# construct the Lagrangian and derive the first order kuhm-tucker conditions for a problem

Question

(Consumption under Certainty) Consider aunit mass of identical consumers with the instantaneous utility function u(Ct ). At time t = 0, the representative consumer maximizes her expected lifetime utility,

Subject to At 0 given initial wealth A0 0, and

,    0

(a) Using the law of motion (*) derive a single lifetime budget constraint. Be specific about what you did for At

(b) Construct the Lagrangian for this problem, and derive the first order kuhm-tucker conditions for the interior solution. Combining them obtain the Euler equation and interpret it

(c)  Show that MRS is given by

t+1, t) = 1/      0             (*)

(d) Assume that ρ= (1-β)/ β (the rate of time preference) equals r. show that

i) (*) implies the lifetime consumption smoothing:

ii) Show that C above is given by   C=

Summary

This question belongs to operations management, given utility and expected life time functions under certain conditions. You are required to understand the concept and answer the given questions.

Total Word Count 189

• Rasha

this is a very good website

• maani

I have 50 questions for the same test your page is showing only 28

• joeanne

• joeanne

hi can anyone help or guide me to my assignments. thanks

• Monik

• Cristina

This solution is perfect ...thanks

• Janete

Hello Allison,I love the 2nd image that you did! I also, had never heard of SumoPaint, is something that I will have to exolpre a bit! I understand completely the 52 (or so) youtube videos that you probably watched. Sometimes they have what you want, sometimes they don't! However, it is always satisfying when you are able to produce something that you have taught yourself. Great job!Debra 0 likes

• Sandeep

Perfect bank of solution.

• Oxana

great !

• Paul Brandon-Fritzius

thanks for the quick response. the solution looks good. :)

• tina Johnson

thnx for the answer. it was perfect. just the way i wanted it.

• Giuseppe

works fine.