Consider two-person households, which run on the principle each should experience the same utility from consumption. let c1 = person 1’s consumption, and c2 = person 2’s consumption. they have $90/day to spend on consumption for the whole household. a) assume the individual’s utility equals how much they consume. determine how much each will consume, and what their utility levels will beb) in this case the first person feels competitive with the second, but the second feels compersion for the first. their respective utility functions are as follows: u1 (c1,c2) = c1 * ( c1/c2), u2(c1,c2) = c1 * c2 determine how much each will consume, and what their utility levels will be. c) let the household be as if in part b. however, person 1 can increase the second person’s sense of compersion by giving a small gift that costs k. when they do utility functions become: u1 (c1,c2) = (c1 – k) * [ (c1 - k) / (c2 + k) ] , u2(c1,c2) = (c1 - k) 2 * (c2 + k) determine the formulas for c1 and c2. if k = .5, determine how much each consumes and their utility levels. d) describe how the gift changed their relationship and shares of consumption. e) assume that a person must consume at least $5/day to sustain the household. which of the above scenarios are sustainable as they are. are there any where the gift giving becomes problematic ? what endogenous constraints would be required to make it sustainable (determine the new consumptions levels and utilities be, can the household still run by the equal utility principle? )