midterm1 - Econ 440 March 1 Peter Norman Midterm 1 1...

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Econ 440 March 1 Peter Norman Midterm 1 1. Consider an economy with two goods, x and y and two agents, A and B: Suppose that the agents are endowed with e A = ° e A x ; e A y ± and e B = ° e B x ; e B y ± units of the two goods. Also suppose that preferences over di/erent consumption bundles are represented by utility functions u A ( x; y ) and u B ( x; y ) respectively. (a) De°ne a competitive equilibrium. (b) De°ne a Pareto optimal allocation. (c) True/False: All competitive equilibria are Pareto Optimal. Explain using a wisely chosen graph. No credit unless explanation satisfactory. (d) True/False: All Pareto optimal allocations are competitive equilibria. Explain using a wisely chosen graph. No credit unless explanation satisfactory. (e) Suppose instead that preferences are given by u A ° x A ; x B ; y ± and u B ° x A ; b B ; y ± : Would this a/ect the answers above? Why? Why not? No credit unless answer contains a reasonable explanation.
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