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10700893Please help me out, I have no ideas to solve this two

problems in homework. Thanks a lot.

attachment_10022019.png

Problem 4: We want to solve the following continuous time dynamic opti-
mization problem:
max
Jo
e- ptu (ct, lt ) dt
subject to
he = - 8k + f ( ke, le ) - c
where c is consumption, ( is labor, & is capital with initial value ko = 1, 6 = 0.1,
p = 0.015,
u (c, () = In(c) -
and f(k, l) = kool -" with a = 0.3. Write a Matlab code with the explicit finite
difference method (with time step size h = 0.5 year over a 200-year horizon)
and fmincon to solve the problem. Plot your solutions (c, (, k) in the first 100
years. (20 points)
Problem 5: Derive the Hamiltonian system of the model in Problem 4, and
solve it using byp4c. (20 points)

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