Suppose that Colin’s preferences for goods X and Y can be represented by the utility function U ( x , y )=min{ x , y },

Suppose that Colin’s preferences for goods X and Y can be represented by the utility function U ( x , y )=min{ x , y }, where x (respectively, y ) is the amount of X (respectively, Y ) that he consumes. min{ x , y } is a function that gives the minimum of the two numbers x and y . For example, min{3,5}=3, mi n{4,2}=2, and min{1,1}=1. a) Give a real world example for such preferences and for goods X and Y . b) Draw the indifference curve along which Colin has a utility of 4. c) Suppose that the price of both X and Y is $1, and Colin’s income is $12. What is his optimal consumption bundle? What if the price of X is $1 and the price of Y is $2? d) Find Colin’s demand functions for X and Y . e) How do the answers to questions (a) – (d) change if his utility function were 55 min x , y }+3? Explain. Would the answers change if the utility function was (min{ x , y }) 2 – 87? 8. John’s utility function for cola and hamburgers is given by U ( C , H )= C 1/3 H 2/3 , where C and H are, respectively, the cans of cola and the number of hamburgers he consumes.

a) Draw two of his indifference curves.

b) What is his marginal rate of substitution of cola for hamburgers (MRS CH )? Does his MRS CH depend on how much of the goods he consumes? What happens to MRS CH as he has more and more colas?

c) Suppose that the price of a can of cola is $1, the price of a hamburger is $3, and J ohn’s income is $27. Draw his budget line.

d) Find John’s optimal consumption bundle.

e) Suppose that price of a can of cola is $2, the price of a hamburger is $6, and John’s income is $54. Draw his budget line, and find the optimal bundle.

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