This handout will help us better understand the nature of negative externality, as well as how we address this problem.
Let’s assume that Person A likes to eat burritos and, because of taking Economics 201, is able to determine his total benefit (TB) and total cost (TC) of eating burritos in terms of the following equations (where x is the number of burritos consumed):
Person A wants to determine how many burritos to eat (x*), and knows that the solution to this problem lies in consuming at the point where the benefit from the last burrito consumed is equal to the cost of consuming that burrito. To do this, A needs to find equations for the marginal benefit (MB) and marginal cost (MC) associated with his burrito-eating. Given TB and TC above, the MB and MC equations here are:
The net benefit maximizing number of burritos to eat corresponds with consuming where 100 – x = 10 + 2x (i.e. where MB = MC). If we solve this equation for x, then we learn that x* = 30. That is, A should eat 30 burritos. We show this on the graph below.
Of course, we aren’t at the end of the story just yet. You see, when person A eats these burritos, the burritos elicit a bodily response we’ll characterize as involuntary combustion, or IC. The existence of IC and any related fumagatory issues impose an external cost on person B. Let’s assume this cost is calculated as 30x.
This helps us derive equations for the Social Benefit (SB) and Social Cost (SC) associated with A’s burrito consumption. SB and SC are simply the sum of TB and any external benefit, and TC and any external cost. As there is no external benefit mentioned in this problem, we have only to derive SC as follows:
The corresponding marginal benefit to society (MBS) and marginal cost to society (MCS) are:
MBS = 100 – x
MCS = 40 + 2x
Society’s net benefit (i.e. the net benefit for A and B combined) from A’s burrito consumption is calculated in a similar manner to that above. We set MBS = MCS and solve for x, the quantity of burritos that society prefers A consume. Society’s prefered level of x (x**) is 20 burritos. We show this on the graph below as well.
As we said before, A’s consumption of burritos imposes an external cost on B. If we assume that every burrito causes person A to experience a bout with IC, then we can characterize this situation as one where B doesn’t want A to stop eating burritos altogether, but that B wants A to just cut back until B no longer feels imposed upon by the IC. This implies that when the problem is solved, there will still be some IC going on, just not as much as right now.
There are several ways we can solve this problem. Here are some suggestions.
1. The government could impose direct controls on burrito consumption and not allow person A to impose this external cost on B. That is, allow a certain amount of burrito consumption, but not to the point where that consumption disturbs the peace (here, that would involve eating only 20 burritos).
2. The government could place a tax on every burrito consumed by person A. That is, a tax of 30, equal to the external cost associated with each burrito consumed, could be levied here. The tax would raise the marginal cost to A of eating burritos to the point where MCA = MCS. Once this occurs, the externality disappears.
3. The government could allow the equivalent of tradeable emissions permits. If we assume that everyone is just like persons A and B in terms of their benefits and costs, then we know we would want people eating an average of 20 burritos. The government could sell tradeable permits that allow consumers to eat burritos. Each permit allows you to buy one burrito, so each person is given 20 permits. We know that some people like burritos more than other people, so by allowing consumers to trade permits, we allow the market to decide who will reduce their burrito consumption and who won’t. Most importantly, however, we know that an average of 20 burritos will still be consumed by society as a whole.
4. Another option would be for person A to reduce their burrito consumption voluntarily.
Of course, by doing so, person A loses some net benefit. If we calculate the net benefit
from consuming 30 burritos and then from consuming 20 burritos, then we can see that the
net benefit for A falls by 150. This is much less than the cost imposed on person B,
however, which is equal to 900. We can infer from these numbers that person B may want
to “bribe” A to eat fewer burritos. If these numbers are measured in cents (i.e. 150
cents and 900 cents), then we know that person B could pay A $1.50 to eat only 20 burritos.
It would be worthwhile for B to do this, because paying $1.50 is better than losing $9 worth
of net benefit. This option corresponds with one potential outcome using the Coase Theorem,
the subject of another handout.