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Page 1 of 5 1. (40 points) Jonathan is training to compete in Nathan's Famous hot dog eating contest, and he thinks he has stumbled upon a winning...

Intermediate Microeconomics

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Page 1 of 5 1. (40 points) Jonathan is training to compete in Nathan’s Famous hot dog eating contest, and he thinks he has stumbled upon a winning formula to beat the reigning champion, Joey Chestnut. His method requires him to drink two 8 oz. bottles of water ( w ) for every three hot dogs ( d ) that he eats. Jonathan is so obsessed with winning this competition that he only spends his income ( m ) on hot dogs and 8 oz. bottles of water (and yes, he still lives in his mother’s basement!). (a). (10 points) Graph Jonathan’s indifference map for hot dogs and water, letting x 1 = d and x 2 = w . Label all axes, important points and include at least three indifference curves on your graph. (b). (10 points) What utility function represents Jonathan’s preferences for hot dogs and 8 oz. bottles of water? Defining p d as the price of hot dogs and p w as the price of water, use the utility function to mathematically derive Jonathan’s demand functions for hot dogs and water. Draw a box around your final expressions for the demand functions.
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Page 2 of 5 (c). (10 points) Graphically derive Jonathan’s demand curve for hot dogs from his indifference map using the relationship p d ’< p d ’’< p d ’’’ . You will need both graphs below: one that combines the indifference map and budget constraints and one that shows the demand curve. Label all axes and points carefully, to include where the demand curve intersects the x-axis!
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a) Hot dogs(X 1)
Increase for hot dogs
Optimum /equivalence point Decrease for water Water(X 2)
b) Utility function ( d , w)=d +w
( d ,W )= Pd*d +Pw *w But there are 3 hot dogs and 2 8 oz water...

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