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, are lower in Paris, the new budget line is flatter thanLA.The new optimal bundle is determined by the tangency of an indifference curve toLF.The new indifference curve must be higher thanI1. If the relative prices,pApF, are higherin Paris, the new budget line is steeper thanLA. The new optimal bundle is determinedby the tangency of the indifference curveI2toLF. The new indifference curveI2must
be weakly higher thanI1. Thus, in either case, the consumer is at least weakly betteroff than he was before.Exercise5Maximize the functionf(x, y) =x+ysubject to the constraintx2+y2= 1. Sketchthe constraint first, and then maximize.