Question

Fit to page Page view A Re 2. Basket A contains 5 apples and 1 orange. Basket B contains 1 apple and 5 oranges. Basket C contains 3 apples and 3 oranges. Assume throughout that tastes are monotonic.

Answer 1

a)

Oranges Apples

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b) Basket C is the average of Basket of A and B. If Anne has chosen A over C on Monday, it implies that A gives more satisfaction to her than C and thus A must lie above C. Given strictly convex preferences, the indifference curve will pass through A (IC1). If she had chosen B over C, then the IC will pass through B (IC2). The two curves intersect each other at basket C, this is against the propoerties of indifference curves. ICs cannot cross each other in an IC map. This further implies that the two ICs must represent two different IC map, i.e. the taste of Anne must havce changed from monday to tuesday.

18 Tuesday [C2 A la Monday 23

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c) If A and B lie on the same IC, given that the averages are at least as good as extremes, this implies that C is at least as good as A and B. Also, Anne may choose A over C on Monday and B over C on tuesday without changing her preference. This implies that the IC that pass thorugh A, B and C is a straight line IC with slope -1. (Figure in part a)

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d)

The equation of an IC is U (x,y) = 3x + 2y = k , where x = apples , y = oranges and k = constant utility.

At choice A, IC gives utility of 3*5 +2*1 = 17 utils

At choice B, IC gives utility of 3*1 +2*5 = 13 utils

At choice C, IC gives utility of 3*3 +2*3 = 15 utils

The maximum utility is given by A.

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