More on public goods 1. For cost of exclusion, the legality of exclusion is irrelevant. We are considering only physical possibility of exclusion -

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1 More on public goods 1. For cost of exclusion, the legality of exclusion is irrelevant. We are considering only physical possibility of exclusion - what is the value of the resources that must be expended to prevent someone from using it. 2. The two definitions of complete nonrivalness (the one in the book and the one in the notes) are equivalent. If the marginal cost (to society) of providing a unit of the good to an additional user is zero, then that means that no one is losing anything by that unit being given to that consumer. This implies that that same unit can still be consumed by another agent. Conversely, if a unit provided to an additional agent does not prevent it from being consumed by another agent, then there is no marginal cost of providing that unit to an additional agent. 3. Goods that have a positive price typically have a relatively low cost of exclusion. However there are exceptions. For instance, it is difficult to prevent people from copying many recordings, yet the CD s have a positive price. Even ignoring legal considerations, some people who don t care about breaking a law would rather pay for the CD than go to the trouble of copying it. 1

2 The free rider problem for public goods Radio broadcast provision Cost, benefit MB2 MB1 MC=SMC MBT 0 Q1 Q2=Qe Q* Quantity Consider the above graph representing the marginal costs and marginal benefits to two individuals from listening to a radio broadcast. Each person gets benefit from the total amount of radio broadcast provided; it does not matter to them who has paid for it. The marginal cost curve is the same for both agents, and represents how much it costs to get an additional unit of the radio broadcast. To analyze the choices of the different agents, we must use ideas from game theory. This is because there is no market for the positive externality generated by the public good. This externality arises because each agent s contribution to provision also gives benefit to the other agent. (Note that for simplicity we are using only two agents, but the analysis could be extended to three or more). Each agent s choice of how much to contribute is called a strategy. A strategy is a plan of action which specifies what to do in every possible situation, given what the agent knows. In this radio contribution game, we assume that no agent knows the other s contribution when deciding how much to contribute. They simultaneously decide on an amount to contribute. Each possible strategy profile yields a payoff for each player. The payoff to a player can be represented by the area under their marginal benefit curve up 2

3 to the quantity of total contribution, minus the area under their marginal cost curve up to the quantity they contributed. The equilibrium concept we will use is Nash equilibrium. A profile of strategies (one for each player) constitutes a Nash equilibrium if each player s strategy is optimal given the other player s strategy. That is, the player s Nash equilibrium strategy generates the highest payoff of all possible strategies, given that the other player is playing its Nash equilibrium strategy. The Nash equilibrium can be viewed as a kind of prediction of what outcome will occur if the players are rational. First analyze the problem with two discrete choices for each player, high or low contribution. The game is an example of a prisoner s dilemma game. There is one pure strategies equilibrium in dominant strategies, but it is inefficient - both players could do better by coordinating on playing high, whereas playing low is a dominant strategy for each player. Now move to the game depicted by the graph, with continuous strategy sets. If the marginal benefits and marginal costs are as in the graph above, then the unique Nash equilibrium has agent 2 (the one with the higher marginal benefit curve) contributing up to where MB 2 intersects MC, and agent 1 contributing nothing. This allocation is inefficient. The efficient allocation would have a total contribution where the total MB curve (the vertical sum of the two MB curves) intersects the MC curve. Because the agents do not take into account in their contributions the benefit to the other agent from their contribution, the equilibrium amount is less than the efficient amount. Show that the allocation is a Nash equilibrium. If agent 1 gives 0 contribution, then agent 2 does best to give Q 2. This is because agent 2 prefers to contribute as long as the marginal benefit from an additional unit of contribution exceeds the marginal cost, given that agent 2 is contributing zero. If agent 2 contributes Q 2, then agent 1 s best response is to contribute zero. This is because at the level Q 2 of contribution, agent 1 s marginal cost of contributing an additional unit is greater than the marginal benefit to agent 2 of contributing an additional unit. Agent 1 therefore prefers to contribute nothing. Thus the allocation (0, Q 2 ) is a Nash equilibrium. Show that it is the only Nash equilibrium. Agent 1 will never contribute any amount above the quantity Q 1 at which its marginal benefit curve intersects its marginal cost curve (such strategies are called dominated as no matter what agent 2 does, there is a better strategy for agent 1). Suppose that agent 1 contributes some amount Q greater than zero, and less than Q 1. Agent 2 s best response is to contribute until the sum of the contributions equals Q 2 ; thus agent 2 contributes Q 2 Q > 0. But given that agent 2 contributes Q 2 Q, the best response for agent 1 is to contribute Q 1 (Q 2 Q) = Q + Q 1 Q 2 or zero, whichever is larger (since 3

4 negative contributions cannot be made). But since Q 1 < Q 2 by assumption, Q + Q 1 Q 2 Q, and since we have assumed Q > 0, 0 Q. Therefore Q is not a best response by agent 1 to agent 2 s choice of Q 2 Q. Thus, since there is no Q > 0 that is player 1 s best response to player 2 s best response to Q, no Q > 0 for player 1 can be part of a Nash equilibrium. Therefore the only Nash equilibrium is (0, Q 2 ). Note that 1. The equilibrium allocation is not efficient. Both players would be better off if more of the public goods were provided. The efficient total quantity of provision is where the total MB curve intersects the MC curve. 2. Agent 1 is free-riding on agent 2 s contribution. If agent 1 were alone in listening to the broadcast, it would contribute Q 1. But since agent 2 also listens to the broadcast, agent 1 contributes nothing but gets to enjoy Q 2 > Q 1 of broadcast units. When is private provision likely to overcome the free rider problem? Cost, benefit MB2 MB1 MBT MC=SMC Qe=Q* Quantity 4

5 Some individuals care more than others. When one individual gets a large benefit from the public good and all other individuals get very little benefit from the public good, it can be efficient to have the first individual pay the entire contribution towards the public good. Consider the graph below, depicting benefits and costs of provision of radio broadcasts. Agent 1 cares so little about radio broadcast provision that the sum of the two agents marginal benefit curves intersects the marginal cost curve at the same place as agent 2 s marginal benefit curve. Thus the efficient amount of radio broadcast provision is also the equilibrium amount. In Nash equilibrium, agent 2 will provide Q e = Q units of radio broadcast and agent 1 will provide nothing. This is the efficient amount of radio broadcast provision in this case. Some agents are altruistic - they care about the well-being of other agents as well as themselves. Brunner (1998) studied public radio stations and found that contributions do not decrease by much as the number of listeners increases. Traditional theory on public goods predicts that people would contribute less as the number of listeners increases, because as the number of listeners increases, it becomes more likely that others will pay - so each individual can expect to free-ride more. The fact that contributions do not decrease much suggests that individuals continue to pay what they feel is an appropriate amount (perhaps related to the benefit they get from listening) regardless of the number of other listeners. Warm glow model - assumes that agents care both about the total amount of public good and about their own contribution to it - they get a benefit from their own contribution. Under this model, individuals will contribute more to a public good than when individuals are assumed to care only about the public good quantity. An example of a partially public good - internet access Internet access has some aspects of a public good. It is mostly nonrival, but subject to congestion if the number of users gets very high. There have been occasions when the congestion affected people, like at the worst period of the financial crisis - people were on the internet looking for news about credit. But most of the time congestion is not a problem. However the cost of exclusion is relatively low. People must gain access through a server. A server is an organization that has a licence to give internet access to other agents through its computers. Examples of servers are Aol, Time Warner Road Runner, all universities (allowed only to give access to their own students, faculty and staff). The server can easily exclude someone, as users are identified by a code, and can have their access blocked. Currently there is both public and private provision of internet. Originally it was completely publicly provided by the the US government. It started in the 70 s as a military communication network, then was extended (in Arpanet) to universities and some other semi-government organizations. At that point, users 5

6 would only pay a fixed price of the technology (the cost of installing the cable to hook up) and could use the service almost for free. Commercial use was illegal. From the late 80s to early 90s, Congress decided to open up internet access to private companies and to allow private companies to act as servers. Now that it is used all over the world, other governments make laws about how it can be used in their countries, but must abide by the rules of the international governing board. A typical consumer or firm gets access to the internet through a server, usually paying a fixed monthly fee which is only rarely related to the number of minutes used (It used to be that people paid for a number of minutes - there was significant congestion because capacity was low. But then the capacity of the internet expanded relative to demand). The market for internet access is close to competitive. This can be seen from the fact that the price of an additional minute of internet service is typically close to the marginal cost of zero. The price of an additional minute of internet service is close to zero because network congestion is relatively rare. The Federal Communications Commission has recently proposed a set of regulations on internet providers that, among other things, mandate net neutrality. This means that internet providers would be required to treat all content in the same way with regard to transmission speed - they could not discriminate among different content. The same principles would hold for wireless networks. For example, a carrier could not ban file-sharing activity on its wireless networks (which AT&T does now). Would there be an interest in having alternate internet networks (other than world wide web)? There are some alternate networks now - for reasons of security, avoiding spam, government control of information. It is possible that some servers would eventually choose to block off their network. Consumers would be willing to pay for the service because it would limit spam and viruses. But the company could also limit news and other information from getting to its users. This is one thing that the government seeks to prevent in creating new regulations. There is a debate about how to reach an efficient allocation in the internet market. The Bush administration believed that (as the Coase idea would predict) by simply assigning property rights and allowing the market to work, an efficient outcome would be reached. This would allow service providers to close off access to certain users - for example big companies could shut out news that they don t like. The Obama administration is proposing rules that would require service providers to give equal access to all types of use. This is a rule that preempts something that would be expected to happen if the rule didn t take effect. The advantage of having many separate networks (the Bush idea) that people pay for is that people would get fast access to pages that they like. The dis- 6

7 advantage is that they would be blocked from viewing anything the network operators find undesirable. The advantage of having one unified network (the Obama idea) is that people have easier access to all possible websites. The disadvantage is that at times access may be slow. 7