure each other’s decision, they can reach the optimal outcome.

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**The free-rider problem**

Solving the free-rider problem The government can decide to provide the public good if the total benefits exceed the costs. The government can make everyone better off by providing the public good and paying for it with tax revenue. But it is not a easy job for the government.

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**The difficult job of cost-benefit analysis**

Cost benefit analysis refers to a study that compares the costs and benefits to society of providing a public good. In order to decide whether to provide a public good or not, the total benefits of all those who use the good must be compared to the costs of providing and maintaining the public good.

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**The difficult job of cost-benefit analysis**

P Supply Value for p2 Demand D2 Value for p2 D1 Q* Q

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**The difficult job of cost-benefit analysis**

A cost-benefit analysis would be used to estimate the total costs and benefits of the project to society as a whole. It is difficult to do because of the absence of prices needed to estimate social benefits and resource costs. For examples, the value of life, the consumer’s time, and aesthetics are difficult to assess.

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Hey, let’s vote! Voting could be a way for a group of individuals to reveal their aggregate preferences. But there exist some problems: It is possible that the aggregate preferences are not transitive. Eg: a majority prefer A to B, B to C, and C to A. So if the group is allowed to vote only once, the outcome depends on the order in which the choices are presented. Cannot reveal the magnitude of preferences

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