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Financial intermediaries trade frequently in many markets using sophisticated models. Their marginal value of wealth should therefore provide a more informative stochastic discount factor (SDF) than that of a representative consumer. Guided by theory, we use shocks to the leverage of securities broker-dealers to construct an intermediary SDF. Intuitively, deteriorating funding conditions are associated with deleveraging and high marginal value of wealth. Our single-factor model prices size, book-to-market, momentum, and bond portfolios with an R² of 77% and an average annual pricing error of 1%—performing as well as standard multifactor benchmarks designed to price these assets.

The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity. This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.

The concentrations of resources in forage are not perfectly balanced to the needs of an animal, and food species differ in these concentrations. Under many circumstances, animals should thus forage on multiple food species to attain the maximum and most balanced intake of several resources. In this article we present a model to extend optimal foraging theory to incorporate concurrent foraging for multiple resources from several food species. A balancing of resources is achieved by representing the amount of a resource as the time during which it is used. Optimization is considered at two hierarchical levels: the time spent in a patch and the proportion of patches of each food species included in the foraging path. Our model results show that the balancing of resource intake can be achieved at the level of the foraging path, while the maximization of intake can be realized at the nested patch level. The choice for a food species should be dependent on the differences in intake and resource ratios between the food species. Under free choice of food species, the optimal patch residence time is subject not to differences between patches but to the local intake rate.

The residential mobility patterns of modern hunter-gatherers broadly reflect local resource availability, but the proximate ecological and social forces that determine the timing of camp movements are poorly known. We tested the hypothesis that the timing of such moves maximizes foraging efficiency as hunter-gatherers move across the landscape. The marginal value theorem predicts when a group should depart a camp and its associated foraging area and move to another based on declining marginal return rates. This influential model has yet to be directly applied in a population of hunter-gatherers, primarily because the shape of gain curves (cumulative resource acquisition through time) and travel times between patches have been difficult to estimate in ethnographic settings. We tested the predictions of the marginal value theorem in the context of hunter-gatherer residential mobility using historical foraging data from nomadic, socially egalitarian Batek hunter-gatherers (n = 93 d across 11 residential camps) living in the tropical rainforests of Peninsular Malaysia. We characterized the gain functions for all resources acquired by the Batek at daily timescales and examined how patterns of individual foraging related to the emergent property of residential movements. Patterns of camp residence times conformed well with the predictions of the marginal value theorem, indicating that communal perceptions of resource depletion are closely linked to collective movement decisions. Despite (and perhaps because of) a protracted process of deliberation and argument about when to depart camps, Batek residential mobility seems to maximize group-level foraging efficiency.

We propose a model of dynamic investment, financing, and risk management for financially constrained firms. The model highlights the central importance of the endogenous marginal value of liquidity (cash and credit line) for corporate decisions.Our three main results are: (1) investment depends on the ratio of marginal q to the marginal value of liquidity, and the relation between investment and marginal q changes with the marginal source of funding; (2) optimal external financing and payout are characterized by an endogenous double-barrier policy for the firm's cashcapital ratio; and (3) liquidity management and derivatives hedging are complementary risk management tools.

We examine the cross-sectional variation in the marginal value of corporate cash holdings that arises from differences in corporate financial policy. We begin by providing semi-quantitative predictions for the value of an extra dollar of cash depending upon the likely use of that dollar, and derive a set of intuitive hypotheses to test empirically. By examining the variation in excess stock returns over the fiscal year, we find that the marginal value of cash declines with larger cash holdings, higher leverage, better access to capital markets, and as firms choose greater cash distribution via dividends rather than repurchases.

We develop a method of analysis for testing the marginal value theorem (MVT) in natural settings that does not require an independent definition or mapping of patches. We draw on recent theoretical work on area-restricted search (ARS) that links turningangle and step-size changes to geographically localized encounterrates. These models allow us to estimate “giving-up times” using encounter-annotated GPS tracking data. Applied to a case study of Nahua mushroom foragers, these models identify distinct forms of intrapatch and interpatch search behavior, with intrapatch search transitioning to interpatch search after a predictable interval of time since the last encounter with a harvested mushroom. Our empirical estimate of giving-up time coincides with the theoretically optimal giving-up time derived under the MVT in the same environment. The MVT is currently underused in studies of human foraging and settlement patterns, due in large part to the difficulty of identifying discrete resource patches and quantifying their characteristics. Our methods mitigate the need to make such discrete maps of patches and thus have the potential to broaden the scope for empirical evaluations of the MVT and related theory in humans. Beyond studies of naturalistic foraging in humans and other animals, our approach has implications for optimization of search behavior in a range of applied fields where search dynamics must be adapted to shifting patterns of environmental heterogeneity affecting prey density and patchiness.

Individuals do not have complete information about the environment and therefore they face a trade-off between gathering information (exploration) and gathering resources (exploitation). Studies have shown individual differences in components of this trade-off but how stable these strategies are in a population and the intrinsic drivers of these differences is not well understood. Top marine predators are expected to experience a particularly strong trade-off as many species have large foraging ranges and their prey often have a patchy distribution. This environment leads these species to exhibit pronounced exploration and exploitation phases but differences between individuals are poorly resolved. Personality differences are known to be important in foraging behaviour but also in the trade-off between exploration and exploitation. Here we test whether personality predicts an individual exploration-exploitation strategy using wide ranging wandering albatrosses (Diomedea exulans) as a model system. Using GPS tracking data from 276 wandering albatrosses, we extract foraging parameters indicative of exploration (searching) and exploitation (foraging) and show that foraging effort, time in patch and size of patch are strongly correlated, demonstrating these are indicative of an exploration-exploitation strategy. Furthermore, we show these are consistent within individuals and appear stable in the population, with no reproductive advantage. The searching and foraging behaviour of bolder birds placed them towards the exploration end of the trade-off, whereas shy birds showed greater exploitation. This result provides a mechanism through which individual foraging strategies may emerge. Age and sex affected components of the trade-off, but not the trade-off itself, suggesting these factors may drive behavioural compensation to maintain resource acquisition and this was supported by the evidence that there were no fitness consequence of any EE trait nor the trade-off itself. These results demonstrate a clear trade-off between information gathering and exploitation of prey patches, and reveals for the first time that boldness may drive these differences. This provides a mechanism through which widely reported links between personality and foraging may emerge.

Research in social neuroscience has increasingly begun to use the tools of computational neuroscience to better understand behaviour. Such approaches have proven fruitful for probing underlying neural mechanisms. However, little attention has been paid to how the structure of experimental tasks relates to real-world decisions, and the problems that brains have evolved to solve. To go significantly beyond current understanding, we must begin to use paradigms and mathematical models from behavioural ecology, which offer insights into the decisions animals must make successfully in order to survive. One highly influential theory—marginal value theorem (MVT)—precisely characterises and provides an optimal solution to a vital foraging decision that most species must make: the patch-leaving problem. Animals must decide when to leave collecting rewards in a current patch (location) and travel somewhere else. We propose that many questions posed in social neuroscience can be approached as patch-leaving problems. A richer understanding of the neural mechanisms underlying social behaviour will be obtained by using MVT. In this ‘tools of the trade’ article, we outline the patch-leaving problem, the computations of MVT and discuss the application to social neuroscience. Furthermore, we consider the practical challenges and offer solutions for designing paradigms probing patch leaving, both behaviourally and when using neuroimaging techniques.