## Papers

- Discrete-Time Recursive Utility
- The Existence of Competitive Equilibrium over an Infinite Horizon with Production and General Consumption Sets
- The Existence of Ramsey Equilibrium
- The Existence of Steady States in Multisector Capital Accumulation Models with Recursive Preferences
- Fundamental Nonconvexities in Arrovian Markets and a Coasian Solution to the Problem of Externalities, with John Conley
- Nash Demand Game and the Kalai-Smorodinsky Solution, with Nejat Anbarci
- Population and Income Sensitivity of Private and Public Weather Forecasting, with Nejat Anbarci, Eric Floehr, Jungmin Lee, and Joon Jin Song
- Recursive Utility and Optimal Capital Accumulation, I: Existence
- Recursive Utility and Optimal Capital Accumulation II: Sensitivity and Duality Theory
- Recursive Utility and the Ramsey Problem
- Recursive Utility: Discrete-Time Theory
- Symmetries, Dynamic Equilibria and the Value Function

## Population and Income Sensitivity of Private and Public Weather Forecasting

### by Nejat Anbarci, John H. Boyd III, Eric Floehr, Jungmin Lee, and Joon Jin Song

*Regional Science and Urban Economics*, vol. 41 (March 2011), 124-133

Published Version: doi:10.1016/j.regsciurbeco.2010.11.001

Accurate weather forecasts have substantial economic value. We examine the provision of accurate forecasts both theoretically and empirically. Theoretically, we use a simple Neo-Hotelling model. In that model, the public forecaster, the National Weather Service (NWS), tries to achieve socially-efficient forecast accuracy operating under a per capita tax constraint; on the other hand, the private providers compete against each other for profits by choosing their optimal level of forecast accuracy in a monopolistically competitive market in which each private provider caters to a market niche while co-existing with the NWS. Empirically, we use a unique data set on daily maximum temperature forecasts for 704 U.S. cities and estimate the nearest neighbor matching and the state fixed effect (FE) models. Our empirical findings are consistent with the predictions of our simple public good model: we find that forecast accuracy is sensitive to economic variables such as population and average household income in that the accuracy increases in these economic variables. Our most surprising theoretical and empirical finding is that population and income sensitivity is found not only for private forecasters but also for the public forecaster, the NWS.

## Nash Demand Game and the Kalai-Smorodinsky Solution

### by John H. Boyd III and Nejat Anbarci

*Games and Economic Behavior*, vol. 71 (January 2011), pp. 14-22

Published Version: doi:10.1016/j.geb.2010.07.009

We introduce two new variations on the Nash demand game. In one, as in all past variants of Nash demand games, the Nash bargaining solution is the equilibrium outcome. The other demand game allows for probabilistic continuation in cases of infeasible joint demands. Specifically, with probability (1-p) the game terminates and the players receive their disagreement payoffs; but with probability p the game continues to a second stage in which one of the two incompatible demands is randomly selected and implemented. Surprisingly, the Kalai-Smorodinsky solution is always the outcome of the most robust equilibrium of this game. Moreover, ranking other solution concepts is impossible.

## Discrete-Time Recursive Utility

### by John H. Boyd III

in the
Handbook on Optimal Growth 1: Discrete-Time
(edited by Rose-Anne Dana, Cuong Le Van, Tapan Mitra, Kazuo Nishimura), Springer, 2006.

This paper focuses on the fundamentals of discrete-time models using recursive utility. We examine the relation between preferences, utility, and aggregator, the existence of optimal paths, and several notions of impatience. In the one-sector model, we characterize optimal paths and derive a turnpike theorem.

## The Existence of Competitive Equilibrium over an Infinite Horizon with Production and General Consumption Sets

### by John H. Boyd III and Lionel W. McKenzie

*International Economic Review*, vol. 34 (February 1993), 1-20

Published Version: JSTOR

Although many theorems have been proved on the existence of competitive equilibrium in production economies with an infinite set of goods and a finite set of consumers, nearly all suffer from a major defect. The consumption possibility sets are required to equal the positive orthant. This rules out trade in personal services and it does not allow for substitutions between goods on the subsistence boundary. Using methods similar to Peleg and Yaari, we show both equilibrium existence and core equivalence for economies with production and general consumption sets.

## The Existence of Ramsey Equilibrium

### by Robert A. Becker, John H. Boyd III, and Ciprian Foias

*Econometrica*, vol. 59 (March 1991), 441-460

Published Version: JSTOR

We demonstrate existence of a perfect foresight equilibrium under borrowing constraints in a one-sector model with infinitely-lived heterogeneous agents. The class of admissible preferences includes, but is not limited to, recursive preferences. Existence is proven using a tatonnement argument under appropriate conditions on preferences and technology. A new measure of discounting, the norm of marginal impatience, is used to determine which technologies are admissible. Depending on the norm of marginal impatience, the admissible technology may either allow for permanent growth, or have a maximum sustainable stock.

## The Existence of Steady States in Multisector Capital Accumulation Models with Recursive Preferences

### by John H. Boyd III

*Journal of Economic Theory*, vol. 71 (October 1996), 289-297

Published Version: doi:10.1006/jeth.1996.0118

This paper proves the existence of a non-trivial stationary optimal path in a multisectoral capital accumulation model with recursive preferences. The reduced-form recursive preferences are represented by an aggregator function. I introduce a new form of delta normality that is appropriate for use with recursive preferences. Under some mild conditions on the aggregator, non-trivial steady states exist when the technology is bounded and delta normal.

## Fundamental Nonconvexities in Arrovian Markets and a Coasian Solution to the Problem of Externalities

### by John H. Boyd III and John Conley

*Journal of Economic Theory*, vol. 72 (February 1997), 388-407

Published Version: doi:10.1006/jeth.1996.2230

Starrett (1972) argues that the presence of externalities implies fundamental nonconvexities which cause Arrow markets to fail. While this is true, we argue this failure is due to the structure of the Arrovian markets that Starrett uses, and not to the presence of externalities as such. We provide an extension of a general equilibrium public goods model in which property rights are explicitly treated. Nonconvexities are not fundamental in this framework. We define a notion of Coasian equilibrium for this economy, and show first and second welfare theorems. In this context, the first welfare theorem is a type of Coase theorem.

## Recursive Utility and Optimal Capital Accumulation, I: Existence

### by Robert A. Becker, John H. Boyd III and Bom Yong Sung

*Journal of Economic Theory*, vol. 47 (February 1989), 76-100

Published Version: doi:10.1016/0022-0531(89)90104-X

This paper demonstrates existence of optimal capital accumulation paths when the planner's preferences are represented by a recursive objective functional. Time preference is flexible. We employ a general multiple capital good reduced-form model. Existence of optimal paths is addressed via the classical Weierstrass theorem. The topology is uniform convergence of capital stocks on compact subsets, which is equivalent to weak convergence of investment flows under our maintained hypotheses. An improved version of a lemma due to Varaiya proves compactness of the feasible set. A monotonicity argument is combined with a powerful theorem of Cesari to demonstrate upper semicontinuity. [PDF version]

## Recursive Utility and Optimal Capital Accumulation II: Sensitivity and Duality Theory

### by Robert A. Becker and John H. Boyd III

*Economic Theory*, vol. 2, #4 (1992), 547-563

Published Version: doi:10.1007/BF01212476

This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we find the value function is differentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sufficient for an optimum. [PDF version]

## Recursive Utility and the Ramsey Problem

### by John H. Boyd III

*Journal of Economic Theory*, vol 50 (April 1990), 326-345

Published Version: doi:10.1016/0022-0531(90)90006-6

This paper examines existence, continuity and characterization of optimal paths under "recursive" preferences. Current utility is a fixed (aggregator) function of current consumption and future utility. For suitable aggregators, a useful refinement of the Contraction Mapping Theorem generates the utility function, as in Lucas and Stokey. A broader class of aggregators is handled via a limiting argument analogous to partial summation. The Weierstrass theorem yields the existence of optimal paths. Under somewhat more stringent conditions on the aggregator and technology, optimal paths are continuous in initial capital stocks, and are characterized by generalized Euler equations and a transversality condition. [PDF version]

## Recursive Utility: Discrete-Time Theory

### by Robert A. Becker and John H. Boyd III

*Hitotsubashi Journal of Economics*, vol. 34 Special Issue (1993), 49-98. (English).

*Cuadernos Economicos*, #46 (1990), 103-160. (Spanish).

Most of the modern literature on capital theory and optimal growth has proceeded on the assumption that preferences are represented by a functional which is additive over time and discounts future rewards at a constant rate. Recent research in the study of preference orders and utility functions has led to advances in intertemporal allocation theory on the basis of weaker hypotheses. The class of recursive utility functions has been proposed as a generalization of the additive utility family. The recursive utility functions share many of the important characteristics of the additive class. Notably, recursive utility functions enjoy a time consistency property that permits dynamic programming analysis of optimal growth and competitive equilibrium models. The purpose of this paper is to survey the discrete time theory of recursive utility functions and their applications in optimal growth theory. [PDF version]

## Symmetries, Dynamic Equilibria and the Value Function

### by John H. Boyd III

in "Conservation Laws and Symmetry: Applications to Economics and Finance",
ed. by R. Ramachandran and R. Sato, Kluwer, Boston, 1990.

This paper presents a geometric approach (symmetries) to dynamic economic problems that integrates the solution procedure with the economics of the problem. Techniques for using symmetries are developed in the context of portfolio choice, optimal growth, and dynamic equilibria. Information on preferences, budget sets, and technology is combined to explicitly compute the solution. By focusing on the geometry of the underlying economic structure, the symmetry method can handle many types of problems with equal ease. Given an appropriate economic structure, it is immaterial whether the problem is in continuous or discrete time, is deterministic or stochastic with a Brownian, Poisson or other process, uses a finite or infinite time horizon, or even whether the rate of time preference is fixed or variable. These details are unimportant as long as the geometry is unchanged. All cases are treated in a unified manner. A major strength of the symmetry technique is its ability to ferret out the solutions to complex models with simple underlying economic structures. For example, a previously unsolved optimal growth model with both time-varying discount rates and technology is easily solved via symmetries.