Phil Rupp, has a sister Ethel who has the utility function U(x, y)  min4x  y, 5y.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a

A) vertical line segment and a horizontal line segment that meet in a kink along the line y  4x.
B) vertical line segment and a horizontal line segment that meet in a kink along the line x  4y.
C) horizontal line segment and a negatively sloped line segment that meet in a kink along the line x  y.
D) positively sloped line segment and a negatively sloped line segment that meet along the line x  y.
E) horizontal line segment and a positively sloped line segment that meet in a kink along the line x  4y.

The utility function given is U(x,y)= min{4x+y,5y}. The diagonal line 4x+y=5y represents the point where the consumer is indifferent between consuming only x or only y. Below this line, the consumer prefers y and above this line, the consumer prefers x. The utility function is such that the consumer prefers to consume as much y as possible while consuming at least some x. This means that the indifference curves will be horizontal lines to the left of the diagonal and downward sloping straight lines to the right of the diagonal. The point where the two segments meet is at (4,4) which is the point where the consumer is indifferent between consuming all x and all y. Therefore, option C is the correct answer.