When preferences in the Edgeworth box are for one agent log utility, and for the second agent Leontief, it is possible to use the standard definition of the contract curve to define the set of Pareto optimal allocations.
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Breanna O.
Two people trade two goods that they cannot produce. Suppose that one consumer's (consumer 1's) indifference curves are bowed away from the origin - the usual type of curves - but the other's (consumer 2's) are concave to consumer 2's origin. In an Edgeworth box, show that a point of tangency between the two consumers' indifference curves is not necessarily a Pareto-efficient bundle by identifying another allocation that Pareto dominates. The figure to the right illustrates an Edgeworth box. 1. Use the 3-point curved line drawing tool to draw an indifference curve for consumer 1 (I1) that is convex to consumer 1's origin and an indifference curve for consumer 2 (I2) that is concave to consumer 2's origin, such that the indifference curves are tangent but do not intersect, and such that the point of tangency is not Pareto efficient. Properly label the lines. 2. Use the point drawing tool to indicate the point of tangency between the two consumers' indifference curves. Label this point 'A'. 3. Use the point drawing tool to indicate an allocation that Pareto-dominates Allocation A. Label this point 'B'. Carefully follow the instructions above, and only draw the required objects.
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Construct, and give the mathematical formulae for, an Edgeworth box in which there is more than one competitive equilibrium from some initial allocations. Hint: you might work with linear preferences.
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