A student will stay in Germany from time 0 until time T. She must plan her consumption, c(t) where t is time. She has total savings in euro of 1000 at time 0 and receives a flow of income of 100, so that her stock of savings, S(t) evolves according to the equation Her utility function is . When she leaves Germany at time T she can take no euro with her.

(a) Write down the Hamiltonian for her optimal consumption problem.

(b) State the necessary conditions for the optimal solution.

(c) Derive the optimal time path of her consumption. Explain whether it is increasing over time, constant or decreasing.

== 100-c