Leading empiricists and theorists of cities have recently argued that the generation and exchange of ideas must play a more central role in the analysis of cities. This paper develops the first system of cities model with costly idea exchange as the agglomeration force. The model replicates a broad set of established facts about the cross section of cities. It provides the first spatial equilibrium theory of why skill premia are higher in larger cities and how variation in these premia emerges from symmetric fundamentals.

We consider the distribution of economic activity within a country in light of three leading theories—increasing returns, random growth, and locational fundamentals. To do so, we examine the distribution of regional population in Japan from the Stone Age to the modern era. We also consider the Allied bombing of Japanese cities in WWII as a shock to relative city sizes. Our results support a hybrid theory in which locational fundamentals establish the spatial pattern of relative regional densities, but increasing returns help to determine the degree of spatial differentiation. Long-run city size is robust even to large temporary shocks.

Introduction to modern corporate finance economic foundations the economic system and contracting the time value of money the valuation of financial securities the techniques of capital budgeting risk and diversification the capital asset pricing model an introduction to options financial leverage financing in imperfect markets the dividend decision corporate ethics and shareholder wealth maximization estimating project cash flows advanced topics in capital budgeting financial analysis and planning working capital and management international finance mergers and reorganizations.

The methods of Gibbons and Ferson (1985) are extended, relaxing the assumption that expected returns are linear functions of predetermined instruments. A model of conditional mean-variance spanning generalizes Huberman and Kandel (1987). The empirical results indicate that more than a single risk premium is needed to model expected stock and bond returns, but the number of common factors in the expected returns is small. However, when size-based common stock portfolios proxy for the risk factors, we reject the hypothesis that four of them describe the conditional expected returns of the other assets.

The methods of Gibbons and Ferson (1985) are extended, relaxing the assumption that expected returns are linear functions of predetermined instruments. A model of conditional mean‐variance spanning generalizes Huberman and Kandel (1987). The empirical results indicate that more than a single risk premium is needed to model expected stock and bond returns, but the number of common factors in the expected returns is small. However, when size‐based common stock portfolios proxy for the risk factors, we reject the hypothesis that four of them describe the conditional expected returns of the other assets.

What causes individual suppliers to allocate goods in such a way that the aggregate allocation satisfies the law of one price? A satisfactory answer to this question must confront two related problems: Equal net prices at all allocations provide no information to suppliers about the quantity to deliver to a specific location, and strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity. This paper develops a simple analytical framework to formalize these two problems, reviews some solutions found in the literature, and reports laboratory evidence on how people solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.

What causes individual suppliers to allocate goods in such a way that the aggregate allocation satisfies the law of one price? A satisfactory answer to this question must confront two related problems: Equal net prices at all allocations provide no information to suppliers about the quantity to deliver to a specific location, and strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity. This paper develops a simple analytical framework to formalize these two problems, reviews some solutions found in the literature, and reports laboratory evidence on how people solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.