<p>This is one possible interpretation. Good 2 being removed from the market can simply be interpreted as <span class="math-container">$x_2 = 0$</span>. In an economic interpretation the good does not simply disappear from the utility function in the sense that preferences do not change, it is just the availability of the good that changes. This is an external condition, so you can simply think of this as a market constraint <span class="math-container">$x_2 = 0$</span>. </p>

<p>Now, looking at indifference curves as the different bundles for which the consumer obtains the same level of utility, and defining this level as <span class="math-container">$k$</span>. It is clear that for any <span class="math-container">$k$</span> when there is only one good, each "indifference curve" will consist of only one point (in particular <span class="math-container">$x_{1}|u(x_1,0) = k$</span>). In a 2-D graph this will simply correspond some point (<span class="math-container">$x_1$</span>,0) for each <span class="math-container">$k$</span> level. </p>

<p>The demand function should be quite straightforward. </p>

CC BY-SA 4.0
2020-06-10T10:52:12.297Z
That makes it a lot easier, thank you!
Pycruncher
CC BY-SA 4.0
2020-06-10T17:15:13.363Z
You're welcome! If your doubt is solved can you accept the answer?
Ali
CC BY-SA 4.0
2020-06-10T17:17:05.203Z
I think I just did, if that means hitting the check mark. Sorry I'm new to this all.
Pycruncher
CC BY-SA 4.0
2020-06-10T17:17:37.040Z
Yes, that's it!
Ali
CC BY-SA 4.0
2020-06-10T10:49:45.297Z
2020-06-10T11:30:16.343Z
2020-06-10T11:30:16.343Z
Ali
<p>Given a quasi-linear utility function: <span class="math-container">$u(x_1, x_2) = f(x_1) + \beta x_2$</span>,  <span class="math-container">$\beta &gt; 0 $</span></p>

<p>What would happen if good 2 (<span class="math-container">$x_2$</span>) is removed from the market? Would the new utility function be: <span class="math-container">$u(x_1) = f(x_1)$</span>? If so, would the demand function simply be <span class="math-container">$x_1 = m/p_1$</span>? I want to find the new demand function as well as the new indifference curves and draw these in a diagram, but I am unsure how to proceed. Surely I cannot graph them in <span class="math-container">$x_1, x_2$</span> space if there is no more <span class="math-container">$x_2$</span>. Or would I still graph them in <span class="math-container">$x_1, x_2$</span> space as vertical lines?</p>

<p>I hope my question is understandable, thx for any help.</p>

<microeconomics><utility><preferences><markets><demand>
Remove Linear Good From Quasi-linear Utility Function
Pycruncher
# Remove Linear Good From Quasi-linear Utility Function

(Asked by: username_0 on 2020-06-10)

Given a quasi-linear utility function: $u(x\_1, x\_2) = f(x\_1) + \beta x\_2$, $\beta > 0 $

What would happen if good 2 ($x\_2$) is removed from the market? Would the new utility function be: $u(x\_1) = f(x\_1)$? If so, would the demand function simply be $x\_1 = m/p\_1$? I want to find the new demand function as well as the new indifference curves and draw these in a diagram, but I am unsure how to proceed. Surely I cannot graph them in $x\_1, x\_2$ space if there is no more $x\_2$. Or would I still graph them in $x\_1, x\_2$ space as vertical lines?

I hope my question is understandable, thx for any help.

**Tags:** microeconomics, utility, preferences, markets, demand


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## 1 answers

### Answer by username_1 on 2020-06-10. Score: 2 | Accepted answer

This is one possible interpretation. Good 2 being removed from the market can simply be interpreted as $x\_2 = 0$. In an economic interpretation the good does not simply disappear from the utility function in the sense that preferences do not change, it is just the availability of the good that changes. This is an external condition, so you can simply think of this as a market constraint $x\_2 = 0$.

Now, looking at indifference curves as the different bundles for which the consumer obtains the same level of utility, and defining this level as $k$. It is clear that for any $k$ when there is only one good, each "indifference curve" will consist of only one point (in particular $x\_{1}|u(x\_1,0) = k$). In a 2-D graph this will simply correspond some point ($x\_1$,0) for each $k$ level.

The demand function should be quite straightforward.

> **Comments:**
> **username_0**: That makes it a lot easier, thank you!  
> **username_1**: You're welcome! If your doubt is solved can you accept the answer?  
> **username_0**: I think I just did, if that means hitting the check mark. Sorry I'm new to this all.  
> **username_1**: Yes, that's it!  

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