Question

Edgeworth box with quasi linearity There are two economic agents, A and B. Utility functions are the following u4(xA, yA) A +YA and uB(xB,yB):= 2\/xB+YB- (a) The endowment for the economy is (ī,g) = (10,20). Find the set of all Pareto efficient allocation such that TA > 0, xg > 0, YA > 0, yB > 0 0 (i.e. y; E (-0, 00) for i E {A, B}). The endowment for the (b) Assume A 20 and TB economy is (, y) = (10,20). Find the set of all Pareto efficient allocation (c) Assume A 0, TB 0, yA > 0,yB 0. The endowment for the economy is (,g) = (10,20). Find the set of all Pareto efficient allocation (d) Pick a Pareto efficient allocation in part (c) such that yA = 0. Find the Price taking equilibrium supporting the allocation

Answer 1

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be dhe same he only diarence.aoud bethe range of cAn take PE n=2AGEO AningXA0 and Xe20, y20 826 henthe endooment frle econom i C,7) - C9a The Set of a pareto effident allo Cation aye; Tke get-EA, Yr>| Mlg = 3, %a = [o, a a paret effrcrent allocetian in Pat Ce) tuch that 0 He mce teabig cquthbrimi suppenting alloadton is: let us take e allotation((a,a), C8,0)) and Oanfuner 1s problem SXA Mak Price Patio Atequilibri) ARS= 1 FA

Sbtuinge vale of r in te adget Contraint PtYapt2o y= Pp+Pap 1 yence, lor nor's s demond nofion is : anleuner as poblem: may Jt ye St XefY= QP. At equilibnRs = Pnie. Ratio. / in te bulg et Contramt Ssbatituthing te vale of P Coniumer as damand ginetion is &p C, Ya) ea^alto total endous nent Total domand +t:[o -9 {