In order to improve growth chamber protocols for lichens, we tested the effect of 1) wet filter paper versus self-drained nets as a substratum for lichens, and 2) gradual versus abrupt transitions between dark and light periods. For Lobaria pulmonaria (L.) Hoffm. cultivated on nets, RGR increased by 60% compared to those on wet papers, whereas abrupt on/off transitions between day/night gave as high growth rates as gradual transitions mimicking sunrise/sunset. Because thalli on nets had less surface water than those on papers, the higher RGR on nets likely resulted from less suprasaturation depression of photosynthesis. By supporting very high growth and eliminating any visible damage, the revised growth chamber protocols facilitate new functional lichen studies.

We study optimal sustainable policies in a benchmark logistic world (where both population and technological progress follow logistic laws of motion) subject to a pollution ceiling. The main policy in the hands of the benevolent planner is pollution abatement, ultimately leading to the control of a dirtiness index as in the early literature of the limits to growth literature. Besides inclusion of demographic dynamics, we also hypothesize that population size affects negatively the natural regeneration or assimilation rate, as a side product of human activities (like increasing pollution, deforestation,...). We first characterize optimal sustainable policies. Under certain conditions, the planner goes to the pollution ceiling value and stays on, involving a more stringent environmental policy and a sacrifice in terms of consumption per capita. Second, we study how the sustainable problem is altered when we depart from the logistic world by considering exponential technical progress (keeping population growth logistic). It’s shown that, as expected, introducing such an asymmetry widens the margins of optimal policies as sustainable environmental policies are clearly less stringent under exponential technical progress. Third, we connect our model to the data, using in particular UN population projections.

This paper surveys the contributions of David Cass, Tjalling Koopmans, and Edmond Malinvaud over the decades during which modern optimal growth theory was developed. By utilizing material ranging from dissertations, drafts, and working papers through conference presentations, discussions, and published papers, we show that both Malinvaud and Cass had significant impacts on the evolution of Koopman's thought, and the development of his part of what is known as “the Cass–Koopmans model.” Based on our findings, we conclude that the modern optimal growth model should include the contributions of Malinvaud, and be retitled “the Cass–Malinvaud–Koopmans” model accordingly.

In this note, we study the basic Ramsey models with labor–leisure choice. We first study the deterministic model and find that a closed-form solution exists and is represented by the Gauss hypergeometric functions. We next incorporate stochastic productivity shocks into the model. We prove that the analytical solution path still exists if the coefficient of relative risk aversion is equal to the capital share.

We incorporate a production technology that exhibits increasing returns to scale for small values of the capital stock and diminishing returns for the higher stocks at the firm level in a discrete-time version of Romer's endogenous growth model. We study the social planner's problem where the social production technology exhibits globally increasing returns to scale. The properties of the optimal paths are characterized. It is proved that for a given quality of knowledge technology, the countries can take off if their initial stock of capital is above a critical value. We analyze the effect of three factors on the critical value: initial knowledge, quality of knowledge technology, and level of fixed costs associated with production.

This paper analyzes optimal paths in a one-sector growth model when the technology is not convex. In such a case, we prove that optimal paths converge to the upper steady state iff the initial wealth is above a critical level. Then, we first show that, thanks to debt and/or R&D, the poverty trap may be avoided. Second, we introduce a distortion: corruption that mostly has dramatic consequences on growth, but may have a beneficial effect if it is not high and if it improves productivity (incentive effect).

William A. Brock has taught in the Departments of Economics at the University of Rochester, Cornell University, and the University of Chicago, before moving to the University of Wisconsin, Madison, where he is now Vilas Research Professor of Economics. He has also been an External Professor at the Santa Fe Institute since 1989. His many awards include election as a Fellow of the Econometric Society in 1974, a Fellow of the American Academy of Arts and Sciences in 1992, and as a Member of the National Academy of Sciences in 1998. His over 100 invited lectures include presentations in Poland, Belgium, France, Mexico, Canada, Japan, Australia, England, Sweden, Norway, and Australia.

Brock has been a leading contributor to the development of methods of intertemporal equilibrium analysis in the areas of growth theory, monetary theory, and finance. More recently, he has played a crucial role in the development of new methods for the analysis of nonlinear dynamics in macroeconomics and finance, and models of expectations that relax the assumption of rational expectations.

I interviewed Buz in the faculty cafeteria near the Social Science Research Institute building, on the Madison campus of the University of Wisconsin, on October 22, 1998. Our interview was interrupted when he had to go to teach, and then was finished by phone on December 11, 1998. The transcript that follows does little justice to the liveliness of Buz's conversation, mainly because of my inability to transcribe the animated facial expressions and hand gestures that made the mathematical references more concrete. I have added several footnotes to the transcript, identifying some of the published sources that were mentioned during our conversation.

David Cass is undoubtedly one of the central contributors to modern dynamic economics. His fundamental contributions include work on optimal growth problems, overlapping-generations models, sunspot equilibria, and general equilibrium models with incomplete markets. His research has shaped in profound ways the manner in which we do both micro- and macroeconomics. From laying the foundations of real business-cycle theory via the Cass-Koopmans model, to providing us with general tools and techniques to analyze dynamic economic models, to furthering our understanding of monetary economics, to making fundamental contributions to the economics of extrinsic uncertainty, Cass's work has played a major part in the development of much of modern macroeconomic theory. In addition to being a first-class scholar, Cass is also truly his own man and a free spirit of the highest order.

In this interview, we tried to gain some insights into the story of David Cass and his approach to economic theory. Also, given the title as well as the intended readership of Macroeconomic Dynamics, we made a real effort to get him to discuss modern macroeconomics and the influence his work has had on its development. We edited out some parts of the discussion in the interests of space, but what remains is essentially unedited. As most readers will know, David Cass has collaborated extensively with Karl Shell over the years. We talked to Shell a few weeks after talking to Cass, and that interview is scheduled to appear in a future issue.

We met with Dave in his office at the University of Pennsylvania's Economics Department just before noon. Amid the boxes and piles of articles, books and CD's, he sat in his standard jeans and T-shirt, looking about as disheveled as he usually does. We chatted there for a while, went out and continued over lunch, and then returned to complete the interview several hours later. It was an unseasonably warm day in February, and Friday the 13th to be exact. That is traditionally an unlucky day, but one that turned out in this case to be a real treat, at least for us! We hope that you get as much out of this conversation with Dave as we did.