<p>Let's say I have a preference relation on <span class="math-container">$ℝ^2$</span> given by
<span class="math-container">$$x≥y \leftrightarrow  x_1+x_2 ≥ y_1+y_2$$</span>
So, from my understanding, the bundle <em>x</em> is preferred at least as much as the bundle <em>y</em> if and only if the quantity of x is as least as big as the quantity of y. I want to draw a indifference curve that illustrates this, but I am not sure how, given that it is a weak preference, and not a strict one. I have only drawn indifference curves earlier when I have been given utility functions. So my question is, how does the indifference curve (if it is possible to draw one) for this preference relation look like?</p>

CC BY-SA 4.0
2024-04-27T10:46:30.747Z
You do have a utility function in sight: $u(x_1,x_2)=x_1+x_2$.
Michael Greinecker
CC BY-SA 4.0
2024-04-27T10:49:35.777Z
So it is perfect substitutes, correct?
Jonathan
CC BY-SA 4.0
2024-04-27T11:29:22.137Z
Yes, that's exactly right.
Michael Greinecker
<microeconomics><preferences>
Indifference curves given preference relation
Jonathan
# Indifference curves given preference relation

(Asked by: username_0 on 2024-04-27)

Let's say I have a preference relation on $ℝ^2$ given by
$$x≥y \leftrightarrow x\_1+x\_2 ≥ y\_1+y\_2$$
So, from my understanding, the bundle *x* is preferred at least as much as the bundle *y* if and only if the quantity of x is as least as big as the quantity of y. I want to draw a indifference curve that illustrates this, but I am not sure how, given that it is a weak preference, and not a strict one. I have only drawn indifference curves earlier when I have been given utility functions. So my question is, how does the indifference curve (if it is possible to draw one) for this preference relation look like?

**Tags:** microeconomics, preferences
> **Comments:**
> **username_1**: You do have a utility function in sight: $u(x_1,x_2)=x_1+x_2$.  
> **username_0**: So it is perfect substitutes, correct?  
> **username_1**: Yes, that's exactly right.  

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