detailed answers to each part and graphs

Question 2 Suppose you are interested in modeling a policy issue involving poor households in Pak- istan. 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 5 liters of water per week and at least 8000 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 plausible map of indifference curves that takes this into account. 4 (c) Subsistence levels are a biological reality for all of us, not just for the poor in Pakistan. Why might we nevertheless not worry about explicitly modeling subsistence levels for policy analysis in richer countries or for rich in Pakistan? Consider the utility function: u(11, 12) = (21 71)" (12 )-a, where a (0,1) and 11, 72 are some fixed and exogenous numbers. (d) When interpreted as a model of tastes, what are the subsistence levels of 11 and 22? for the utility function above? Hint: Any bundle in which consumption of any good is below its subsistence level will lead to a lower level of overall utility, relative to any other bundle in which all commodities are consumed above their bare minimum, subsistence levels. (e) How does this utility function treat tastes below subsistence levels? (f) What is the MRS when consumption is above subsistence levels? (g) Suppose that instead of water and food for someone poor in Pakistan, we modeled calories from food 21 and dollars spent on vacations 12 for someone in the developed world (taking for granted that he or she is consuming his or her desired quantity of water). How would you modify the utility function given in question, assuming that you still want to recognize the absence of tastes for food levels below subsistence? (h) Solve the utility maximization problem with the standard budget constraint with two goods i.e p101 + P2X2 = I when the utility function is u(11, 12) = (21-1)" (22 - 22)-a. Derive the own price demand curves ci and x and interpret these demand functions in light of subsistence level consumption and expenditure shares on both goods