Cross-section data often show that the wealth of the elderly increases with age even at advanced ages. These and other results suggest that the life-cycle hypothesis of consumption should be augmented to include a bequest motive for saving. In this paper, the author proposes a model of bequests, and a test for a bequ est motive. Using panel data, he finds that over a ten-year period the elderly in the data set dissaved, in contradiction to most cross- section results. The test offers no support for a bequest motive.

Though public intervention in the market for research is virtually universal, economists have paid surprisingly little attention to the choice of the form of research incentive in a given market structure. Many studies concentrate on patents, but any assumption of their superiority over other incentives has been founded on intuition rather than on formal analysis. In this paper I analyze the choice between three of the most alternative means of public intervention in the research market, namely, patents, prizes, and direct contracting for research services. I show why, and under what conditions, any one of the three may be preferred by a social welfare-maximizing administrator in a competitive economy, using a model that, for the first time, pays explicit attention to differences in the informational roles of each of these alternatives. In the extensive literature on the economics of patents (see Arnold Plant, 1934; Fritz Machlup, 1958; Charles Taylor and Z. A. Silberston, 1973; Morton Kamien and Nancy Schwartz, 1975; and F. M. Scherer, 1977, for valuable surveys), formal analysis weighs the benefits of patents as a solution to the market failure associated with the inappropriability of knowledge against the welfare cost due to the restriction on the use of the knowledge generated, and this tradeoff is optimized by patent life adjustment in William Nordhaus (1969). Scant analytical attention is paid to alternative incentive mechanisms. (An exception is Ben Yu, 1981, who considers the role of prior contracting for inventions.) But as many writers (for example, Dan Usher, 1964; Yoram Barzel, 1968; Joseph Stiglitz, 1969; Carole Kitti, 1973; Glenn Loury, 1979; Partha Dasgupta and Stiglitz, 1980a) have pointed out in various contexts, the incentive offered by an unlimited patent to competitive researchers may be excessive, due to the common pool problem discussed further in Section I below. If the patent administrator and researchers share the same information, as implicitly assumed in previous models, then the patent life limitation can be adjusted to provide the optimal patent incentive, given the pool problem. But in all such models, patents would not be chosen in a fully optimized fiscal system. Researchers and the administrator are assumed to have identical information about the shadow price of potential inventions; a patent is just a means of turning this shadow price into a monetary reward. But monetary compensation can instead be offered directly to researchers by the state. Assuming that patent revenues incur a higher deadweight loss than an equivalent amount of public funds financed by less distortionary means (for example, a minimally efficient tax system), appropriate prizes or government contracts are socially preferable to patents with optimal lives. If the patent is ever to be the optimal incentive mechanism for research, it must possess advantages not captured in existing models. Informal discussions of patents emphasize their informational role. To include the latter as a justification for decentralized invention incentives, I incorporate an ex ante imbalance of information about costs and benefits of research in the model presented in Section II. But this alone is not quite enough. It is further necessary to specify that the terms of the award must be fixed before *Department of Economics, Economic Growth Center, Box 1987 Yale Station, Yale University, New Haven, CT 06520. I thank, with the usual caveat, Marguerite Alejandro-Wright, Cindy Arfken, Martin Baily, Nuong Brennan, Steven Englander, Robert Evenson, Richard Levin, Richard Nelson, Susan Rose-Ackerman, Denis Wright, and two referees for assistance of various kinds.

Unlike the vast preponderance of planets, earth has been bequeathed a hospitable environment in which to thrive. Up to now, man's activities have affected this environment negligibly. Scientists are becoming convinced, however, that release of carbon dioxide (CO2) from combustion of fossil fuels will lead to a significant modification of the global climate (see Woodwell). How should we think about such a destruction of our heritage? Should it be treated as anathema, like bondage? Or should the pace and extent of use of our global commons be subject to the same reasoned balancing of costs and benefits as other economic activities? The present paper takes the second approach -- asking how fast the global economy should allow a buildup of atmospheric CO2. The first section reviews the current scientific knowledge on this subject, while the second puts this into an optimal growth framework. The third section then presents a numerical example, while the last presents some realistic policy views on the subject.