INTRODUCTION I. HOW AND WHY IS PROPERTY LUMPY? A. What's Lumpy? 1. Steps and Lumps 2. What's in the Lump? B. Lumpy Demand, Lumpy Supply, and the Law C. Property Lumps II. LUMPY DOCTRINES A. Enforcing Exclusion B. Limiting Configurations C. Dividing and Aggregating 1. Eminent Domain 2. Regulatory Takings 3. Judicial Takings 4. Ordinary Adjudication III. LUMPINESS AND PROPERTY THEORY A. Bundles and Sticks B. Exclusion, Obligation, Aggregation IV. LEARNING FROM LUMPINESS A. Empty and Constructed Lumps B. Compelling Lumps C. Choosing Lumps CONCLUSION INTRODUCTION
A bridge stretching only three-quarters of the distance across a chasm is useless, while a bridge that is longer than necessary does no more good than one that just spans the gap. This standard, intuitive example of a lumpy, indivisible, or "step" good makes regular appearances in the literature on collective action. (1) But it also illustrates a point about discontinuities and complementarities that has broad, and mostly unexplored, significance for property law. (2) From land assemblies to takings doctrines to cotenant partitions to public housing to the numerus clausus principle, we see property delivering value--and being delivered to us--in certain identifiable, discontinuous chunks. This Article examines the implications of lumpiness for property theory and doctrine. While strains of this conceptual element run through some of the existing theoretical work on property, (3) the ways in which lumpiness may explain, justify, and challenge features of property law have not been systematically analyzed.
Viewing property through the lens of lumpiness matters for at least three reasons. The first is descriptive accuracy. Property law is lumpy as a positive matter, filled with doctrines and approaches that deal with the world in discrete, hard-to-divide chunks. Understanding how property operates thus requires an appreciation of its lumpiness. Second, optimal property design requires evaluating the chunkiness that is built into property doctrines and asking whether and how it corresponds to underlying discontinuities in the production or consumption of property. Third, many of property law's most important conflicts can be usefully framed as "lump versus lump." For example, an exercise of eminent domain may achieve a valuable spatial aggregation by splitting up some other aggregation, such as lengthy temporal attachments to the land or a cohesive community that shares social capital. (4) Recognizing the significance of nonlinearities in such stories can offer new traction on contemporary property debates.
The analysis here proceeds in four parts. Part I explains how and why we might regard property as lumpy. Part II examines how ideas connected to lumpiness enter into property law, whether as rationales for legal intervention, justifications for doctrinal protections, or bases for judicial or administrative outcomes. Part III turns to property theory, where notions of lumpiness map onto current debates over the bundle-of-rights metaphor and over the relationship between exclusion and social obligation. This discussion also raises questions about the mutability and social contingency of property's lumpy nature. Part IV offers some analytic lessons that property scholars can take away from a study of lumpiness.
HOW AND WHY IS PROPERTY LUMPY?
Property entitlements that encompass strongly complementary elements may be said to have a lumpy or indivisible quality. To take a simple example, a dwelling's four walls, roof, and foundation are generally viewed as strongly complementary: removing any one element changes a fully contained private shelter into a windbreak, a cubicle, or a lean-to. Just as the last segment of a bridge delivers a disproportionate amount of utility, so too will a dwelling's last wall. Similar claims might implicitly underpin a variety of legal doctrines and interventions, including minimum standards for the quality and size of housing, minimum tenure lengths, minimum bundles of property rights, and the use of eminent domain to assemble land into larger chunks. Before we can analyze these and other examples, however, we first need to lay some definitional and taxonomic groundwork.
As Michael Taylor and Hugh Ward observe, some goods "cannot be usefully provided in any amounts but only in more or less massive 'lumps.'" (5) A good is lumpy (in one sense) if it provides benefits only when a particular quantity threshold is reached, rather than delivering utility in smoothly scalable units as quantities increase. (6) More broadly, the notion of lumpiness is associated with various kinds of discontinuities, indivisibilities, nonlinearities, and complementarities.
Steps and Lumps
Lumpiness is a matter of degree. At the extreme, a good might take a "step" form, like the prototypical bridge shown in Figure 1.
[FIGURE 1 OMITTED]
As Figure 1 shows, the structure is worthless until all the segments required to span the gap are in place, and it becomes no more valuable as superfluous segments are added. (7)
Such pure step goods are rare. (8) But equally rare are perfectly linear goods--those with a smooth, continuous production function in which each infinitesimally fine unit of input is matched by a similar adjustment in output or utility. Between these two extremes, we find different degrees of nonlinearity or indivisibility. (9)
I will use the term "lumpiness" broadly here to refer to severe discontinuities or nonlinearities in the production function, whether or not those functions take a pure step form or intersperse sharply increasing or decreasing returns with ranges exhibiting linearity. (10) These differences in shape are important, however, because they can influence the prospects for cooperation and the risks of strategic behavior. (11)
Figure 2 shows another example of a (relatively) lumpy good. Although this good does not deliver all its value in a single shot, its production function contains ranges over which the marginal effect of added segments is sharply increasing or decreasing.
[FIGURE 2 OMITTED]
The S-curve shown in Figure 2 matches up with many collective goods that require a critical mass of participation to succeed, but that at some point plateau. (12) It might also fit with certain kinds of land assembly projects, where value increases sharply once a certain number of parcels are aggregated, but where having all the parcels is not essential. (13)
Of course, nonlinearities might take many other forms; Figure 1 and Figure 2 offer just two examples.
What's in the Lump?
So far, I have spoken of "segments" that produce value when aggregated together. As this formulation suggests, lumpiness or indivisibility often refers to quantities of relatively fungible inputs--pieces of a bridge, lengths of railroad track, tires for a car, units of work, years of housing tenure, and so on. Yet it may also refer to organic systems made up of heterogeneous elements, such as a machine that cannot operate without each and every one of its parts. (14) In the context of land assembly, the unique spatial location of each parcel may make the component parts of the desired assembly nonfungible. What matters most to the shape of a given assembly problem is not whether the components are interchangeable with each other, but rather whether close substitutes exist for each of the components required for a given assembly. (15) Thus, both homogenous and heterogeneous aggregations fit within the broad conception of lumpiness pursued here.
It is also worth emphasizing that the components in question may be temporal in nature. Some goods, such as private residences, are often viewed as disproportionately valuable when consumed in lengthy, unbroken temporal chunks. Often, these valuable temporal chunks are defined by reference to external events, such as the length of a life, a job, or an educational program. Property intentionally bundles along the temporal dimension and, at least in the case of the fee simple absolute, it does so in a very open-ended way.
Lumpy Demand, Lumpy Supply, and the Law
A good may exhibit lumpiness either because it is considerably less valuable when divided or because it is very expensive to divide (or to produce in smaller units in the first instance). The loss in consumption utility associated with dividing a lumpy good corresponds to lumpiness in demand, while the increase in production cost associated with making goods in particular quantities or configurations corresponds to lumpiness in supply. Lumpiness becomes noticeable and relevant when there is a mismatch between the units that users demand and the units that producers supply.
Consider first lumpy demand. Most people have two feet of similar size and follow the social custom of shodding them identically; thus, they buy shoes in lumps of two. Likewise, the users of bridges drive vehicles that are sensitive to gravity; consequently, they demand complete rather than partial bridges. In these cases and many others, the indivisibility relates to consumption utility, not to production processes that compel the provision of goods in particular chunks. (16) The lumpiness shows up in the demand curve, with little or no demand for quantities of the good below the critical threshold. (17)
In other instances, lumpiness stems not from consumption utility, but rather from the costs or technological limits of production. For example, the fixed costs associated with certain kinds of factory upgrades or expansions may make them affordable only in chunks of certain sizes. (18) Lumpiness in supply can also manifest itself in limited menus of products, where each variety requires a fixed minimum outlay. (19) Consider, for example, Henry Ford's decision to offer Model T purchasers "a car painted any colour that he wants so long as it is black." (20) Here, the lumpiness is a function of the indivisible cost of setting up a particular production run.