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, min{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 5min{x,y}+3? Explain. Would the answers change if the utility function was (min{x,y})2 -87?