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Need some help with these questions please !!

Hiii,
I really need some help with these exam questions , thank you in advance :

1). Agents 1,2 and 3 consume a common resource of magnitude X. Agent i’s consumption is denoted by xi
, i = 1, 2, 3. The utility function of i is ui(x1, x2, x2) = ln(xi) + ln(X
x1 x2 x3), i = 1, 2, 3. Each agent choses how much to consume. Choices are madesimultaneously.
(i) What are the Nash equilibrium choices of the agents?
(ii) What are the Pareto optimal choices?
(iii) How are the choices compared? Why?

2) Assume you are shipwrecked and the 16 of you are in a lifeboat in the middle of the ocean. You know that it will take 10 days to reach shore and that there are food supplies for just 10 person-days (hence only one person can survive if he/she uses the food supplies exclusively; notice also that you need food supplies for 160 person-days for all of you to survive). How would you allocate the food supplies among yourselves? You may use the Pareto criterion and also any other criteria you think are suitable.


4. Discuss how the problems of adverse selection and moral hazard are detrimental to theoperation and the welfare generated in a market. Don’t forget to give some examples.

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