Three friends (Patrick, Jeff, and Steve) are at a bar, discussing their preferences for burgers and pizza. The following are their utility functions, where 'b' stands for burger consumption and 'z' st

Three friends (Patrick, Jeff, and Steve) are at a bar, discussing their preferences for burgers and pizza. The following are their utility functions, where 'b' stands for burger consumption and 'z' stands for pizza consumption.:

PROBLEM IN FILE

Patrick claims their preferences for burger and pizza are all different; Jeff states that they are actually the same preferences, and Steve claims that two of them have the same preference and one of them has different preferences than the rest. Who is right? You points depend on your justification, not just your final answer.