Review Session.pdf - Intermediate Microeconomics Revision...

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Intermediate Microeconomics Revision exercises Exercise 1: non-convex preferences Ben’s utility depends on two commodities, x and y , and it has the following form: u ( x, y ) = 2 x 2 + y 2 . Notice that there are no ”kinks” in this utility function. Moreover, you know that Ben’s income equal to $6, price of good x equals $6 and the price of good y is $3. (1) Sketch Ben’s preferences and his budget constraint. (2) What bundle does Ben optimally choose?
Exercise 2: unexpected corner solutions Marie’s preferences are represented by the following utility function: u ( x, y ) = xy + 2 x - 3. Suppose that her disposable income is $3, and that the prices of the commodities are ( p x , p y ) = (2 , 3). (1) Draw Marie’s budget constraint. What is the maximum quantity of commodity x that she can consume? (2) What bundle does Marie optimally choose?
Exercise 3: on WARP You live in a jungle. Here, the typical consumption bundle of monkeys includes bananas and mangos (and everything is priced in terms of nuts). Suppose that the price of a banana is 12 nuts, and the price of a mango is 4 nuts. Fix the monkey income in terms of nuts at m . In this scenario, the monkey picks a bundle with 2 bananas and 3 mangos. Now suppose that the price of mangos changes to 3 nuts per mango (i.e. they become cheaper). Now the monkey picks a bundle with 4 mangos and 2 bananas. Does this behavior show a violation of WARP by the monkey? 1

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