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Principle Of Economics

) Matching utility functions and indifference curve maps

Consider the following 6 utility functions:

a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met.

b) Next, try to picture what indifference curves will look like, and see if you can find a matching graph below. [Try not to rely too much on brute force calculations of utility values – what if the grid was not shown and you couldn't easily identify the coordinates at any given point?]

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Principle Of Economics

Suppose Mindy and Tulip are roommates. Mindy works part-time at Roberto's and can bring homefour carne asada burritos for free every week. Tulip works part time at Tapioca Express and can bringhome eight steamed pork buns for free every week. Use x to denote the number of burritos, and yto denote the number of pork buns.

a. Suppose Mindy is always willing to trade one burrito (x) for two pork buns (y), regardless ofhow many she has.

i. Draw a couple of her indifference curves in the graph.

ii. Are Mindy's preferences convex?

Tulip is also indifferent between having 4 burritos and no pork buns and having 8 pork bunsand no burritos. However, she would prefer to have 2 burritos and 4 pork buns instead.

i. Draw a couple of Tulip's indifference curves (what they might plausibly look like – you don't have enough information to draw them precisely)

ii. Are Tulip's preferences convex?

c. Might the girls decide to share/trade food with each other? Find one possible exchange so that neither of the girls is worse off, and at least one of them is strictly better off.

Consider the following possible specifications of utility functions:

\text { i. Which of these functions is/are consistent with Mindy's initial preferences? }

ii. Which utility function(s) is/are consistent with Tulip's preferences? [Hint: consider that indifference curves may look different from the way you drew them.]

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