Introduction. Externalities - I. Joint Effects. Joint Products. Review:

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1 Introduction Externalities - I Philip A. Viton May 24, 2012 Review: Condition M : markets exist. (for everything in individuals utility functions or firms production functions). Theorem: If Condition M holds, a Competitive Equilibrium is Pareto Optimal. We now investigate the consequences of a failure of Condition M. We do so in the context of joint effects. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Joint Effects Joint Products A joint effect occurs when The same activity gives rise to two or more necessarily linked effects (consequences). These effects are in fixed proportions : you cannot alter the mix of the effects/consequences. Joint effects can occur in both production and consumption contexts. In the production case, we have joint products. We will initially conduct our analysis in terms of joint products (ie in a production setting) but exactly the same analysis applies to joint consumption. Consider (following Call+Holahan) a profit-maximizing cattle rancher producing steers ( ) for market. Each steer gives rise to (at least) two salable outputs: hides (1 ) and meat (2 ).These will be our joint products. Suppose the rancher observes the demand functions for both meat and hides. What is the demand curve for steers? Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

2 Vertical Addition Vertical Addition The crucial insight is that the same animal is a source of both meat and hides. It therefore makes no sense to consider a price and add the demand for meat and for hides at that price. That would be a classic case of adding apples and oranges. Adding the demands for meat and hides certainly will not give us the demand for steers. To find the demand for steers, we turn the problem around and ask: since demand functions are the rancher s average revenue functions, what is the average revenue she would get from some number, say, steers? This is easy: the average revenue from steers is the average revenue from the meat from the steers plus the average revenue from the hides from the steers. This is the idea of vertical addition of demand functions. Note that it will be valid only in the case of joint effects (products). Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Vertical Addition I Vertical Addition II p 1 p 12 p 11 D 1 Corresponding to an output of steers (horizontal axis): The rancher can get p 11 for the hides (demand curve D 11 ). And she can get p 12 for the meat (demand curve D 12 ). The average revenue for steers is therefore p 1 = p 11 + p 12. By varying the quantity we trace out D 1, the demand curve for steers. The result is the average revenue (= demand) for steers, computed by vertical addition of the individual demand functions of the joint products. D 11 D 12 So (, p 1 ) is a point on the demand (average revenue) curve for steers. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

3 Market Effects The Pareto-Optimal Output Consider an industry composed of many small profit-maximizing ranchers producing steers, all of which yield both meat and hides as joint products. We can derive an aggregate consumer demand function for meat: this is the horizontal sum of the demand functions by individual consumers for meat (horizontal addition is appropriate here, since meat+meat = meat). We can derive an aggregate demand function for hides, again by horizontal addition of individual demands for hides. Using these, we can derive the industry demand curve for steers, this time by vertical addition of the aggregate demands for meat and hides. p 1 S = Σ MC D 1 D 11 D 12 The industry supply function S will be the horizontal sum of (the relevant portions of) the individual ranchers MC functions. Equilibrium output is where supply equals demand (for steers). The equilibrium output is x 1 and the market price for steers is p 1. On our story, this is a competitive equilibrium, hence Pareto-Optimal. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Market Failure Market Failure S = Σ MC D 1 D 11 D 12 Now suppose that for whatever reason the ranchers cannot exchange hides for money. How will they determine their output? Clearly they will base their decisions on marginal cost, but only on the demand function (D 12 ) for meat. The result is an output of, where D 12 = S. But this is not the Pareto-Optimal level of output for steers. This is an example of what happens when a market does not exist, known as market failure. The general result is that market failure will lead people to alter their decisions (actions). In a competitive economy, market failure will lead profit-maximizing producers to the wrong (not Pareto-Optimal) level of output. Note that is market failure and not the presence of joint products that is the problem. Jointness by itself has no negative implications for Pareto Optimality. It is jointness plus non-existence of a market that leads to problems. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

4 Externalities Positive and Negative Externalities We say that an activity gives rise to an externality when: 1. The activity gives rise to joint impacts. 2. The market for at least one of the impacts does not exist for the actor. Another way of stating (2) is that the actor does not bear the full financial (monetary) consequences of his or her actions. We distinguish two kinds of externalities: If the unpriced joint effect (the effect subject to market failure) is a good effect (enters positively into utility functions) we say that the activity gives rise to positive externalities. If the unpriced joint effect is a bad effect (enters negatively into utility functions) then we say that the activity gives rise to negative externalities. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Recognizing Externalities Practical Externalities Practically speaking, the easiest way to show that an activity gives rise of an externality is to argue that: In order to show that an activity in question gives rise to an externality you must show that: 1. There is a joint effect: the activity has impacts on at least two classes of actors in the economy. 2. At least one of the effects is not priced: the person undertaking the activity has no market incentive to take account of the impact of his or her actions. 1. Doing the activity has an impact on the actor him- or herself. (This is almost always true, otherwise why would someone do the activity in the first place?). Call this the private impact of the activity. 2. Doing the activity has an impact on someone else. This is the non-private or external impact. 3. The doer of the activity has no monetary (market) incentive to take into account of the non-private impact (that is, the impact on the someone else ). The first two points establish the existence of joint impact; it is the third that constitutes the market failure and leads to a non-pareto-optimal level of the activity. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

5 Example 1 House Painting Decreasing Marginal Benefit Consider an individual homeowner s decision of how often to paint her house. Painting more frequently leads to benefits to the homeowner herself (she maintains the value of her home). But the benefits increase at a decreasing rate. If you are currently painting at a very low frequency (once a decade say) then increasing the frequency could have a large impact (increase in benefit to the homeowner). But if you are currently painting once a year, then doing it more often (every six months, say) will yield a very small increase in benefits. We represent the (private) benefits to the homeowner of increasing the frequency of painting via the marginal benefits function. Our observations on painting imply that the marginal benefits function decreases with frequency. Benefit B 3 B 2 B TB Level The total benefits curve TB increases at a decreasing rate. As the level of the activity increases, adding 1 more unit of the activity provides a smaller increase in total benefits. This is a decreasing marginal benefit. Equivalently, the slope of the total benefits curve decreases as the level of the activity increases. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Example 1 House Painting I Example 1 House Painting II To demonstrate this, we must show: Is there a case that the homeowner will adopt the wrong (non-pareto-optimal) frequency of house painting? One approach is to argue that there is an externality present. 1. The frequency of painting has a private impact. We ve already done this: painting helps the homeowner to maintain the value of her house. 2. Is there an impact on someone else? Arguably, Yes: the frequency of painting will affect the appearance of the whole neighborhood, and this affects the value (selling price) of the neighbors houses. 3. Does the homeowner have an incentive to take the impact on the neighbors into account? No, because she receives no part of the price the neighbor gets when he sells his house, even though she has contributed to increasing or maintaining its value. This is the market failure. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

6 Example 1 House Painting III House Painting A Positive Externality MC MB priv : private marginal benefit to homeowner. MB oth : marginal benefit to neighbors. MB tot : vertical sum of MB priv + MB tot. Since the level of the homeowner s painting frequency provides a positive benefit to the neighbors, this is an example of a positive externality We see that in the presence of a positive externality the individual s level of the activity will be too small relative to the Pareto-Optimum MB oth x 1 MB tot MB priv MC = private marginal cost of painting. x 1 = PO level; = observed level with externality. There is an interesting empirical question here: what is the extent of the neighborhood: that is, how far do these effects extend? This can be studied with spatial econometric techniques, analyzing the determinants of house values (prices). Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Example 2 Leaf Burning I Example 2 Leaf Burning II To make an externality argument, we need to show: Consider an individual homeowner s decision on how many leaves to burn in his back yard in the autumn (as opposed to composting them or sending them to a landfill). Note that in many cities it is actually illegal to burn leaves. Can we suggest why a law to this effect is needed? That is, can we argue that left to their own devices an individual homeowner will burn too many leaves? One strategy is to argue that leaf-buring gives rise to an externality. 1. There is an impact on the homeowner himself. This is clearly true (the homeowner gets rid of unwanted leaves); and we will again represent it by downward-sloping private marginal benefits curve. 2. Is there an impact on someone else? Yes, again on the neighbors. According to EPA, the particles released into the air by the burning leaves can damage the health of people who breathe them in. So we have a joint effect. 3. Does the individual homeowner have a monetary incentive to worry about this impact on the neighbors? Arguably no: in the absence of a legal cause of action, it is the neighbor who absorbs the costs of any increased sickness. And even with tort law, it is not clear that the leaf burner can be brought to bear the entire cost imposed on the neighbors. Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26

7 Example 2 Leaf Burning III Leaf Burning A Negative Externality The important thing here is that MB oth is negative. MC MB priv MB tot MB oth So vertical addition of MB priv + MB oth results in MB tot which is below MB priv. PO level = x1 ; observed level =. Observed level is too high relative to the PO level. In this example, the impact on others is negative (reduces their health). This is therefore an example of a negative externality. We see that in the presence of a negative externality, an actor will tend to do too much relative to the Pareto-Optimum. In the picture, the optimal level of the activity is not zero. What would have to be true to justify a total ban on leaf burning, the legal standard? Philip A. Viton CRP 781 () Externalities - I May 24, / 26 Philip A. Viton CRP 781 () Externalities - I May 24, / 26