Balanced equilibrium in a consumption loans model

In a consumption loans model with many generations, Gale's theorem on the existence of balanced equilibrium is generalized, allowing more general preferences. The new theorem shows that there are plausible conditions under which there exists a Pareto optimal (non-optimal) balanced equilibrium whenever there exists (does not exist) a monetary golden rule equilibrium.     

Money and capital as competing media of exchange

We construct a model where capital competes with fiat money as a medium of exchange, and establish conditions on fundamentals under which fiat money can be both valued and socially beneficial. When the socially efficient stock of capital is too low to provide the liquidity agents need, they overaccumulate productive assets to use as media of exchange. When this is the case, there exists a monetary equilibrium that dominates the nonmonetary one in terms of welfare. Under the Friedman Rule, fiat money provides just enough liquidity so that agents choose to accumulate the same capital stock a social planner would.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

About optimal harvesting policies for a multiple species forest without discounting

We study the optimal harvesting of a mixed forest composed of multiple species, each one having a different maturity age, where only mature trees can be harvested. We prove the existence of an optimal program and the equivalence of maximal, optimal and minimal value-loss programs. We characterize the unique golden rule stock and prove that it is sustainable, i.e., it is invariant along the optimal program. Furthermore, we also prove that along any good program from any initial condition there is convergence of the forest’s state to this sustainable state. Finally, we define a value function in the set of forest states and define a pre-order that provides an alternative way of characterizing the golden rule stock and may potentially have independent interest.     

Capital market imperfections in a monetary growth model

Summary. We consider a monetary growth model essentially identical to that of Diamond (1965) and Tirole (1985), except that we explicitly model credit markets, a credit market friction, and an allocative function for financial intermediaries. These changes yield substantially different results than those obtained in more standard models. In particular, if any monetary steady state equilibria exist, there are generally two of them; one of these has a low capital stock and output level, and it is necessarily a saddle. The other steady state has a high capital stock and output level; either it is necessarily a sink, or its stability properties depend on the rate of money creation. It follows that monetary equilibria can be indeterminate, and nonconvergence phenomena can be observed. Increases in the rate of money creation reduce the capital stock in the high-capital-stock steady state. If the high-capital-stock steady state is not a sink for all rates of money growth, then increases in the rate of money growth can induce a Hopf bifurcation. Hence dynamical equilibria can display damped oscillation as a steady state equilibrium is approached, and limit cycles can be observed as well. In addition, in the latter case, high enough rates of inflation induce the kinds of “crises” noted by Bruno and Easterly (1995): when inflation is too high there are no equilibrium paths approaching the high-activity steady state. Received: November 18, 1995; revised version: March 26, 1996     

On Equilibrium Dynamics Under Externalities in a Model of Economic Development

This paper studies a discrete-time version of a model of economic development proposed by Lucas, in which the average stock of human capital produces a positive externality in the production of the physical capital good. It establishes the existence of equilibrium programmes from arbitrary initial conditions, and of an equilibrium steady-state programme. The principal results are concerned with the global dynamic behaviour of equilibrium programmes off the steady state. They show that the asymptotic growth rates of consumption, physical and human capital on any equilibrium programme will equal the growth rates of the respective variables along the equilibrium steady state
JEL Classification Numbers: C62, D90, O41     

Optimality and monetary equilibria in stationary overlapping generations models with long-lived agents: Growth versus discounting

This paper studies the relationship between the existence and optimality of a monetary steady state and the nonoptimality of nonmonetary steady states. We construct a sequence of stationary overlapping generations economies with longer and longer-lived generations in which all agents maximize a discounted sum of utilities with a common discount rate. Under some assumptions the following result is established: If the discount rate is greater (less) than the population growth rate, then eventually every nonmonetary steady state is optimal (nonoptimal) and a monetary steady state does not exist (exists and is optimal).     

Money-Hoarding as a Behaviour Towards Uninsured Idiosyncratic Risk

This paper explores the implications of the presence of uninsured idiosyncratic risks for the hoarding of intrinsically useless fiat money in an overlapping-generations model. It is shown that: (a) monetary equilibria exist in almost all cases; (b) the valuation of money is not necessarily Pareto-improving since the non-monetary steady state may Pareto-dominate the monetary one; and (c) the accelerating inflation may, moreover, reduce the long-run capital stock.
JEL Classification Number: E41.     

Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households

We prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two-sector model with infinitely lived heterogeneous agents. The most patient agent holds all the capital in this solution. We also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock, then the aggregate capital stock eventually is monotonic and converges to the steady state stock. If the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions. Periodic equilibria are shown to exist under weaker hypotheses. Journal of Economic Literature Classification Numbers: D52, D90, E13.     

On the Phelps–Koopmans theorem

We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. We argue that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that “capital overaccumulation” need not always imply inefficiency. Under mild regularity and smoothness assumptions, we provide an almost-complete characterization of situations in which every path with limit in excess of the smallest golden rule must be inefficient, so that a version of the Phelps–Koopmans theorem can be recovered. Finally, we establish that a nonconvergent path with limiting capital stocks above (and bounded away from) the smallest golden rule can be efficient, even if the model admits a unique golden rule. Thus the Phelps–Koopmans theorem in its general form fails to be valid, and we argue that this failure is robust across nonconvex models of growth.     

On the Multi-Country Version of the Solow–Swan Model

I study a multi-country version of the Solow–Swan model of capital accumulation. Capital is perfectly mobile and flows instantaneously to countries providing the highest return. I show that, in general, the model possesses infinitely many stationary equilibria that differ from each other in terms of the world interest rate and world output. Analysing the dynamics of the model, I find that multiple equilibria exist for any given initial allocation of capital. Finally, I discuss a generalization of the golden rule to the multi-country version of the Solow–Swan model and show that it satisfies a Nash equilibrium property.
JEL Classification Numbers: F20, O41     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Sustainability of public debt,public capital formation,and endogenous growth in an overlapping generations setting

Under the golden rule of public finance for public investment with a constant budget deficit/GDP ratio, we show that for the sustainability of government budget deficits there is a threshold of the initial public debt for a given stock of public capital, and that this threshold level of public debt is increasing in the stock of public capital. If the initial public debt is greater than the threshold, the government can no longer sustain budget deficits, while if it is smaller, the government can conduct a permanent deficit policy, which eventually leads to a positive public debt/GDP ratio.     

Does Money Always Make People Happy?

This paper presents an overlapping generations model with private information, in which the use of fiat money and the rampant moral hazard incentives sustain each other. It is shown that there is a monetary equilibrium, despite the fact that the rate of return on the nonmonetary asset is significantly higher than the rate of economic growth in the nonmonetary case; the valuation of money is not necessarily Pareto-improving, but rather can be harmful to almost all generations; an inflationary policy can improve the welfare of all generations except the initial one. Journal of Economic Literature Classification Number: E41.     

Pollution control and the Ramsey problem

Pollution is an inevitable by-product of production and is only gradually dissolved by the environment. It can be reduced by producing less and by cleaning up the environment, but neither occur when they are left to the market. Cleaning activities and the optimal emission charges increase with the stock of pollutants. When one allows for pollution of the environment in the classical Ramsey problem, the capital stock is less than in the market outcome and a fortiori less than under the golden rule. The analysis distinguishes between stock and flow externalities arising from pollution. An increase in impatience can lead to more capital accumulation, even though this leaves less room for current consumption.     

Bertrand Games and Sharing Rules

We consider asymmetric Bertrand games with arbitrary payoffs at ties or sharing rules, and identify sufficient conditions for the zero-profit outcome and the existence of Nash equilibria. Subject to some technical conditions on non-tied payoffs the following hold. If the sharing rule is strictly tie-decreasing all players but one receive zero equilibrium payoffs, while everybody does so if non-tied payoffs are symmetric. Mixed (pure) strategy Nash equilibria exist if the sharing rule is (norm) tie-decreasing and coalition-monotone. I would like to thank Fernando Branco, the audience at Pompeu Fabra (Barcelona), ISEG (Lisbon), University of Mannheim, ESEM 2003 (Venice), EARIE 2005 (Porto), two anonymous referees, and the editor Dan Kovenock for very useful comments. This research received financial support under project POCTI/ECO/37925/2001 of FCT and FEDER.     

MONEY AS A MECHANISM IN A BEWLEY ECONOMY*

We investigate the efficiency property of a monetary economy with spot trade. We prove a conjecture that is essentially due to Bewley (Models of Monetary Economics (1980); Econometrica 51 (1983), 1485–504). The gist is that monetary spot trading is nearly efficient ex ante in an environment where very patient agents can accumulate large enough money stocks to be completely self‐insured. We also study examples where a nonmonetary mechanism is preferred ex ante to any monetary mechanism in a stationary environment, and where an inflationary monetary mechanism is preferred ex ante to a laissez‐faire or deflationary monetary mechanism in an environment with impatient agents.     

A note on the existence of monetary equilibria in overlapping generations models with storage

Wallace's result for an OG model with nonstochastic storage is extended, by provision of a necessary and sufficient condition for fiat currency to be valued in equilibrium in an OG model with stochastic storage. It is shown that a monetary equilibrium exists if and only if the real rate of return on currency that would obtain in the stationary monetary equilibrium exceeds the risk-free real rate of return that obtains in the nonmonetary equilibrium.     

Money and Price Dispersion

We relax restrictions on the storage technology in a prototypical monetary search model to study price dispersion. In this case, buyers and sellers enter matches with potentially different willingness to trade. Across the distribution of possible bilateral matches, prices generally will differ even though agents have identical preferences and technologies. We provide existence conditions for a particularly simple equilibrium pattern of exchange. We prove that in the limiting case where search frictions are eliminated, equilibrium prices are uniform. We also show that a higher initial money stock can raise the average price level and increase price dispersion.     

Undiscounted optimal growth with consumable capital and labor-intensive consumption goods

This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is labor-intensive. The results suggest that if the initial capital stock is above a threshold level, that depends upon the consumption of capital, every optimal program is monotonic, converges to the golden rule stock in a finite number of periods, and undergoes either unemployment or excess capacity of capital.