<p>Generally you would write the hicksian demand <span class="math-container">$h(p_x,p_y,U)$</span>. But when you graph it is easier to think of it as a single variable function.</p>
<p>What you see on a typical demand curve (assuming it is a hicksian one) is actually <span class="math-container">$h(p_x,\overline{p_y},\overline{U})$</span>, i.e. you would graph the quantity as a single variable function of its price, for given values of the other variables.</p>
<p>Changes on the other variables <span class="math-container">$p_y, U$</span>, cause the “curve” to shift. In the context of graphing, the other variables can be thought of as parameters.</p>

CC BY-SA 4.0
2023-02-14T17:18:18.167Z
Thanks again @Nicolas for another great answer! This fits my expectation. The Hicksian demand function keeps $P_y$ and $U$ as variables, but when we graph it, we want to show demand given these particularly values, and we so fix them as parameters.
CormJack
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2023-02-14T18:04:30.633Z
Exactly @CormJack, you got it!
Nicolas Torres
CC BY-SA 4.0
2023-02-14T18:10:25.187Z
Thank you, I also just commented on another post you are involved in, where the answer above yours seems to contradict your answer? Perhaps you can provide clarity. https://economics.stackexchange.com/questions/54209/how-to-determine-convexity-or-concavity-of-an-indifference-curve/54232#comment89272_54232
CormJack
CC BY-SA 4.0
2023-02-14T18:11:00.610Z
I also find it hilarious how there seems to be a gang of hardcore users here that just go around helping everyone. Of which you seem to be in that gang. Much appreciated!
CormJack
CC BY-SA 4.0
2023-02-11T01:02:57.523Z
2023-02-11T01:02:57.523Z
Nicolas Torres
<p>My question is whether our demand functions e.g. Hicksian (compensated) demand, are ever functions of 3 or more variables, or if the other price variables and utility are always fixed, and hence just parameters.</p>
<p>E.g. The classic problem: Max: <span class="math-container">$U(x,y) = (xy)^{1/2}$</span> s.t. <span class="math-container">$p_xx + p_yy = m$</span></p>
<p>Hicksian demand for <span class="math-container">$x$</span> is: <span class="math-container">$h_x = U(\frac{p_2}{p_1})^{1/2}$</span></p>
<p>Should I be writing this as <span class="math-container">$h_x = \bar{U}(\frac{\bar{p_2}}{p_1})^{1/2}$</span>  to indicate that <span class="math-container">$p_2$</span> and <span class="math-container">$U$</span> are fixed?</p>
<p>I.e. Is the function <span class="math-container">$h$</span> always: <span class="math-container">$h(p_x, \bar p_y, \bar U)$</span> or can we write it generally as <span class="math-container">$h(p_x, p_y, U)$</span></p>
<p>One reason we might not assume the other variables are always fixed is so that we can account for shifts in the demand curve caused by <span class="math-container">$∆p_y$</span> &amp; <span class="math-container">$∆U$</span> is that correct?</p>
<p>A brief outline of when is and isn't appropriate to fix the other variables could be most helpful if someone has time. Thanks!</p>

<utility><optimization><demand>
Are other 'variables' in demand functions always fixed?
CormJack
# Are other 'variables' in demand functions always fixed?

(Asked by: username_0 on 2023-02-10)

My question is whether our demand functions e.g. Hicksian (compensated) demand, are ever functions of 3 or more variables, or if the other price variables and utility are always fixed, and hence just parameters.

E.g. The classic problem: Max: $U(x,y) = (xy)^{1/2}$ s.t. $p\_xx + p\_yy = m$

Hicksian demand for $x$ is: $h\_x = U(\frac{p\_2}{p\_1})^{1/2}$

Should I be writing this as $h\_x = \bar{U}(\frac{\bar{p\_2}}{p\_1})^{1/2}$ to indicate that $p\_2$ and $U$ are fixed?

I.e. Is the function $h$ always: $h(p\_x, \bar p\_y, \bar U)$ or can we write it generally as $h(p\_x, p\_y, U)$

One reason we might not assume the other variables are always fixed is so that we can account for shifts in the demand curve caused by $∆p\_y$ & $∆U$ is that correct?

A brief outline of when is and isn't appropriate to fix the other variables could be most helpful if someone has time. Thanks!

**Tags:** utility, optimization, demand


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## 1 answers

### Answer by username_1 on 2023-02-11. Score: 2 | Accepted answer

Generally you would write the hicksian demand $h(p\_x,p\_y,U)$. But when you graph it is easier to think of it as a single variable function.

What you see on a typical demand curve (assuming it is a hicksian one) is actually $h(p\_x,\overline{p\_y},\overline{U})$, i.e. you would graph the quantity as a single variable function of its price, for given values of the other variables.

Changes on the other variables $p\_y, U$, cause the “curve” to shift. In the context of graphing, the other variables can be thought of as parameters.

> **Comments:**
> **username_0**: Thanks again @Nicolas for another great answer! This fits my expectation. The Hicksian demand function keeps $P_y$ and $U$ as variables, but when we graph it, we want to show demand given these particularly values, and we so fix them as parameters.  
> **username_1**: Exactly @username_0, you got it!  
> **username_0**: Thank you, I also just commented on another post you are involved in, where the answer above yours seems to contradict your answer? Perhaps you can provide clarity. https://economics.stackexchange.com/questions/54209/how-to-determine-convexity-or-concavity-of-an-indifference-curve/54232#comment89272_54232  
> **username_0**: I also find it hilarious how there seems to be a gang of hardcore users here that just go around helping everyone. Of which you seem to be in that gang. Much appreciated!  

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