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It was very early in the morning. She was looking at the yard from behind a window. The tree was in full bloom. She removed a lock of white hair from her forehead. It was the forty-first time that she was watching the tree blossom. She was standing in front of the window in her thick white nightgown with long sleeves and closed collar. She was a bit cold. The wind made the blossoms shiver. It seemed that the flowers never felt cold. The woman recalled the very first time she watched them.She has awakened to the sound of her husband's voice, "Wake up! Come and see! The tree has blossomed!" They have stood watching together at the window. Her long white nightgown was sleeveless and thin, with lace around its open collar. She wasn't cold, or perhaps it was her sense of decency that made her forget the cold.

Using a vertical differentiation model of endogenous growth with stochastic R&D activity, we characterise the optimal patent lifetime a government would set in order to maximise economic growth. We show that a finite patent lifetime does exist and is unique provided that the expected rate of return from R&D is sufficiently large. Additionally, we analyse the impact of the level of competition in the R&D sector, the interest rate, the monopoly profit and the productivity parameter of research technology on this optimal patent lifetime.

Freedom is one of the central values in political and moral philosophy. A number of theorists hold that freedom (or, relatedly, opportunity) should either be the only or at least one of the central distribuenda in our theories of distributive justice. Moreover, many follow Mill and hold that a concern for personal freedom should guide, and limit, how paternalist public policy can be. For the most part, theorists have focussed on a person's freedom at one specific point in time but have failed to give proper attention to freedom across time. Given that we care about personal freedom now, we have reason to care about future freedom too. But what kind of distribution of freedom across a person's lifetime should we promote as a matter of legislation and public policy? I argue that none of the candidate principles for the distribution of freedom across time is plausible. Neither a starting gate view, nor a maximisation nor a sufficientarian view is satisfactory, because none adequately reflects our various reasons to value freedom. I show that this result presents a tough challenge for theories of distributive justice and paternalism that set great store by personal freedom.

Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital, estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth -- features which are chosen to match observed properties of earnings dynamics by cohorts. We find that as of age 20, differences in initial conditions account for more of the variation in lifetime utility, lifetime earnings and lifetime wealth than do differences in shocks received over the lifetime. Among initial conditions, variation in initial human capital is substantially more important than variation in learning ability or initial wealth for determining how an agent fares in life. An increase in an agent's human capital affects expected lifetime utility by raising an agent's expected earnings profile, whereas an increase in learning ability affects expected utility by producing a steeper expected earnings profile.

This paper challenges the notion that on-the-job training investments are quantitatively important for workers' welfare and argues that on-the-job training may not increase lifetime income by more than 1 percent. I argue that it is very difficult to reconcile the slowdown in wage growth late in a worker's career with optimizing behavior unless the technology for learning on the job is such that it generates very low gains from training. The analysis is based on a nonparametric methodology for estimating the learning technology from wage profiles; the results are arrived at by comparing the lifetime income when the worker optimally invests in his human capital to the one where he does not make any investments.

Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital, estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth. We find that, as of age 23, differences in initial conditions account for more of the variation in lifetime earnings, lifetime wealth, and lifetime utility than do differences in shocks received over the working lifetime. (JEL D31, D91, J24, J31)

Studies of the empirical relationship between income and mortality often rely on data aggregated by geographic areas and broad population groups and do not distinguish disabled and nondisabled persons. We investigate the relationship between individual mortality and lifetime income with a large micro data base of current and former retired participants in the U. S. Social Security system. Logit models by gender and race confirm a negative relationship. Differences in age of death between low and high lifetime income are on the order of two to three years. Income-related mortality differences b

As modern economies become predominantly service-based, companies increasingly derive revenue from the creation and sustenance of long-term relationships with their customers. In such an environment, marketing serves the purpose of maximizing customer lifetime value (CLV) and customer equity, which is the sum of the lifetime values of the company's customers. This article reviews a number of implementable CLV models that are useful for market segmentation and the allocation of marketing resources for acquisition, retention, and cross-selling. The authors review several empirical insights that were obtained from these models and conclude with an agenda of areas that are in need of further research.