<p>You can solve this question by breaking the Utility function into 2 parts.</p>

<p>Use <em>U(x,y)</em> = </p>

<p><em>i) 6x+y if 6x+y &lt; x+2y</em></p>

<p><em>ii) x+2y if x+2y &lt; 6x+y</em></p>

<p>This would simplify into the Utility Function </p>

<p><em>U(x,y)</em> =</p>

<p><em>i) 6x+y if 5x &lt; y</em></p>

<p><em>ii) x+2y if 5x > y</em></p>

<p>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. </p>

<p>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)</p>

CC BY-SA 4.0
2018-05-23T19:26:52.500Z
Thank you! I thought so because otherwise the slope could not be as listed in the answers. Definitely there will be kinks.
TheLight OI
CC BY-SA 4.0
2018-05-23T18:42:48.213Z
2018-05-23T18:42:48.213Z
S.Rana
<p>What's the graph for this utility function? How can it be represented graphically?</p>

<p>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.</p>

<p><a href="https://i.sstatic.net/obMij.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/obMij.jpg" alt="enter image description here"></a></p>

<microeconomics><preferences><perfect-complements>
Unusual perfect complements utility function min{ax+y, x+2y}
TheLight OI
# Unusual perfect complements utility function min{ax+y, x+2y}

(Asked by: username_0 on 2018-05-23)

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.

[![enter image description here](https://i.sstatic.net/obMij.jpg)](https://i.sstatic.net/obMij.jpg)

**Tags:** microeconomics, preferences, perfect-complements

---

## 1 answers

### Answer by username_1 on 2018-05-23. Score: 1

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)

> **Comments:**
> **username_0**: Thank you! I thought so because otherwise the slope could not be as listed in the answers. Definitely there will be kinks.  

---

