5. Suppose that a household faces the following optimization problem maxu(co) + 3u(c1) s.t. coxo, c1 1 x1 = (xoco) (1 + r − ɛ) xo given. where & is equal to 0 < 1 < r with probability a and equal to 0 < 2 2. Assume that u() satisfy the assumptions we stated in the first class. Use the Lagrangian method (Kuhn-Tucker conditions) and the dynamic programming method to solve this problem and compare the results.

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5. Suppose that a household faces the following optimization problem
max u(co) + 3u(cı)
s.t. co < xo, c1 < x1
x1 = (xo – co)(1+r – €)
xo given.
where e is equal to 0 < ɛ1 <r with probability a and equal to 0 < ɛ2 < r with probability 1 – a,
and ɛ1 > 82. Assume that u(:) satisfy the assumptions we stated in the first class. Use the Lagrangian
method (Kuhn-Tucker conditions) and the dynamic programming method to solve this problem and
compare the results.
Transcribed Image Text:5. Suppose that a household faces the following optimization problem max u(co) + 3u(cı) s.t. co < xo, c1 < x1 x1 = (xo – co)(1+r – €) xo given. where e is equal to 0 < ɛ1 <r with probability a and equal to 0 < ɛ2 < r with probability 1 – a, and ɛ1 > 82. Assume that u(:) satisfy the assumptions we stated in the first class. Use the Lagrangian method (Kuhn-Tucker conditions) and the dynamic programming method to solve this problem and compare the results.
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