Subsistence Levels of Consumption: Suppose you are interested in modeling a policy issue involving poor households in an under-developed country.
A: The households we are trying to model are primarily worried about survival, with a minimum quantity of certain goods (like food and water) necessary for survival. Suppose that one cannot live without at least 4 liters of water per week and at least 7,500 calories of food per week. These quantities of water and food are then subsistence levels of water and food.
(a) Suppose you graph weekly liters of water on the horizontal axis and weekly intake of calories on the vertical. Indicate the bundle required for subsistence.
(b) If life below the subsistence quantities is not sustainable, we might find it reasonable not to model tastes below the subsistence quantities. Illustrate a plausiblemap of indifference curves that takes this into account.
(c) Subsistence levels are a biological reality for all of us, not just for the poor in developing countries.
Why might we nevertheless not worry about explicitly modeling subsistence levels for policy analysis in richer countries?

B:

(a) When interpreted as a model of tastes such as those described in part A, what are the subsistence levels of x1 and x2?
(b) How does this utility function treat tastes below subsistence levels?
(c) What is the MRS when consumption is above subsistence levels?
(d) Suppose that instead of water and food for someone poor in the developing world, we modeled calories from food (x1) and dollars spent on vacations (x2) for someone in the developed world (taking for granted that he is consuming his desired quantity of water). How would you modify the Stone-Geary utility function assuming that you still want to recognize the absence of tastes for food levels below subsistence?

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T1 )α (X2-72)11-α), where 0< α < 1