Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.

• Most up-to-date, comprehensive textbook on optimal control theory, perennially important subject for economists/operations researchers • Subject matter taught around the world to graduate students in advanced mathematical methods across the sciences/social sciences • Exercises at end of each chapter on elementary and specialized topics

### Contents

1. Essential elements of continuous time dynamic optimization; 2. Necessary conditions for a simplified control problem; 3. Concavity and sufficiency in optimal control problems; 4. The maximum principle and economic interpretations; 5. Linear optimal control problems; 6. Necessary and sufficient conditions for a general class of control problems; 7. Necessary and sufficient conditions for isoperimetric problems; 8. Economic characterization of reciprocal isoperimetric problems; 9. The dynamic envelope theorem and economic interpretations; 10. The dynamic envelope theorem and transversality conditions; 11. Comparative dynamics via envelope methods; 12. Discounting, current values, and time consistency; 13. Local stability and phase portraits of autonomous differential equations; 14. Necessary and sufficient conditions for infinite horizon control problems; 15. The neoclassical optimal economic growth model; 16. A dynamic limit pricing model of the firm; 17. The adjustment cost model of the firm; 18. Qualitative properties of infinite horizon optimal control problems with one state variable and one control variable; 19. Dynamic programming and the Hamilton-Jacobi-Bellman equation; 20. Intertemporal duality in the adjustment cost model of the firm.