# HW1 - Homework Assignment 1 Econ 382 Professor Platt BYU...

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Homework Assignment 1 Econ 382, Professor Platt, BYU Due in class, January 14th, 2009 1 Warmup These question provide practice with problems similar to those worked in class. They are optional — points earned in this section can oﬀset points lost elsewhere (though the maximum score for the assignment is still 100 points). Credit is only given if you show all steps taken to obtain your answer. 1. Alex and Bob are new college roommates. On arrival at their dorm, they discovered that both had brought cereal and ramen noodles from their parents’ pantry. Suppose that Alex brought 12 boxes of cereal and 20 packs of noodles, while Bob brought 10 boxes of cereal and 10 packs of noodles. Alex has a utility function U a ( c a ,n a ) = c 0 . 75 a n 0 . 25 a , and Bob’s utility function U b ( c b ,n b ) = c 0 . 5 b n 0 . 5 b . (a) (2 pts) Set up the consumer’s problem for each roommate. (b) (2 pts) List the conditions that must be satisﬁed for a particular set of allocations and prices to be a competitive equilibrium. (c) (2 pts) Solve for Alex’s demand for cereal and noodles. You should get c a = 3(3 p c +5 p n ) p c and n a = 3 p c +5 p n p n . (d) (2 pts) Solve for Bob’s demand for cereal and noodles. You should get c b = 5 p c +5 p n p c and n b = 5 p c +5 p n p n . (e) (2 pts) Solve for equilibrium prices. Which good is more expensive? You should get p * c = 1 and p * n = 0 . 4 or anything in similar ratio. (f) (2 pts) Solve for equilibrium allocations. Who bought/sold noodles (and how much was traded)? Who bought/sold cereal (and how much was traded)? c

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HW1 - Homework Assignment 1 Econ 382 Professor Platt BYU...

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