 Welcome to the second technical lecture for the political economy of the environment. Today we're going to examine utilitarianism using social welfare functions. First we'll show why economists argue to restrict consumption when the environmental costs outweigh the private benefits. We'll also show why there is a case for stronger environmental protections if consumption is competitive. That is, if people care not only about their own consumption, but about how their level of consumption compares to the consumption of their peers. Economists often specify social welfare functions to explicitly state their assumptions on how to view economic and environmental trade-offs. Consider the social welfare function for a society of three people. This is the most general social welfare function. It simply says that the social welfare depends on the utility of people A, B and C. Moreover, the utility of each of these people depends on X, how many goods each individual consumes, and P, how much pollution each individual endures. Next we will make some assumptions about A, B and C's utility functions. First we will assume that more is better. That is, that people are always happier when they have more goods or when X is higher. If this seems unrealistic, consider Goodstein's example of ice cream. After eating enough ice cream cones, you might not want to eat another one because eating that might make you sick. However, if you received another cone for free, it would still raise your utility somewhat, because you could give it to a friend or sell it and buy something else. We illustrate the fact that each individual's utility increases with the number of goods they consume by placing a plus sign over those arguments in each utility function. Second, we will assume that pollution is bad. That is, that people are always less happy when they must endure more pollution. We illustrate the fact that every individual's utility decreases with the amount of pollution they endure by placing a minus sign over those arguments in each utility function. Note that we have not set how much people's utility will change, with, say, an additional one dollar of consumption or an additional one pound of pollution. For example, A's utility function could be given by the following equation. u equals x minus p, where x is measured in dollars and p is measured in pounds. However, it is probably unrealistic that the marginal dollar of consumption would increase A's utility by the same amount regardless of whether its consumption is very low or very high. Another description of A's utility might be given by the following equation. u equals the square root of x minus p. Here A's utility is still increasing with consumption, but the marginal utility of consumption is declining. The first unit of consumption increases utility by one utility, but A needs three more units of consumption to increase utility by another utility. Today we'll stick with general utility functions, which simply specify that increasing any individual's consumption increases their utility by some amount, and increasing the pollution any individual endures decreases their utility by some amount. Economists also make assumptions about social welfare functions, which aggregate the utility of all individuals. Social welfare increases in each individual's utility, where we illustrate by placing a plus sign over those arguments in the social welfare function. Social welfare function is often given by the following equation. Social welfare equals utility of A plus utility of B plus utility of C, in which social welfare is simply the sum of individual utilities. Utilitarianism suggests that policies should seek to maximize social welfare. If social welfare were the sum of individual utilities, utilitarianism would, for example, provide an argument for policies that are able to increase A's utility by more than it decreases B and C's utility. How do we analyze environmental policy in this social welfare framework? Assume that given our technology, each dollar of consumption requires one pound of pollution. When individual A decides how much to consume, he will consider how the resulting pollution impacts him, but he'll ignore the externality imposed on B and C. Suppose an increase in A's consumption by an additional dollar increases utility by one utility, but also causes pollution that reduces each individual's utility, including his own, by half a utility. In this case, then A's private benefit from a marginal dollar of consumption is half a utility, but the environmental cost he imposes on B and C is one utility, so this increased consumption reduces social welfare. Economists would therefore oppose this increase in consumption on environmental grounds. A policy solution may be to tax consumption, so that A pays not just the cost of producing a good, but also the environmental costs that consumption imposes upon B and C. Environmental externalities are not the only conceivable externality. If consumption is a competitive process, in which we're all trying to keep up with the Joneses, then if A increases its consumption by a dollar, it could reduce the utility of B and C, both by increasing pollution and reducing B and C's relative status. We can analyze the effect of competitive consumption using a modified utility function, such as this, in which each individual's utility is a function of N, the non-competitive goods they consume, C, the competitive goods they consume, C tilde, the competitive goods that others consume, and P, the pollution they endure. Again, we assume that more is better and pollution is bad, but we also assume that when anyone consumes more of the competitive good, it reduces others' status. If people purchase environmentally harmful goods, such as large homes or large cars, partly to display their status to others, then there is a strong utilitarian case for discouraging these forms of consumption. The optimal tax for a competitive good would be equal to the sum of the environmental and status costs it imposes upon others. On your own, think a bit about your own utility function. Do you think that consumption is in part competitive? Can you think of specific goods that are more competitive than others? Are there significant environmental costs of producing and consuming those goods? And if so, do you think there are policies that make this market failure internalize these externalities and raise social welfare? Thanks for listening to your second technical lecture on the political economy and the environment.