[This paper establishes a simple existence result for solutions to variational problems of the form ∫_0^∞ G(x, ẋ, t) dt or ∫_0^∞ G(x, ẋ, ẍ, t) dt. The key assumptions are that G have an integrable upper bound, that it satisfy a growth condition, and that it be concave as a function of the highest order derivative in the problem, other arguments held constant. The discussion illustrates why three well known types of problems fail to have solutions. For two of these—chattering and cake eating—extended solution concepts are contrasted with simple modifications that restore the existence of a conventional solution. In a third case—state variables with jumps—the source of the difficulty is fundamental. For these problems a natural extended solution, analogous to the extension from probability density functions to general distribution functions, is suggested.]

The economic analysis of property rights proceeds in two steps. The first distinguishes rival from nonrival goods. The second contrasts the welfare effects of property rights for these two types of goods. For rival goods, strong property rights lead to efficient outcomes. For nonrival goods, property rights involve the trade-off formalized by William Nordhaus (1969): Weak property rights lead to under-provision. Strong property rights create monopoly distortions. Recent discussions of copyright protection for recorded music have obscured the underlying economic issues. Interested firms deny that music-sharing will reduce the incentives for firms to release new recordings. Artists and recording companies never acknowledge the efficiency costs of prices that far exceed marginal cost. It is left to economists with no stake in the outcome to clarify these issues. (Full disclosure: I have not consulted for anyone in the Napster case.) The stakes in the battle over the music business are small enough to get lost in rounding

Mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in the languages of words as opposed to symbols, and between statements with theoretical as opposed to empirical content. Because it is difficult to distinguish mathiness from mathematical theory, the market for lemons tells us that the market for mathematical theory might collapse, leaving only mathiness as entertainment that is worth little but cheap to produce.

Economists devote too much attention to international flows of goods and services and not enough to international flows of ideas. Traditional trade flows are an imperfect substitute for flows of the underlying ideas. The simplest textbook trade model shows that a welfare-enhancing move toward freer flows of ideas should be associated with a reduction in conventional trade. The large quantitative effect from the flow of ideas is evident in the second half of the 20th century as the life expectancies in poor and rich countries began to converge. Another example comes from China, where authorities dramatically reduced accident rates by adopting rules of civil aviation that were developed in the United States. All economists, including trade economists, would be better equipped to talk about international flows of technologies and rules if they adopted a consistent vocabulary based on the concepts of nonrivalry and excludability. An analysis of the interaction between rules and technologies may help explain important puzzles such as why private firms have successfully diffused some technologies (mobile telephony) but not others (safe municipal water.)

Mistakes give us a window into the brain. Just as optical illusions help us understand visual information processing, mistaken choices help us understand decision-making. The mistakes described below suggest that economics can usefully segregate decision mechanisms into two broad categories - those based on thoughts and those based on feelings. Consideration of these mistakes suggests that economists will be better able to interpret the growing body of seemingly anomalous evidence about human behavior if they treat thoughts and feelings more symmetrically.

Growth in this model is driven by technological change that arises from intentional investment decisions made by profit-maximizing agents. The distinguishing feature of the technology as an input is that it is neither a conventional good nor a public good; it is a nonrival, partially excludable good. Because of the nonconvexity introduced by a nonrival good, price-taking competition cannot be supported. Instead, the equilibrium is one with monopolistic competition. The main conclusions are that the stock of human capital determines the rate of growth, that too little human capital is devoted to research in equilibrium, that integration into world markets will increase growth rates, and that having a large population is not sufficient to generate growth.