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Gains and losses from transfers of solid waste.

Abstract

Municipal solid waste is often transferred to landfills in other regions or states. While municipalities frequently resist imports, the interpretations of the Interstate Commerce Clause require that landfills accept waste regardless of its origin. This may require importers to act in ways that are not in their own best interest. The analysis of this paper suggests that importers benefit from trade when their landfill is so large that it is not exhausted at the end of the planning period. However, when landfill capacity is sufficiently scarce, importing waste is not welfare enhancing. Such municipalities have considerable motivation to try to de facto exclude waste from outside the municipality. (JEL L51)

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Introduction

Transfers of municipal solid waste between municipalities garner the occasional headline or grass roots political response. However, such reactions belie the daily occurrence of waste transfers. For example, in 2001, the Chicago Metro Region exported 26 percent of its waste while all other regions in Illinois were net importers. The amount of waste imported as a fraction of the waste generated locally ranged from about 40 percent to over 300 percent. As a whole, transfers accounted for about a third of all waste landfilled in the state. Waste transfers take place not only within a given state but also between states. Ley, Macauley, and Salant [2002, p. 190] report that about 10 percent of municipal solid waste is transferred between states nationwide. They also summarize the most important institutional aspect of waste transfers: a potential exporter can always choose not to export, but an importer faces great difficulty in excluding waste from outside its jurisdiction because of Supreme Court rulings [Ley, Macauley, and Salant, 2002, pp. 190-92]. This fact notwithstanding, in their numerical simulations, trade in waste always improves welfare compared to no-trade or autarky.

Therefore, why do states (and citizen groups) resist and try to limit imports if importing is welfare enhancing? Are states and citizens simply making bad policy decisions? In fact, most states have attempted to restrict or ban waste imports. However, "most of these restrictions have been struck down by the courts as violations of the Interstate Commerce Clause of the United States' Constitution" [Ley, Macauley, and Salant, 2002, p. 191]. The primary result of this paper is that the potential benefits for an importer depend on the size of the importer's landfill relative to its internal demand for landfill space.

To simplify the analysis, suppose there is a waste exporter and a waste importer. (This paper abstracts from the question of whether the importer and exporter are thought of as states, regions, or municipalities. Instead, they are referred to as municipalities.) The exporter has a landfill but its capacity is relatively small and so it also transfers (exports) waste to the importer's landfill. Thus, the importer's landfill accepts waste from its own residents and transfers (imports) waste from the exporting municipality. Waste which is not landfilled is recycled. Recycling is a backstop waste disposal technology, which is more expensive per unit than landfilling. All prices are exogenous except for the tipping fee, which is endogenous. The market structure is such that the exporter is always a price-taker with regard to the tipping fee. The importer is modeled both as a price-taker and a price-setter.

This paper may be best thought of as complementary to Ley, Macauley, and Salant [2002] and the earlier version of that paper [Ley, Macauley, and Salant, 2000]. They do a numerical simulation of the welfare effects of various policy proposals compared to a baseline model. Demand for waste disposal is linear and the measure of welfare is consumer surplus (less costs). While this paper also relies on numerical simulation, it begins with utility functions rather than demand curves, and most importantly, does not find that importing waste is always welfare enhancing. Most of the work of the paper will be to find ranges of parameters where trade is welfare enhancing and ranges where it is not.

Besides Ley, Macauley, and Salant [2000, 2002] and this paper, other papers in the municipal waste management literature that consider a landfill as an exhaustible resource and other methods of waste disposal (recycling or incineration) as backstop waste disposal technologies (but do not focus on transfers) are Huhtala [1997] and Highfill and McAsey [1997, 2001a, 2001b]. Other approaches to waste management include Callan and Thomas [2001], who focus on the cost side of waste disposal; Calcott and Walls [2000], who have a static model of optimal policy designed to reduce consumer waste; and Huhtala [1999], who has a dynamic model of renewable resources and waste accumulation (without an upper bound on landfill capacity). In addition to considering the welfare benefits of trade in waste, this paper can also be thought of as contributing to the literature on endogenous tipping fees (see Ready and Ready [1995] for example). Finally, there are a large number of recent empirical studies of recycling, landfilling, and related matters. See Baden and Coursey [2002], Craighill and Powell [1996], Fullerton and Kinnaman [1995], Fullerton and Wolverton [2000], Kinnaman and Fullerton [2000], Linderhof et al. [2001], Nestor and Podolsky [1998], Sterner and Bartelings [1999], and Tiller, Jakus, and Park [1997].

The Model

Assume that there exists a single consumption good which is either landfilled or recycled. The amount of the consumption good which is recycled is z(t) and the amount of the consumption good landfilled

is w(t). The importer imports waste from a single price-taking exporter: y(t) [equivalent to] y(t,p(t)) denotes the demand for landfill space in the importer's landfill by the exporter at tipping fee, p(t) and time, t. The demand function y(t,p(t)), is decreasing as a function of p. In addition to the exogenous income stream I(t), the importer derives some (endogenous) income from allowing the importing of waste, [theta]p(t)y(t,p(t)), where 0 < [theta] < 1; [theta] is net of any monetary costs of imports absorbed by the municipality as well as NIMBY-type social costs, measured in dollar terms. To simplify the notation, the price of purchasing a unit of consumption is set to zero. Thus, the only prices are for waste disposal. The unit of measurement is chosen so that the unit price of recycling is one. The tipping fee, p(t), has an exogenous lower bound [p.sub.s]; that is, for any problem of interest, disposing of waste in the importer's landfill is not free. Except for the tipping fee, all prices are exogenous, although the major result of the paper is independent of whether the importer is a price-taker or a price-setter with regards to the tipping fee.

To summarize, the problem for the importer is to choose (w(t),y(t),z(t)), (and p(t) in the case of the price-setter) to maximize the total discounted utility [n.summation over (t=0)] [[beta].sup.t]U(w(t), z(t)), subject to the budget constraint:

I(t) + [theta]p(t)y(t) = p(t)w(t) + z(t), (1)

and the landfill space constraint:

[n.summation over (t=0)][w(t) + y(t)] [less than or equal to] s. (2)

Note that the total of the domestic use of the landfill, w(t), plus the amount of waste imported, y(t), cannot exceed the landfill space available in the importing municipality where s is the initial landfill capacity for the importer.

In the case of no trade in waste, simply set y(t) to zero. It can be shown that the preferred tipping fee in autarky is its minimum: p(t) [equivalent to] [p.sub.s].

The primary concern of this paper is whether the legal environment causes the importer to accept outside waste that it would be in its best interest to not accept. Surprisingly, much of the analysis requires only an examination of the constraints (and thus, requires very weak assumptions on either the utility function or the sense in which the trade is welfare enhancing). Further, the qualitative welfare results are independent of whether the importer is a pricetaker or a price-setter. On the other hand, the results do crucially depend on whether the importer's landfill will be exhausted during the planning period. Since it is possible for the importer to simply not use its landfill (and recycle all waste), this paper argues that importing waste enhances welfare over not using the landfill (Formal proofs of all of the welfare theorems can be found in Highfill and McAsey [2003]). Not using the landfill would imply that I = z in each period, that is, all the income is spent on recycling. Then a feasible trade solution would be to use I in each period on recycling, to allow importing in some period, and to use the importer's portion of the revenue from importing to purchase additional consumption goods. So trade would be consumption increasing and welfare enhancing.

This paper also argues that if a landfill cannot be exhausted in trade, then, a) it cannot be exhausted in autarky and b) trade is consumption increasing. In this case, the budget constraint implies an upper bound on the amount of landfilling. The relationship of this upper bound to the size of the landfill can be used to argue part (a). If the landfill cannot be exhausted, then the landfill constraint is not active. Allowing waste imports will provide additional income, [theta] p(t)y(t,p(t)), to purchase additional consumption goods and enhance welfare.

Intuitively, a municipality with a sufficiently large landfill to accommodate both its own demand for landfill space and the demand for landfill space from the exporter would not exhaust in autarky, and has space that would have been unused if it had not been used to dispose of the exporter's waste. Thus, allowing for importing does not have an opportunity cost in terms of valuable (at the margin) landfill space (the user cost of landfill space is zero). So, any revenue gained by importing simply improves welfare without there being any offsetting loss of valuable (at the margin) landfill space.

Now consider the case of an importer with a relatively small landfill so that its landfill space would be used up in autarky (It is assumed that the landfill is relatively small but not so small that the municipality cannot be an importer). It is assumed that the welfare results are considerably murkier. There exists a feasible path (not necessarily optimal) in trade that will exhaust the landfill. Furthermore, there is some time at which the amount of landfilling will be less in trade than in autarky. Thus, if the landfill is small enough that the municipality would exhaust in the absence of imports (yet large enough to accommodate the exporter's demand), then importing always involves a trade-off. Particularly, the importer is using less of its landfill space to dispose of its own waste in trade as compared to autarky because the imported waste uses some of that space. However, it derives revenue from importing waste which can be spent on the consumption good that is recycled. Since this trade-off exists, trade does not increase consumption in all periods. Whether it is utility improving depends on how the utility function evaluates its arguments. Clearly, there exists a possibility that trade is worse than autarky. The next section shows that losses can exist with very standard utility functions.

Importer Solutions: Two Sample Utility Functions

The previous section stated the welfare results that can be established independently of the utility function and the tipping fee. In addition, to further explore the question of whether the importer may lose from trade, this paper also considers whether there is any necessary relationship between exhaustion and nonexhaustion of the landfill and the optimal tipping fee. In general, this paper seeks the relationship between landfilling, the tipping fee, and recycling.

Constant Marginal Utility

In the first example, assume a static problem (all variables are independent of time) and that the municipalities derive the same utility from a unit of the consumption good regardless of how it is disposed of (except possibly for the constant (k) discussed below): that is, there is no diminishing marginal utility derived from the method of waste disposal: U(w, z) = w + kz. Although the constant (k) allows for a higher weight to be placed on recycling than landfilling, the paper assumes that it is not large enough to imply that the municipalities will recycle first, recalling that, by assumption, recycling is more expensive than landfilling. Note that with this utility function, the importer is assumed to be a price-setter because the pricetaker's problem does not yield enough information to arrive at a solution. (The details of the solution and specific assumptions on parameter values can be obtained from the authors.)

The optimal solution for the exporter is to exhaust its own landfill and then export waste to the importer's landfill. It never recycles. The optimal solution for the importer is considerably more complicated. To help organize the possibilities, consider Figure 1. The horizontal axis is the initial landfill endowment of a city which is a potential importer of waste while the vertical axis is the income of the same city. (1) A point on this figure is to be interpreted as a municipality that has landfill and income endowments (s, I). The goal of Figure 1 is to classify properties of solutions to the utility optimization problem. The properties of interest are: landfill exhaustion, the tipping fee, and the existence of recycling. These properties will be characterized as functions of landfill endowment and income.

First, consider whether a city will exhaust its landfill. The thick line on Figure 1 (which can be constructed explicitly) separates the Exhaust region from the Non Exhaust region. Municipalities with endowments below and to the right of the line have a relatively large landfill and a small income. Although they landfill rather than recycle, they do not exhaust the landfill and the tipping fee is its minimum. Municipalities above and to the left of the line have a relatively small landfill and a large income. They will exhaust the landfill but otherwise, their solutions differ with regard to recycling and the tipping fee.

Second, consider tipping fees as a function of landfill endowment. As shown in the vertical strip on the left side of Figure 1, the tipping fee is at its maximum for municipalities with smaller landfills. The tipping fee is at its minimum for municipalities with relatively large landfills in the Exhaust region of Figure 1 and for all municipalities in the Nonexhaust region of the figure. Intuitively, a high tipping fee implies a small quantity of landfill space demanded and is thus associated with a small landfill. Municipalities with moderately sized landfills have tipping fees which are determined by the first order condition with respect to the tipping fee, [partial derivative]U/[partial derivative]p = 0, except for region A. In this small region of Figure 1, the first order condition yields a tipping fee that would give a value for the amount of recycling that is less than zero and therefore, such a tipping fee is not feasible. For municipalities with endowments in region A, the optimal solution is to set recycling at zero and set the tipping fee at its minimum. In brief, nonexhaustion implies a minimum tipping fee but the converse is not true. On the other hand, if the tipping fee is at its maximum or determined by the first order condition, then the municipality exhausts its landfill but again, the converse is not true.

Third, consider recycling as a function of landfill endowment and income. If a municipality does not exhaust its landfill, it will not recycle. A municipality that exhausts its landfill will recycle except for those represented by region A, near the Nonexhaust region of Figure 1. Thus, recycling is associated with exhaustion of the landfill but exhaustion does not imply recycling will occur.

Reading horizontally across Figure 1 allows a comparison of the tipping fees and recycling for two municipalities which are identical except for landfill endowment. Reading from left to right, for a fixed income, the municipality with the larger landfill endowment will have a lower tipping fee and do less recycling (unless these values have reached their minima). Reading Figure 1 vertically, it can be seen that for a fixed landfill capacity, municipalities with different incomes will often have the same tipping fee as seen on the left side of the figure. When the tipping fees differ as in the middle of the figure, the municipality with the higher income has the higher tipping fee. Higher incomes are also associated with higher levels of recycling, except in the Nonexhaust region or region A, which is close to the Nonexhaust region.

[FIGURE 1 OMITTED]

To summarize, there are three independent properties of a solution: tipping fee, exhaustion or nonexhaustion, and recycling. Knowledge of one of these will not determine either of the other two. Next this paper will discuss the kind of welfare results considered in the previous section. Because these depend on exhaustion or nonexhaustion, the most important conclusion to be drawn from Figure 1 is that municipalities with a large landfill (relative to income) do not exhaust while those with a small landfill do exhaust. In order to concentrate on the welfare results, Figure 2 omits any information on the tipping fee (and region A).

[FIGURE 2 OMITTED]

Figure 2 can be used to illustrate gains from trade in waste for importers. The line in Figure 1 dividing the Exhaust region from the Nonexhaust region in trade is reproduced in Figure 2 and labeled Exhaust-Trade. Exhaustion (in trade) regions above the Exhaust-Trade line are labeled E--Tr. Nonexhaustion (in trade) below the line is labeled NE--Tr. The analogous line for autarky is labeled Exhaust-Autarky. The Autarky Exhaust region is labeled E-Aut while the Autarky Nonexhaust regions are labeled NE-Aut. The thick curve labeled GFT between the two exhaustion curves divides the figure into two regions. The region below the curve represents municipalities with endowments (s, I) that, have more utility in trade than they do in autarky. These regions are labeled Gain in Figure 2. Those municipalities represented by endowments above the GFT curve which have losses from trading in waste are labeled Loss.

Actual numerical results can be computed given specific parameter values. It can be shown that the demand for space in the importer's landfill, as derived from the exporter's problem is y = [[I.sub.X] - [p.sub.s] [s.sub.X]]/[p+a], where [I.sub.X] is the exporter's exogenous income, [s.sub.X] is the exporter's landfill endowment, and a is the per unit transportation cost of exporting waste. (Algebraic details are available from the authors.) For example, Table 1 summarizes the gains and losses from trade for various combinations of income and landfill capacity when [s.sub.X] = 75, [I.sub.X] = 200, a = 0.02, k = 1.05, [theta] = 0.04, and [p.sub.s] = 0.75.

Recall that an importer who does not exhaust the landfill in trade does not exhaust the landfill in autarky and gains from trade. All municipalities which do not exhaust in trade (NE-Tr) gain from trade (Example 1 in Table 1). Next, consider the municipalities which exhaust the landfill in autarky (E-Aut). As noted in the preceding section, general results are not possible. As Figure 2 is drawn with the parameter values used there, all such municipalities experience loss from importing waste (Examples 2 and 3 in Table 1). For these municipalities, the trade-off of less landfilling of domestic waste for more recycling yields less utility in trade than in autarky (because imported waste uses up space in the landfill that the importer itself would use in autarky). Thus, importing waste is not utility maximizing under all circumstances. Although unlikely, it is possible (that is, there exists parameter values) that the GFT line could lie above the Exhaust-Autarky line, in which case, trade is utility maximizing for some (but not all) municipalities that exhaust in autarky.

There are municipalities which are not covered by either of the results stated in the preceding section, namely those that do not exhaust their landfill in autarky but do exhaust in trade. Such municipalities lose from trade if they are above the GFT line (have a relatively high income for a given landfill size). While they do not exhaust in autarky, landfill capacity is not large enough to accommodate the exporter's waste in addition to its own waste. Thus, some units of waste must be recycled (at a higher price) in trade. In autarky, all units were landfilled. When the increase in income from importing waste is not enough to offset the added expense of recycling, there is a loss from trade (Examples 4 and 5 in Table 1). They gain from trade if they are below the GFT line (have a relatively high landfill capacity for a given income (see examples 6, 7, and 8 in Table 1). The analysis behind Figure 2 helps to draw conclusions about municipalities which could not be drawn from the general results of the previous section.

Thus, losses from trade, which were only a theoretical possibility at the end of the last section, have been shown to exist for municipalities with sufficiently high incomes and small landfills.

Diminishing Marginal Utility

For a second example, suppose that the utility function is U(w, z) = log(w) + klog(z), where again k is a positive constant greater than one (usually close to one). This utility function assumes that there is diminishing marginal utility associated with landfilling as compared to recycling. In this case, it is possible for the importer to be either a price-taker or a price-setter. Since the previous example was of a price-setter, the paper assumes here that the importer is a price-taker. Also, notice that this utility function precludes endpoint solutions where z (or w) is zero. Thus, the number of solution types is much smaller than it was for the linear utility function.

The optimal tipping fee (and other elements of the solution) also depends on whether the importer exhausts its landfill or not. (2) Figure 3 can be used to illustrate the various possibilities. As in Figures 1 and 2, a point on this figure is interpreted as a municipality that has landfill and income endowments (s, I).

The Exhaust-Trade line is analogous to that in Figure 2 with nonexhaustion lying below the line and exhaustion above. Again, the GFT line is similar to that in Figure 2 with gains below the line and losses above. All municipalities which do not exhaust in trade have gains from trade. Those municipalities which exhaust but are close to the Exhaust-Trade line lying between the Exhaust-Trade and GFT lines have gains from trade as well. Those with small landfills that are above and to the left of the GFT line have a loss from importing waste. The latter conclusion holds regardless of whether or not they would exhaust in autarky, so the Exhaust-Autarky line has been omitted from this figure. The primary conclusion from Figure 3 (as it was from Figure 2) is that losses from trade are not only a theoretical possibility but will occur for some municipalities.

[FIGURE 3 OMITTED]

Similar calculations can be done for other utility functions. Although the results are not reported here, both losses and gains are found with the preceding logarithmic utility function when the importer is a price-setter, with other common utility functions (log(1 + w + z) + klog(1 + z) and (w + z)[.sup.[alpha]][z.sup.1-[alpha]]) in the price-taker case, and with Leontief preferences under both price-taker and price-setter assumptions. It is likely that losses could be found for other utility functions that have not been tried. Further, although all the examples mentioned so far are static, a two-period model with logarithmic preferences when the importer is a price-taker has been calculated. (3) The most important result is that the dynamic model also generates some cases which yield gains and some which yield losses from trade. In a case where the importer's landfill is relatively large and income is small, the importer gains from trade. In a case where the importer's landfill is small and income is large, the importer does not gain from trade.

Conclusion

The primary question addressed in this paper is whether trade in waste benefits the importing municipality. The analysis suggests that importers benefit if they have spare room in their landfill, that is, if it is not exhausted in trade. The authors predict that importers that exhaust but are close to not exhausting also benefit from importing (see Figures 2 or 3). However, it is possible that importers do not benefit from importing waste if their landfill is relatively small.

Thus, the results suggest that municipalities with large landfills benefit from importing waste and that local resistance to imports in such municipalities does not make (economic) sense. On the other hand, municipalities with sufficiently small landfills might be harmed if they cannot exclude outsiders' waste. Such municipalities are potentially harmed by the interpretations of the Interstate Commerce Clause that require landfills to accept waste regardless of origin and have considerable motivation to try to find ways to de facto exclude waste from outside the municipality.
TABLE 1 Numerical Results for Constant Marginal Utility Simulation

         Sample
Example  Solutions   s    I     w      z      y     p      U

1        Autarky    260   40   53.3    0.0    0.0  0.75   53.3
         Trade      260   40   66.8    0.0  186.7  0.75   60.8
2        Autarky    200  200  200.0   50.0    0.0  0.75  252.5
         Trade      200  200   28.1  177.5  171.9  0.82  219.9
3        Autarky    250  220  250.0   32.5    0.0  0.75  284.1
         Trade      250  220   63.3  162.3  186.7  0.75  250.3
4        Autarky    200  100  133.3    0.0    0.0  0.75  133.3
         Trade      200  100   28.1   77.5  171.9  0.82  114.9
5        Autarky    250  125  167.7    0.0    0.0  0.75  167.7
         Trade      250  125   63.3   67.3  186.7  0.75  150.6
6        Autarky    200   30   40.0    0.0    0.0  0.75   40.0
         Trade      200   30   28.2    7.5  171.9  0.82   41.4
7        Autarky    250   65   86.7    0.0    0.0  0.75   86.7
         Trade      250   65   63.3    7.3  186.7  0.75   87.6
8        Autarky    190   10   13.3    0.0    0.0  0.75   13.3
         Trade      190   10    3.3   12.3  186.7  0.75   17.1

         Sample
Example  Solutions  Exhaust?  Gain?

1        Autarky    Non-Ex
         Trade      Non-Ex    Gain
2        Autarky    Exhaust
         Trade      Exhaust   Loss
3        Autarky    Exhaust
         Trade      Exhaust   Loss
4        Autarky    Non-Ex
         Trade      Exhaust   Loss
5        Autarky    Non-Ex
         Trade      Exhaust   Loss
6        Autarky    Non-Ex
         Trade      Exhaust   Gain
7        Autarky    Non-Ex
         Trade      Exhaust   Gain
8        Autarky    Non-Ex
         Trade      Exhaust   Gain


Footnotes

(1) Since values of the quantities in the model near zero are rarely interesting, the intersection of the axes in this and all figures should be interpreted as somewhere strictly inside the first quadrant.

(2) Although the calculations are omitted, the demand function from the exporter's problem is:

y = [[I.sub.x]/[(1 + k)(p + a)]] - [[[p.sub.s] + k(p + a)]/[(1 + k)(p + a)]].

Again, the importer's solution depends on whether it exhausts its landfill or not. In the exhaustion case, the utility maximization condition (the first order condition) yields:

y = [[1 + k(1 + [theta])]/[(1 + [theta])(1 + k)]]s - [I/[(1 + [theta])(1 + k)p]],

which is the importer's supply function (that is, the supply of the space available for the exporter's waste).

The equilibrium in the static model is found by setting demand equal to supply and solving for p. (Once p is known, the values of the other variables can be calculated in a straightforward fashion.)

When the importer does not exhaust its landfill, the tipping fee is simply its minimum [p.sub.s] and y is found by substituting [p.sub.s] into the demand function. Once the value of y is known, the first order condition for the importer's problem yields

w = [I/[(1 + k)[p.sub.s]]] + [[[theta].sub.y]/[1 + k]].

(3) It is not surprising that the computations for the dynamic problems are more lengthy than for the analogous static problems. In both cases, while the importer does not exhaust in autarky, it exhausts in trade and uses the tipping fee from the first order condition in both periods.

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JANNETT HIGHFILL AND MICHAEL MCASEY*

*Bradley University--U.S.A.
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Publication:International Advances in Economic Research
Date:May 1, 2004
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