We consider an economy with three cities producing different outputs. Two cities produce intermediate goods, a type 1 city producing an intermediate “agricultural” good with capital and labor only, and a type 2 city producing an intermediate “industrial” good with capital, labor, and human capital. A type 3 city produces the final good which is obtained from the two intermediate goods and labor. The asymmetric introduction of human capital allows us to prove that the three cities experience, at equilibrium, heterogeneous endogenous growth rates which are proportional to the growth rate of human capital. We show that the “industrial” type 2 city is characterized by the larger growth rate while the “agricultural” type 1 city experiences the lower growth rate, and thus the type 3 city is characterized by a growth rate which is a convex combination of the two former growth rates. This implies that the relative size in terms of output of the “agricultural” city decreases over time. This property allows us to recover the empirical fact that most non-agricultural production occurs in growing metropolitan areas. But, simultaneously, as we prove that total labor employed in each city is proportional to the total population, the relative population size distribution of cities is constant over time, as shown in empirical studies.

The interplay between growth and public debt is addressed considering a Barro‐type (1990) endogenous growth model where public spendings are financed through taxes on income and public debt. The government has a target level of public debt relative to GDP, and the long‐run debt‐to‐GDP ratio is used as a policy parameter. We show that when debt is a large enough proportion of GDP, two distinct balanced‐growth paths (BGPs) may coexist, one being indeterminate. We exhibit two types of important trade‐offs associated with self‐fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the debt‐to‐GDP ratio while the highest one is increasing. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, local and global indeterminacy may arise and self‐fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth, welfare, and macroeconomic fluctuations. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.

We investigate the role of nonseparable preferences in the occurrence of macroeconomic instability under a balanced-budget rule where government spending is financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of nonseparable utility functions, we find that expectations-driven fluctuations occur easily when consumption and labor are Edgeworth substitutes or weak Edgeworth complements. Under these assumptions, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability.

This book presents the state-of-the-art in non-linear dynamics and sunspots. These two topics have been the core of an international conference on instability and public policies in a globalized world, organized at Aix-Marseille School of Economics and GREQAM in honor of Jean-Michel Grandmont. He has made significant contributions on general equilibrium theory, monetary theory, learning, aggregation, non-linear dynamics and sunspots. This book assembles contributions by Jean-Michel Grandmont's colleagues, students and friends that have been influenced by his works and that are at the frontier of research in this domain today.