A price competition game under free entry

This study builds a game of Bertrand-like price competition in a market with free entry. Under the assumption of a standard U-shaped average cost curve, it demonstrates that even if the number of sellers is small, a long-run competitive outcome can be supported as a Nash equilibrium. This game provides unifying treatments to the standard Bertrand equilibrium, the long-run competitive outcome, Demsetz’s equilibrium as well as other types of equilibria that have not been known in the existing literature.This paper is dedicated to Professor Mukul Majumdar to celebrate his sixtieth birthday. I am deeply indebted to Mukul for his generosity and kindness towards me throughout my career. I am also grateful to Tapan Mitra and anonymous referees for their very useful comments and suggestions in the revision and to Fumio Dei, Jim Friedman, Koji Ishibashi, Atsushi Kajii, Takashi Kamihigashi, Kunio Kawamata, Kei-ichi Koda, Takashi Negishi, Michihiro Ohyama, Santanu Roy, and Yoshimasa Shirai for useful conversations and correspondence and, in particular, Motonari Kurasawa, who drew to my attention Demsetz’s work.     

Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.This paper is dedicated to Professor Mukul Majumdar on his 60th birthday. His research with various co-authors in the late 70s and the 80s pioneered innovative techniques for the analysis of nonconvex dynamic optimization models – both deterministic and stochastic. Roy considers himself particularly fortunate for having had the opportunity to learn economic theory and mathematical economics from Professor Majumdar. This paper has benefited from helpful comments and suggestions by an anonymous referee. Financial support from the 21st Century COE Program at GSE and RIEB, Kobe University, is gratefully acknowledged.     

A dynamic two country Heckscher–Ohlin model with non-homothetic preferences

We examine the properties of a two-country dynamic Heckscher–Ohlin model that allows for preferences to be non-homothetic. We show that the model has a continuum of steady state equilibria under free trade, with the initial conditions determining which equilibrium will be attained. We establish conditions under which a static Heckscher–Ohlin theorem will hold in the steady state, and also conditions for a dynamic Heckscher–Ohlin theorem to hold. If both goods are normal, each country will have a unique autarkic steady state, and all steady state equilibria are saddle points. We also consider the case in which one good is inferior, and show that this can lead to multiple autarkic steady states, violations of the static Heckscher–Ohlin theorem in the steady state. Furthermore, there may exist steady state equilibria that Pareto dominate other steady states. These steady states will be unstable if discount factors are the same in each country, although they may exhibit dynamic indeterminacy if discount factors differ.     

Migration under Asymmetric Information and Human Capital Formation

We study the migration of skilled workers, along with the skill acquisition incentives created by the prospect of migration. We trace out the dynamics of migration as foreign employers accumulate experience in deciphering the skill levels of individual migrants. It is found that migration by the relatively highly skilled is followed by return-migration from both tails of the migrant skill distribution; that the possibility of migration induces skill acquisition at home; that until the probability of discovery reaches its steady state equilibrium, migration consists of a sequence of moves characterized by a rising average skill level; and that migration of skilled workers can entail a home-country welfare gain.     

Quasi-fundamental exchange rate variation

Summary. This paper uses a general equilibrium model to study the determination of the exchange rate in an economy with fundamental uncertainty. The model has steady state equilibria in which the exchange rate is constant. These equilibria may coexist with “quasi-fundamental” equilibria – nonstationary equilibria in which the exchange rate displays stochastic fluctuations that are correlated with the fluctuations in fundamental random variables. The quasi-fundamental equilibria are Pareto dominated by the corresponding constant-exchange-rate steady states. They also converge to these steady states, inevitably or with positive probability. Received: October 2, 1999; revised version: March 26, 2002 RID="*" ID="*" This paper began as a joint project with Alex Mourmouras, who has made many helpful comments and suggestions but is not responsible for any errors or deficiencies. In addition, I thank an anonymous referee for helpful comments.     

Investment-specific technological change, skill accumulation, and wage inequality

Wage inequality between education groups in the United States has increased substantially since the early 1980s. The relative number of college-educated workers has also increased dramatically in the postwar period. This paper presents a unified framework where the dynamics of both skill accumulation and wage inequality arise as an equilibrium outcome driven by measured investment-specific technological change. Working through equipment–skill complementarity and endogenous skill accumulation, the model does well in capturing the steady growth in the relative quantity of skilled labor during the postwar period and the substantial rise in wage inequality after the early 1980s. Based on the calibrated model, we examine the quantitative effects of some hypothetical tax-policy reforms on skill accumulation, wage inequality, and welfare.     

Dynamics of endogenous growth

Summary We present an overlapping generations model of endogenous fertility and growth. The cost of child rearing and the effect of population size on total factor productivity determine the dynamics of competitive equilibrium path of our model. The non-linear dynamics of the model generates a plethora of outcomes (depending on the functional forms, parameters and initial conditions) that include not only the neo-classical steady state with exponential growth of population with constant per capita income and consumption, but also growth paths which do not converge to a steady state and are even chaotic. Exponential, and even super exponential, growth of per capita output are possible in some cases.We would like to thank Mukul Majumdar, Kazuo Nishimura and an anonymous referee for many comments.     

Indeterminacy in a dynamic two-country model

The purpose of this paper is to show that indeterminacy can arise in a simple competitive two-country dynamic model of international trade, free of externalities, imperfect competition, and government intervention. This seemingly surprising result is based on an assumption that there is no international credit market. As will be shown later, the assumption implies that dynamic equilibrium paths of our two-country, therefore heterogeneous consumer, model are not generally Pareto-optimal.The paper is dedicated to Professor Mukul Majumdar on the occasion of his 60th birthday with great respect. We thank Takashi Kamihigashi, Tapan Mitra and Makoto Yano for their useful comments on the earlier version of this paper.     

Variety-skill complementarity: a simple resolution of the trade-wage inequality anomaly

The Stolper–Samuelson theorem predicts that the relative wage of high-skilled to low-skilled labor will increase in the high-skill abundant US but decrease in low-skill abundant Mexico after trade liberalization, while it actually began to rise in both countries in the late 1980s. We present a simple resolution of this “trade-wage inequality anomaly” in a model of variety trade. Variety trade increases the variety of intermediate goods used by the final good. If the varieties and high-skilled labor are complements, the skill premium rises in both countries. This linking of imports of new foreign varieties—the extensive margin—to wage inequality is compatible with evidence. Our numerical examples illustrate that small amounts of variety trade can produce a significant increase in relative wage.     

Government Spending Shocks and Rule‐of‐Thumb Consumers with Steady‐State Inequality*

In the body of literature concerning fiscal policy, a central result is that government spending might stimulate private consumption because only some households save, while others spend their entire income each period. Although such heterogeneity naturally causes inequality, this complication is commonly avoided by assuming that transfers redistribute steady‐state wealth. I show that this steady‐state assumption drives short‐run results. Without redistribution, the equilibrium is indeterminate, and the labor‐market structure that is imposed to support the expansive result is theoretically inconsistent. On a more positive note, I propose a labor‐market formulation under which the expansive effects of government spending might arise.     

Implementing Steady State Efficiency in Overlapping Generations Economies with Environmental Externalities

We consider in this paper overlapping generations economies with pollution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that the dynamical inefficiency of a competitive equilibrium steady state with capital–labor ratio exceeding the golden rule ratio still holds. Moreover, the range of dynamically efficient steady state capital ratios increases with the effectiveness of the environment maintenance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the transition to the social planner's steady state.     

Is inequality the price to pay for higher growth in middle-income countries?

An evolutionary two-sector model is used to study the impact of skill-biased technological change on the growth and inequality paths of a middle-income developing economy. We present four scenarios resulting from changes in a country’s structural conditions and the characteristics of the shock. We show that wage inequality is neither a necessary nor a sufficient condition for growth. A Kuznets dynamic may emerge in the long run in the case of successful catching-up to the high-growth steady state. However, this only happens if adjustment costs significantly hamper the process of skill upgrade. The business cycle and the process of structural change may give rise to sizeable rises in wage inequality in the short term, even when the economy does not break out from the low-growth steady state.     

The technological determinants of long‐run inequality

I explore the effect of skill‐biased technological change and unbiased technological progress on long‐run inequality using a theoretical model in which the supply of skilled and unskilled workers is endogenous. The main assumption of the model is that young agents can finance their education and become skilled workers by borrowing against their future income on an imperfect credit market. I show that whenever the rate of unbiased technological progress is sufficiently high there is no steady‐state inequality, independent of the degree of skill bias. If instead the rate of unbiased technological progress is low, then the long‐run skill premium increases with the technological skill bias. Therefore, similarly to the short run, in the long run higher technological skill bias may cause higher inequality. However, contrary to the short run, in the long run unbiased technological progress is more important than technological skill bias in determining inequality. I also discuss how the efficiency of the educational technology and the degree of financial development affect long‐run inequality.     

SKILL REQUIREMENTS,SEARCH FRICTIONS,AND WAGE INEQUALITY*

We analyze wage inequality, extending the Burdett and Mortensen (International Economic Review 39 (1998), 257–73) model by incorporating worker heterogeneity through skill requirements. We provide sufficient conditions for existence of an equilibrium where more productive firms offer higher wages. The unique such equilibrium is characterized in a closed form solution. Both within‐ and between‐group inequality are explicitly calculated. We then calibrate the model to explain the joint movement of both within‐ and between‐group inequality in the late 1980s and 1990s, an explanation that has been elusive in the literature so far.     

Optimal balanced growth in a general multi-sector endogenous growth model with constant returns

I will study a multi-sector endogenous growth model with general constant returns to scale technologies and demonstrate the existence, uniqueness and the saddle-path stability of the balanced growth equilibrium. I will first demonstrate the existence of a balanced growth equilibrium, by showing that the balanced growth rate associated with the balanced growth equilibrium is solely determined by solving a Frobenius root problem of the price equations derived from the Euler equations and the property of the nonsubstitution theorem. Then I will show the saddle-path stability of the balanced growth equilibrium without any capital intensity conditions, which is a generalized property proved in the two-sector endogenous growth models by de Guevara et al. (J Econ Dyn Control 21, 115–143, 1997), Bond et al. (J Econ Theory 68, 149–173 1996) and Mino (Int Eco Rev 37, 227–251 1996). The theorem clearly implies that the balanced growth equilibrium has a transition path in the neighborhood of the balanced growth equilibrium. The paper was presented at the conferences “Irregular Growth: Beyond Balanced Growth” held on June 19–21, 2003 in Paris and “Economic Growth and Distribution: On the Nature and Causes of the Wealth of Nations” held on June 16–18, 2004 in Lucca, Italy. From the discussion with Alain Venditti at CNRS-GREQAM, Gerhard Sorger at University of Vienna and the conference participants, I have been benefited much by writing this paper. Especially Alain Venditte had given me a chance to take a look at his unpublished paper titled ” Indeterminacy and the Role of Factor Substitutability” jointly written with Kazuo Nishimura at Kyoto University and published in Macroeconomic Dynamics, Vol. 8. The author also would like to thank an anonymous referee for useful suggestions.     

Fiscal policies, environmental pollution and economic growth

This paper develops a model of endogenous economic growth with special consideration to the role of productive public expenditure and environmental pollution; and analyses the properties of optimal fiscal policy in the steady state growth equilibrium. We consider the level of consumption as the source of pollution. Government allocates its tax revenue between pollution abatement expenditure and productive public expenditure. Optimum ratio of productive public expenditure to national income is equal to the competitive output share of the public input, when productive public expenditure is depicted as tax revenue minus abatement expenditure. However, the proportional income tax rate exceeds the competitive output share of the public input. There is no conflict between the social welfare maximizing solution and the growth rate maximizing solution in the steady state growth equilibrium. The unique steady state growth equilibrium appears to be a saddle-point when the growth rate is above a critical level and the steady state equilibrium growth rate in the market economy is not necessarily lower than the socially efficient growth rate.     

Human capital and economic growth in an overlapping generations model

The paper describes an aggregative optimal growth model, the essential features of which are that individuals are mortal and obtain their labor skill through educational training. The process of human capital formation is described by an education function which relates the pass rate to the educational expenditure per student. Two alternative scenarios, private and public education regimes, are separately investigated. Under the decentralized education regime, risk-neutral individuals borrow to finance their education when young. Under the centralized education regime, the cost of education is financed by taxes imposed on the workers in the economy, and the central government maximizes a long-term social target function. The equilibria of both regimes are analyzed and various comparative static results derived. It is shown that educational investment in a decentralized equilibrium is higher than that in the centralized steady state. We also establish that there exists a time discount rate at which or above which the decentralized per capita consumption exceeds that of the centralized steady state whereas for time rates of discount sufficiently near the population growth rate, the above result will be reversed.     

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 a clear day you might see an environmental Kuznets curve

We shed some new light on the Environmental Kuznets curve (EKC) and show how it can be viewed as a particular form of equilibrium relationship, where technology and preference parameters determine the shape of the curve. In contrast to most of the literature on the EKC, we estimate a theoretically consistent model on long-run data (Swedish sulfur emission, covering the period 1900–2002). Furthermore, we test and date structural change. The model suggests four regimes, 1900–1918, 1919–1933, 1934–1967 and 1968–2002, generating four rather different patterns for pollution over time. The policy-conclusions are consonant with Pearce’s general view about the EKC: there is no theoretical presumption that it has an inverted U shape, nor should any country try to “grow out of the environmental problems” without analyzing the benefits and costs of so doing.     

Income inequality and economic growth

Despite the extensive existing literature on income inequality and economic growth, there remains considerable disagreement on the effect of inequality on economic growth. Existing literatures find either a positive or a negative relationship. In this paper, we attempt to theoretically examine that relationship with a stochastic optimal growth model. We make the disagreement clear within a single model. We conclude (i) that both are possible – that is, higher inequality can retard growth in the early stage of economic development, and can encourage growth in a near steady state, (ii) that income redistribution by high income tax does not always reduce income inequality. Income inequality can be reduced by higher income tax in a near steady state, but it cannot be reduced in the early stage of economic development, and (iii) that two government polices – rapid economic growth and low income inequality – can be achieved by low income tax in the early stage of economic development, but both cannot be achieved simultaneously in a near steady state.