# Unusual perfect complements utility function min{ax+y, x+2y} [closed]

What's the graph for this utility function? How can it be represented graphically?

Is this function perfect complements? I do not fully understand that in the question attached in the picture, the slope cannot be a fractionnary number since the goods are perfect complements.

You can solve this question by breaking the Utility function into 2 parts.

Use U(x,y) =

i) 6x+y if 6x+y < x+2y

ii) x+2y if x+2y < 6x+y

This would simplify into the Utility Function

U(x,y) =

i) 6x+y if 5x < y

ii) x+2y if 5x > y

When you graph the function you'll get 5x=y as the line of kinks. When 5x>y, that is, to the right of the line of kinks, the corresponding IC will be have a slope -(1/2) since it lies on the line x+2y. Points to the left of line of kinks correspond to the line 6x+y and have the slope -6.

Given point (8,9) clearly lies to the left of the line of kinks in the area where 5x>y, therefore this point lies on the Utility line x+2y having slope -(1/2)

• Thank you! I thought so because otherwise the slope could not be as listed in the answers. Definitely there will be kinks. May 23, 2018 at 19:26