Competitive Equilibrium

Consider a 2 x 2 exchange economy in which individuals a and b have preferences over con sumption of goods 1 and 2 , represented by quasi-linear utility functions: an (anal, $92) 2 335,1 + 20 In 3:32, tab (351, $52) = 3:51 + lhiatbg The xed total endowment of each good is ll. Thus: $.11 + ibi = 60., $13.12 + $52 = 5'3 [a] [30%] In a competitive equilibrium, the price ratio p1 ,1 p; is equal to own; for each individual 3'. Show that, given the above total endowments, this implies: $2=4l 3'22 = 20: loll/(3)222 (b) [10%] Dcscribc in words (without showing it diagrammatically) thc Edgcworth box repre senting this situation, and the shape and location of the eiciency locus (i.e. the contract curve) within the box. Assume that individual a's origin is at the bottom left, with l:- \"s at the top right, and that good 1 is measured horizontally. (c) [30%] Suppose that a and b are endowed with an equal amount (30 units) of each good. Explain how it can be inferred from (a) that, given this endowment, the competitive equi- librium is at: $31 = 25, $32 = 40., I'M = 35, 53m = 2D [(1) [30%] Show that the competitive equilibrium allocation in (c) is fair