Elements of Numerical Mathematical Economics with Excel

Exercises

• 1. A first-order system is described by the following equation of motion in the state variable:
• y ˙ = − y + u

  
•     with initial condition y(0)   =   4 and y(T) free.
•     Find in Excel the optimal control (unconstrained) that minimizes the following performance measure:
• J ( u ) = ∫ 0 1 1 2 u 2 d t + y 2 ( 1 )

  
•     where the function outside the integral can be defined as a salvage value function h(y(T), T).
•     The costate equation is λ ˙ ( t ) = − λ ( t ) and ...