Humphrey and Lauren must split 10 pounds of food and 10 gallons of water. Suppose we can represent Humphrey‘s preferences with the utility function UH = F 2 HWH, and Lauren‘s preferences with the utility function UL = min{FL,WL}. Initial endowments are such that w(FH,WH) = (2,5) and w(FL,W) = (8,5)
(a) Draw the Edgeworth box for this exchange economy (with Humphrey on the lower vertex), including the initial endowment point and some indifference curves for each.
(b) What is Humphrey’s marginal utility for each good?
(c) Add the contract curve to your graph.
(d) What is the ratio of the price of food to the price of water in competitive equilibrium?
(e) Add the budget line to your graph. (f) What would the equilibrium allocation point that Humphrey and Lauren will trade to?