Essays in Dynamic General Equilibrium Theory

Recent anti-trust cases exacerbated the concerns of investors regarding the effects of a firm’s monopoly power on its production choice, shareholder value, and the overall economy. We address this issue within a dynamic equilibrium model featuring a large monopolistic firm whose actions not only affect the price of its output, but also effectively influence the valuation of its stock. The latter renders time-inconsistency to the firm’s dynamic production choice. When the firm is required to pre-commit to its strategy, the ensuing equilibrium is largely in line with the predictions of the textbook monopoly model. When the firm behaves in a time-consistent manner, however, the predictions are strikingly at odds. The trade-off between current profits and the valuation of future profits induces the firm to increase production beyond the competitive benchmark and cut prices. This policy may result in destroying shareholder value, and does indeed fully wipe out the firm’s profit in the limit of the decision-making interval shrinking to zero, in line with the Coase conjecture.

In a stationary state, ineffciency is established if some marginal perturbation leads to a positive surplus for all commodities. We consider the case when, though the original perturbation itself results in positive and negative changes, an adequately chosen combination of such perturbations is conclusive. A characterization in terms of the positive roots of a polynomial is obtained.

Sectors with increasing returns to scale have been shown to amplify business cycles exhibiting more volatility than others [13]. Our hypothesis is that this volatility could be a cause of the “jobless recovery” suggesting policies for employment generation. To test this hypothesis we introduce a general equilibrium model with involuntary unemployment. The economy has two sectors: one with increasing returns that are external to the firm and endogenously determined — the knowledge sector — and the other with constant returns to scale. We define a measure of employment volatility, a ‘labor beta’ that is a relative of the ‘beta’ used in finance. A ‘resolving’ equation is derived from which it is proved that increasing return sectors exhibit more employment volatility then other sectors. The theoretical results are validated on US macro economic data of employment by industry (2–3 digits SIC codes) of the 1947–2001 period, showing that the highest ‘labor betas’ are in the service sectors with increasing returns to scale. Policy conclusions are provided to solve the puzzle of the ‘jobless recovery’, where small firms in the services industry play a key role. We conclude with policy recommendations on how to create jobs in the knowledge economy.

We consider economies with additively separable utility functions and give conditions for the two-agents case under which the existence of sunspot equilibria is equivalent to the occurrence of the transfer paradox. This equivalence enables us to show that sunspots cannot matter if the initial economy has a unique spot market equilibrium and there are only two commodities or if the economy has a unique equilibrium for all distributions of endowments induced by asset trade. For more than two agents the equivalence breaks and we give an example for sunspot equilibria even though the economy has a unique equilibrium for all distributions of endowments induced by asset trade.

The last twenty years have witnessed a significant growth of the literature on the “survival problem”, primarily in the context of the causes and remedies of famines. Once a subject essentially of empirical development economics, economic survival became an issue of analytical economics and, most recently, of general equilibrium theory. We review several issues of the survival problem in the general equilibrium framework. First, we consider a Walrasian economy with intrinsic uncertainty affecting the endowments and compute the asymptotic probability of survival under different assumptions of dependence among the agents. Next, we show how the presence of extrinsic uncertainty in a dynamic economy may lead to a ruin in a sunspot equilibrium. Finally, we analyze the link between survival and specialization in production.

It is understood that rational expectations equilibria may not be incentive compatible: agents with private information may be able to affect prices through the information conveyed by their market behavior. We present a simple general equilibrium model to illustrate the connection between the notion of informational size presented in McLean and Postlewaite (2002) and the incentive properties of market equilibria. Specifically, we show that fully revealing market equilibria are not incentive compatible for an economy with few privately informed producers because of the producers’ informational size, but that replicating the economy decreases agents’ informational size. For sufficiently large economies, there exists an incentive compatible fully revealing market equilibrium.

Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agent’s subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguity averse decision maker evaluates an act by the minimum expected value that may be associated with it.

In spite of wide and long-standing support among economists for indexation of loan contracts there has been relatively little use of indexation, except in situations of extremely high inflation. The object of this paper is to provide a (theoretical) explanation for this puzzling phenomenon based on the hypothesis that economic agents are ambiguity averse. The present paper considers a general equilibrium model based on (Magill and Quinzii, 1997), with ambiguity averse agents, where both nominal and indexed bond contracts are available for trade and all relevant prices are determined endogenously. We obtain conditions which prompt an endogenous cessation of trade in indexed bonds: i.e., conditions under which there is no trade in indexed bonds in any equilibrium; only nominal bonds are traded. We argue that the obtained conditions mirror the known stylized facts about trade in indexed financial contracts.

We consider two periods economies with both intrinsic and extrinsic uncertainty. Asset markets are incomplete in the certainty economy. If assets are nominal, there are enough commodities and the number of agents is greater than two and smaller than the total number of states of nature “tomorrow” (minus one), then a sunspot-invariant equilibrium is generically Pareto dominated by some sunspot equilibria. When assets are real, and there are enough commodities, whenever there are sunspot equilibria, typically there are also sunspot equilibria Pareto dominating the sunspot-invariant equilibria under the same restriction on the number of agents (and stronger restrictions on the number of commodities).

We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist.

The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space. Furthermore, we show that there exist large economies with a countable infinity of Pareto ranked static sunspot equilibrium allocations with aggregate pro capita consumption invariant both across equilibria as well as across realizations of the uncertainty. This implies that these equilibria are equilibria of a pure exchange economy with non-convex preferences.

A pure-exchange, competitive economy with date-specific units of account is studied. It differs from the standard pure-exchange model in having unit-of-account endowments. For such an economy, conditions are given for an outside agent, a central bank, to be able to control the nominal rate of interest. It can do so provided it has positive unit-of-account endowments. A more general outside agent that has a positive endowment of some good and positive unit-of-account endowments can select the time path of the price level.