6. Equations of Motion

This chapter delves into the fundamental role of equations of motion in dynamic optimization problems, focusing on difference and differential equations. It begins by introducing the concept of time as a key factor in these equations, using examples like the cake-eating problem to illustrate basic principles. The chapter then explores difference equations, highlighting their use in discrete-time problems and their analogy to differential calculus. A notable example is the cobweb model, which demonstrates how supply and demand dynamics can lead to market equilibrium or divergence. The text also covers differential equations, their forms, and solutions, with examples like depreciating investment and renewable natural resources. The chapter concludes with a practical application of a fisheries model, illustrating how equations of motion can be used to manage and sustain natural resources. Throughout, the chapter emphasizes the importance of understanding these equations for solving real-world economic and environmental problems.