The author proves several versions of the second welfare theorem for exchange economies with non convex preferences. One theorem asserts that, given a Pareto optimum f, one can find income transfers and a Walrasian quasiequilibrium g s uch that all but k agents are indifferent between f and g, where k is the number of commodities. Another theorem shows that, with probabil ity one in a particular formulation of a random sequence of economies , every Pareto optimum is close to a Walrasian equilibrium with incom e transfers. Copyright 1988 by The Econometric Society.

Examines the sequences of economies constructed by successive sampling from any characteristics of agents. In this paper author considers closeness of commodity bundles to demand sets, dependency of the agents bundles on convexity, relationship between core allocations and demand sets.

We consider the market value of excess demand as a measure of disequilibrium. We show that, in a fixed exchange economy, there exist approximate equilibria whose measures of disequilibrium depend only on the endowments and not on the preferences. A related bound on the norm of excess demand, depending on the endowments and the approximate equilibrium price, is also obtained. We show the existence of allocations which are nearly competitive, as measured by the largest proportion of demand given up at the allocation by any trader. We use these results to obtain, for very general sequences of exchange economies, allocations giving all traders bundles close in norm to their demands. This result includes a 0(l1/n) rate of convergence in the case of uniformly bounded endowments.

We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand's book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary.

[We give an elementary statement and proof of a core equivalence theorem.]

We prove the existence of general economic equilibrium under uncertainty when agents form econometric models of the relationship among their private information, prices, and the state of the environment. The functional form of each agent's model is specified in advance, with a finite number of parameters to be determined. Agents are then thought of as performing linear least squares estimation of the parameters. Equilibrium requires not only that markets clear, but also that each agent be using the vector of parameter values which, within a compact convex set of parameters, gives the least squares best fit to the data that is generated by the working of the economy when agents adhere to their models.

We propose two general equilibrium models, quota equilibrium, and emission tax equilibrium. Government specifies quotas or taxes on emissions, and then refrains from further action. All results remain valid regardless of how government chooses its emissions target. Quota equilibrium exists; the allocation of emission property rights impacts the distribution of welfare. If the only externality arises from total net emissions, quota equilibrium is Pareto optimal among all feasible outcomes with the same total net emissions. For certain tax rates, emission tax equilibrium may not exist. Every quota equilibrium can be realized as an emission tax equilibrium and vice versa. However, different quota prices may arise in equilibrium from a single quota, and different emission levels may arise in equilibrium from a single tax rate. This leads to inequivalence between quota and emission tax equilibria.

We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and from a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy.

The authors examine core convergence for economies with a large finite number of agents and an infinite number of commodities. They find a serious disconnection between economies with a large finite number of agents and economies with a continuum of agents: the authors provide examples of nonconvergence of the core for large finite economies in L[superscript 1], a commodity space for which core equivalence holds for continuum economies. In addition, they show that, if preferences exhibit uniformly vanishing marginal utility of consumption at infinity, core convergence is restored.

We propose a new determinant of firm value within a business group: controlling shareholders' value (CSV), the value of controlling shareholders' stake in an affiliate divided by their stake in all affiliates. We posit that controlling shareholders focus attention on the high-CSV affiliates. Using data on Korean family-controlled business groups, we find that CSV has greater explanatory power for firm performance than traditional cash flow rights (CFR). We also find that, among affiliates with non-family CEOs, higher CSV is associated with higher Tobin's Q and lower EBITDA, indicating that controlling shareholders and non-family CEO have successfully addressed their principal-agent problem.