John H. Boyd

Recursive utility and optimal capital accumulation. I. Existence

Abstract This paper demonstrates existence of optimal capital accumulation paths when the planners 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.

The Existence of Ramsey Equilibrium

The authors 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 t

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

2Ctonnement 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. Copyright 1991 by The Econometric Society.

Looting and risk shifting in banking crises

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 suff er from a major defect. The consumption possibility sets are required t o equal the positive orthant. This rules out trade in personal service s and it does not allow for substitutions between goods on the subsistence boundary. Using methods similar to B. Peleg and M. E. Yaari (1970), the authors show both equilibrium existence and core equivalence for economies with production and general consumption sets. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

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

We construct a model of the banking firm with inside and outside equity and use it to study bank behavior and regulatory policy during crises. In our model, a bank can increase the risk of its asset portfolio (“risk shift”), convert bank assets to the personal benefit of the bank manager (“loot”), or do both. A regulator has three policy tools: it can restrict the bankʼs investment choices; it can make looting more costly; and it can force banks to hold more equity. Capital regulation may increase looting, and in extreme cases even risk shifting. Looting penalties reduce both looting and risk-shifting.

Symmetries, Dynamic Equilibria, and the Value Function

SummaryThis 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.

Nash demand game and the Kalai–Smorodinsky solution

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 contexts 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.

Discrete-Time Recursive Utility

We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the Kalai- Smorodinsky solution always finishes on top, there is no possible general ranking among the remaining solution concepts considered; in fact, the rest of the solution concepts take their turns at the bottom at various bargaining problems, depending on the specifics of the bargaining setup.

Capital theory, equilibrium analysis, and recursive utility

This chapter 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. Topics beyond the scope of this paper include continuous time recursive utility, models involving uncertainty, the turnpike property in multisector models, and properties of Pareto optima and equilibrium in multisector models. Section 9.1 discusses the limitations of time additive preferences and some of the benefits of using a more general recursive utility specification. Section 9.2 examines the relation between recursive preferences and the associated aggregator function. A general result on existence of optimal paths is shown in Section 9.3. Sections 9.4 and 9.5 focus on the one-sector model. Existence of optimal paths and dynamic programming is considered in Section 9.4. Section 9.5 characterizes optimal paths via the Euler equations and then goes on to prove a one-sector turnpike theorem. Finally, Section 9.6 takes a brief look at the case where preferences are both homothetic and recursive.