The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, - provements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who ?nd our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsaeter, Arne Strom, Peter Berck From the preface to the third edition Thepracticeofeconomicsrequiresawide-rangingknowledgeofformulasfrommat- matics, statistics, andmathematicaleconomics. Withthisvolumewehopetopresent a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas often used by economists, this volume contains many purely economic results and theorems. It containsjusttheformulasandtheminimumcommentaryneededtorelearnthema- ematics involved. We have endeavored to state theorems at the level of generality economists might ?nd useful. In contrast to the economic maxim, "everything is twice more continuously di?erentiable than it needs to be," we have usually listed theregularityconditionsfortheoremstobetrue.Wehopethatwehaveachieveda level of explication that is accurate and useful without being pedantic."

A changing climate is likely to have a drastic impact on crop yields in Africa. The purpose of this book is to document the effects of climate change on agriculture in Africa and to discuss strategies for adaptation to hotter weather and less predictable rainfall. These strategies include promoting opportunities for farmers to adopt technologies that produce optimal results in terms of crop yield and income under local agro-ecological and socioeconomic conditions. The focus is on sub-Saharan Africa, an area that is already affected by changing patterns of heat and rainfall. Because of the high prevalence of subsistence farming, food insecurity, and extreme poverty in this region, there is a great need for practical adaptation strategies. The book includes empirical research in Ethiopia, Kenya, South Africa, Tanzania, and other Sub-Saharan countries, and the conclusion summarizes policy-relevant findings from the chapters. It is aimed at advanced students, researchers, extension and development practitioners, and officials of government agencies, NGOs, and funding agencies. It also will provide supplementary reading for courses in environment and development and in agricultural economics.

The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, - provements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who ?nd our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsaeter, Arne Strom, Peter Berck From the preface to the third edition Thepracticeofeconomicsrequiresawide-rangingknowledgeofformulasfrommat- matics, statistics, andmathematicaleconomics. Withthisvolumewehopetopresent a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas often used by economists, this volume contains many purely economic results and theorems. It containsjusttheformulasandtheminimumcommentaryneededtorelearnthema- ematics involved. We have endeavored to state theorems at the level of generality economists might ?nd useful. In contrast to the economic maxim, "everything is twice more continuously di?erentiable than it needs to be," we have usually listed theregularityconditionsfortheoremstobetrue.Wehopethatwehaveachieveda level of explication that is accurate and useful without being pedantic."