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Chapter 23 / Externalities

23.2 Market Externalities in the Supply and Demand Model

Let’s consider as our first model the competitive model of supply and demand, which we developed in Part IV of this book. In particular, in chapter 15, we analyzed the way in which the demand curve represented the marginal benefit ($MB$) to consumers from a good, and the supply curve represented the marginal cost ($MC$) to producers. If all consumers and producers are price takers, then each consumer buys up to the point where their marginal benefit is equal to the price ($MB = P$), and each firm produces as up to the point where the price equals their marginal cost ($P = MC$), and since they all face the same price, in equilibrium the quantity produced is the one which sets $MB = MC$.

However, implicit in this analysis was the assumption that the only relevant benefits were the ones accruing to consumers from their private consumption, and the only relevant costs were the ones borne by the firms as part of their production processes. However, suppose there are benefits or costs which are external to the market transaction…what then? For example, suppose that in order to produce a good, the firm generates pollution which harms consumers; this cost is not accounted for in the kind of analysis we did in Chapter 15. Or, suppose that when a consumer buys some beautiful flowers to spruce up their front lawn, they bring pleasure not only to themselves but to their neighbors as well; how do we account for those benefits?

In such cases, we need to draw a distinction between private benefits and costs (the benefits to the consumers, the costs to the firms), and external benefits and costs to people outside the immediate transaction. The sum of private and external benefits and costs are called social benefits and costs.

The diagram below extends the kind of analysis we did in Chapter 15. At first, it looks just the same: in the left graph, we see the gross benefit to consumers if the market produces $Q$ units of a good, as the area under the marginal benefit curve; in the middle, it shows the total cost to firms, as the area under the marginal cost curve; and in the right graph, it brings these two together to show the total welfare (benefit to consumers minus cost to firms) as the area below the MB curve and above the MC curve, representing the net benefit of each unit of the good produced (i.e. its marginal benefit minus its marginal cost):

Now, if you check the box marked “show the case of a negative externality,” you can see how the existence of external costs affects the analysis. The firm’s private marginal cost is labeled $PMC$. A brown line appears; this is the marginal external cost ($MEC$). The sum of the $PMC$ and $MEC$ is the social marginal cost, $SMC$. This line represents all of the costs generated by firms producing this good, including the costs they face ($PMC$) and the costs they impose on others via pollution or some other negative externality ($MEC$). As you can see from the right-hand graph, the socially optimal quantity lies at the intersection of the $MB$ and $SMC$ curves, because we want to produce the good up until the point where the marginal benefit to consumers is just offset by all the marginal costs of production. If we were to ignore these costs and produce at the point where $MB = PMC$, the last units produced would have a benefit that was great enough to offset the private costs, but not the additional external costs.

Solution: Pigovian Taxes

The fundamental problem here is that because market actors only make their decisions based on their own private costs and benefits, the market results in an overproduction of a good with a negative externality. (Likewise, it also results in an underproduction of a good with a positive externality, like those beautiful flowers in the front yard.) One solution to this is to adjust the incentives faced by firms so that they make the “right” decision, and produce the socially optimal quantity.

One way to achieve this would simply be to issue an edict that a certain quantity of the good (i.e. the socially optimal quantity) be produced. However, this would assume that some institutional authority knew exactly how much of a good was optimal; which is often not the case, as government’s don’t accurately know every consumer’s marginal benefit and every firm’s marginal cost.

Another method, suggested by the economist Arthur Pigou, was to levy a tax which would effectively force the firms to pay the external costs they would otherwise avoid: in other words, charge them for the marginal external cost they are imposing on others. If they have to pay that cost, the reasoning goes, they will stop producing when the price (plus tax) equals their private cost plus the external cost: \(P + \text{tax} = PMC + MEC\) You can see how this works in the graph below. The quantity $Q^E$ represents the market equilibrium quantity; if you check the box saying “show negative externality,” the quantity $Q^\star$ represents the socially optimal quantity. If you levy a tax, by adjusting the slider, you can reduce the equilibrium quantity bought and sold in this market. And if you levy just the right amount of tax, you can achieve the socially optimal quantity:

Note that, as in this case, the amount of external cost may depend on how much of the good is being produced. The trick, then, is to choose a tax scheme so that, as much as possible, the amount of tax paid per unit is equal to the marginal external cost at the optimal quantity. In this case, the MEC at the optimal quantity of $Q^\star = 50$ is $€20$ per unit; so a tax of that amount will result in the efficient quantity being produced.

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