<p>Given that <span class="math-container">$a&gt;0$</span>, one can see that the utility function is, <span class="math-container">$U =x-ay$</span>. Which gives us linear indifference curves. Which also tells us that <span class="math-container">$x$</span> is a “good” and <span class="math-container">$y$</span> is a “bad”. </p>

<p>Thus the consumer spends all income on <span class="math-container">$x$</span> and purchases no units of <span class="math-container">$y$</span>. You are correct in what you mention in your question. </p>

<p>You can not apply the equimarginal principle here since all you get is a corner solution. </p>

CC BY-SA 4.0
2018-09-11T06:53:55.950Z
Ok thanks for the clarification. Does this mean that I shouldn't be worrying about calculations (equimarginal principles / tangency solutions) in such a question and revert back to the basics and go by the definition instead?
statsguy21
CC BY-SA 4.0
2018-09-11T06:59:02.257Z
You can’t use equimarginal principle here. So yes, go by applying logic and you find that the only good bought will be x. The IE becomes really easy. And there is no SE in the sense that no money is ever spent on Y.
erik
CC BY-SA 4.0
2018-09-11T06:50:29.937Z
2019-12-15T14:40:28.090Z
2019-12-15T14:40:28.090Z
erik
<p>I am trying to calculate substitution and income effect for 2 goods, <span class="math-container">$x$</span> and <span class="math-container">$y$</span>.</p>

<p>Given that marginal utility <span class="math-container">$\mathrm{MU}_x = 1$</span>, marginal utility <span class="math-container">$\mathrm{MU}_y = -a$</span> (unknown number), price  of <span class="math-container">$p_x = 16$</span>, price of <span class="math-container">$p_y = 20$</span>, how should I proceed? I am unable to use the equal marginal principle, since I cannot have a negative price. But without using the marginal principle, I am also unable to find the optimal basket.</p>

<p>I was also considering that the marginal rate of substitution of <span class="math-container">$x$</span> will always be greater than that of <span class="math-container">$y$</span>. Hence, the optimal basket would just be to spend all the income on <span class="math-container">$x$</span>. Could that count as an optimal basket?</p>

CC BY-SA 4.0
2018-09-10T16:28:50.967Z
Is there any information which says that a has to be positive?
erik
CC BY-SA 4.0
2018-09-11T01:35:47.847Z
Yes, it is given in the question that a > 0
statsguy21
CC BY-SA 4.0
2018-09-11T06:46:34.833Z
Then you should mention that in the post I think. Thanks.
erik
CC BY-SA 4.0
2018-11-10T07:56:02.610Z
This question might be helpful, although note that this is an example where both goods yield positive utility; https://economics.stackexchange.com/questions/25384/income-and-substitution-effect-for-perfect-substitutes
Ubiquitous
<microeconomics>
How to calculate income and substitution effect when equal marginal principle is violated
statsguy21
# How to calculate income and substitution effect when equal marginal principle is violated

(Asked by: username_0 on 2018-09-10)

I am trying to calculate substitution and income effect for 2 goods, $x$ and $y$.

Given that marginal utility $\mathrm{MU}\_x = 1$, marginal utility $\mathrm{MU}\_y = -a$ (unknown number), price of $p\_x = 16$, price of $p\_y = 20$, how should I proceed? I am unable to use the equal marginal principle, since I cannot have a negative price. But without using the marginal principle, I am also unable to find the optimal basket.

I was also considering that the marginal rate of substitution of $x$ will always be greater than that of $y$. Hence, the optimal basket would just be to spend all the income on $x$. Could that count as an optimal basket?

**Tags:** microeconomics

> **Comments:**
> **username_1**: Is there any information which says that a has to be positive?  
> **username_0**: Yes, it is given in the question that a > 0  
> **username_1**: Then you should mention that in the post I think. Thanks.  
> **username_2**: This question might be helpful, although note that this is an example where both goods yield positive utility; https://economics.stackexchange.com/questions/25384/income-and-substitution-effect-for-perfect-substitutes  

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## 1 answers

### Answer by username_1 on 2018-09-11. Score: -1

Given that $a>0$, one can see that the utility function is, $U =x-ay$. Which gives us linear indifference curves. Which also tells us that $x$ is a “good” and $y$ is a “bad”.

Thus the consumer spends all income on $x$ and purchases no units of $y$. You are correct in what you mention in your question.

You can not apply the equimarginal principle here since all you get is a corner solution.

> **Comments:**
> **username_0**: Ok thanks for the clarification. Does this mean that I shouldn't be worrying about calculations (equimarginal principles / tangency solutions) in such a question and revert back to the basics and go by the definition instead?  
> **username_1**: You can’t use equimarginal principle here. So yes, go by applying logic and you find that the only good bought will be x. The IE becomes really easy. And there is no SE in the sense that no money is ever spent on Y.  

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