<p>Here is a way to approach the problem:</p>

<p>An indifference curve is a set of consumption bundles all of which yield the same utility (the consumer being, of course, <em>indifferent</em> to which she consumes). Nonetheless, the numerical level of utility is inconsequential, it is just a placeholder for the more fundamental (and ordinal) preference--any monotone transformation of a utility function represents the preferences. </p>

<p>So let $I_U(x_1,x_2)$ denote the indifference curve (of $U$) that contains $(x_1,x_2)$. That is $$I_U(x_1,x_2) = \{(x'_1,x'_2) \in X \mid U(x'_1,x'_2) = U(x_1,x_2)\}$$
Define $I_V$ in an analogous way.</p>

<p>So showing the indifference curves are the same amounts to showing $I_U(x_1,x_2)= I_V(x_1,x_2)$ for all $(x_1,x_2) \in X$. </p>

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2017-09-18T21:56:38.493Z
2017-09-18T21:56:38.493Z
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<p>I'm being asked to verify that two utility functions, $U(x_1,x_2)$ and $V(x_1,x_2)$ have the same indifference curves and the same MRS.</p>

<p>There is no problem in verifying the MRS to be the same, but how can it be verified that the two utility functions have the same I.C.?
Should I assign a random level of utility and set them equal?</p>

<microeconomics><utility>
Verify Indifference curves of two utility function to be the same
Eren Tonney
# Verify Indifference curves of two utility function to be the same

(Asked by: username_0 on 2017-09-18)

I'm being asked to verify that two utility functions, $U(x\_1,x\_2)$ and $V(x\_1,x\_2)$ have the same indifference curves and the same MRS.

There is no problem in verifying the MRS to be the same, but how can it be verified that the two utility functions have the same I.C.?
Should I assign a random level of utility and set them equal?

**Tags:** microeconomics, utility


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## 1 answers

### Answer by username_1 on 2017-09-18. Score: 2

Here is a way to approach the problem:

An indifference curve is a set of consumption bundles all of which yield the same utility (the consumer being, of course, *indifferent* to which she consumes). Nonetheless, the numerical level of utility is inconsequential, it is just a placeholder for the more fundamental (and ordinal) preference--any monotone transformation of a utility function represents the preferences.

So let $I\_U(x\_1,x\_2)$ denote the indifference curve (of $U$) that contains $(x\_1,x\_2)$. That is $$I\_U(x\_1,x\_2) = \{(x'\_1,x'\_2) \in X \mid U(x'\_1,x'\_2) = U(x\_1,x\_2)\}$$
Define $I\_V$ in an analogous way.

So showing the indifference curves are the same amounts to showing $I\_U(x\_1,x\_2)= I\_V(x\_1,x\_2)$ for all $(x\_1,x\_2) \in X$.


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