We evaluate the income elasticity of the aggregate budget share spent on a sub-group of commodities, in a competitive framework, by a continuum of agents having the same income, but heterogeneous behavior described by an "homothetic preferences scaling factor" having a bounded Pareto distribution in the population. If individual budget share increases globally significantly in the limit from low to large incomes, aggregate budget share is locally increasing with medium range incomes when the logarithm of the heterogeneity factor has an increasing (exponential) density with a large support. Aggregate income elasticity converges to that exponential density parameter when its support becomes infinitely large. Symmetric results hold in the decreasing case. Applications are made to market expenditures, wealth effects on portfolio choice with many risky assets, concave expenditures, that are compatible with standard (expected) utility maximization or other "behavioral" decision making processes.

The Implications of Heterogeneity and Inequality for Asset Pricing provides a unified framework to better understand this large literature and to reconcile several of the seemingly inconsistent results found in some seminal papers.

We provide a systematic analysis of the properties of individual returns to wealth using twelve years of population data from Norway’s administrative tax records. We document a number of novel results. First, during our sample period individuals earn markedly different average returns on their financial assets (a standard deviation of 14%) and on their net worth (a standard deviation of 8%). Second, heterogeneity in returns does not arise merely from differences in the allocation of wealth between safe and risky assets: returns are heterogeneous even within asset classes. Third, returns are positively correlated with wealth: moving from the 10th to the 90th percentile of the financial wealth distribution increases the return by 3 percentage points - and by 17 percentage points when the same exercise is performed for the return to net worth. Fourth, wealth returns exhibit substantial persistence over time. We argue that while this persistence partly reflects stable differences in risk exposure and assets scale, it also reflects persistent heterogeneity in sophistication and financial information, as well as entrepreneurial talent. Finally, wealth returns are (mildly) correlated across generations. We discuss the implications of these findings for several strands of the wealth inequality debate.

The U.S. population is aging. Social Security projections suggest that between 2013 and 2050, the population aged 65 and over will almost double, from 45 million to 86 million. One key driver of population aging is ongoing increases in life expectancy. Average U.S. life expectancy was 67 years for males and 73 years for females five decades ago; the averages are now 76 and 81, respectively. It has long been the case that better-educated, higher-income people enjoy longer life expectancies than less-educated, lower-income people. The causes include early life conditions, behavioral factors (such as nutrition, exercise, and smoking behaviors), stress, and access to health care services, all of which can vary across education and income. Our major entitlement programs - Medicare, Medicaid, Social Security, and Supplemental Security Income - have come to deliver disproportionately larger lifetime benefits to higher-income people because, on average, they are increasingly collecting those benefits over more years than others. This report studies the impact the growing gap in life expectancy has on the present value of lifetime benefits that people with higher or lower earnings will receive from major entitlement programs. The analysis presented in The Growing Gap in Life Expectancy by Income goes beyond an examination of the existing literature by providing the first comprehensive estimates of how lifetime benefits are affected by the changing distribution of life expectancy. The report also explores, from a lifetime benefit perspective, how the growing gap in longevity affects traditional policy analyses of reforms to the nation's leading entitlement programs. This in-depth analysis of the economic impacts of the longevity gap will inform debate and assist decision makers, economists, and researchers.

Pricing is an essential aspect of the marketing mix for brands and products. Further, pricing research in marketing is interdisciplinary, utilizing economic and psychological concepts with special emphasis on measurement and estimation. This unique Handbook provides current knowledge of pricing in a single, authoritative volume and brings together new cutting-edge research by established marketing scholars on a range of topics in the area. The environment in which pricing decisions and transactions are implemented has changed dramatically, mainly due to the advent of the Internet and the practices of advance selling and yield management. Over the years, marketing scholars have incorporated developments in game theory and microeconomics, behavioral decision theory, psychological and social dimensions and newer market mechanisms of auctions in their contributions to pricing research. These chapters, specifically written for this Handbook, cover these various developments and concepts as applied to tackling pricing problems. Academics and doctoral students in marketing and applied economics, as well as pricing-focused business practitioners and consultants, will appreciate the state-of-the-art research herein.

This volume is devoted to a reappraisal of the Marginal Revolution on the occasion of its 150th anniversary. The year 1871 should be remembered as one of the most important turning points in the history of economics. W. S. Jevons, C. Menger, and L. Walras published epochal works at the very beginning of the 1870s. Although these works were written independently, they shared a common mathematical structure based on classical analysis. For this reason, the emergence of the trio is called the Marginal Revolution. Indeed, 1871 is the starting point of modern economics in the proper sense. In 1971, several academic conferences were held on the occasion of the 100th anniversary of the Revolution, which exerted the stimulating influence upon the historical researches into the Revolution. Now more than fifty years have passed since then. Economic theory has experienced further substantial changes in researchers’ central interest, the way of reasonings and the styles of description during this period. In view of the new achievements acquired in recent fifty years, it seems an indispensable task for us to review and reevaluate the Marginal Revolution based upon the present status of economics. We also keep in mind that some concepts and doctrines once discarded could reappear in a later stage of history in a more or less transfigured form. The introductory chapter will be a guide for readers not only from the economics community but also from the mathematics community.