<p>First, your utility function is strictly increasing in both goods, so you know that your budget will bind so you can set $I=p_xx+p_yx$. </p>

<p>Second, your utility function is known as "quasilinear", where the good y is linear in your utility and the other good is there in some increasing function not connected to y. That's why the marginal utility for y is just a constant.</p>

<p>Finally,  solve for x as you did, where x is a function of prices, then plug that into the budget constraint to solve for y. y should be a function of prices and income. </p>

CC BY-SA 3.0
2016-08-18T15:48:27.617Z
2016-08-18T15:48:27.617Z
VCG
<p>Here's the question that I really need help with:</p>

<p>$$U(x,y)=(x^{0.5})+y$$</p>

<p>$MUx=\frac{1}{2x^{0.5}}$ and $MUy=1$, where $x$ is food, $y$ is clothing</p>

<p>$Px$ is the price of food, $Py$ is the price of clothing and $I$ is income.</p>

<p>For the purposes of this question you should assume that $I/Py \ge Py/4Px$.</p>

<p>My question is <strong>I don't know how to find the demand function for $y$.</strong></p>

<p>I use $MUx/MUy=Px/Py$ and I can only find the demand function (or opportunity set) for $x$.</p>

<p>Is $I/Py&gt;=Py/4Px$ the budget constraint? If it is, that's the weirdest form I've ever seen. </p>

<p>I'd really appreciate it if any of you could give me a hint how to solve for this question. </p>

CC BY-SA 3.0
2016-08-17T13:24:29.323Z
I would take the budget constraint to be a natural $xP_x+yP_y \le I$
Henry
<microeconomics><utility><consumer-theory>
Consumer Theory (Finding demand function)
Jill
# Consumer Theory (Finding demand function)

(Asked by: username_0 on 2016-08-17)

Here's the question that I really need help with:

$$U(x,y)=(x^{0.5})+y$$

$MUx=\frac{1}{2x^{0.5}}$ and $MUy=1$, where $x$ is food, $y$ is clothing

$Px$ is the price of food, $Py$ is the price of clothing and $I$ is income.

For the purposes of this question you should assume that $I/Py \ge Py/4Px$.

My question is **I don't know how to find the demand function for $y$.**

I use $MUx/MUy=Px/Py$ and I can only find the demand function (or opportunity set) for $x$.

Is $I/Py>=Py/4Px$ the budget constraint? If it is, that's the weirdest form I've ever seen.

I'd really appreciate it if any of you could give me a hint how to solve for this question.

**Tags:** microeconomics, utility, consumer-theory

> **Comments:**
> **username_1**: I would take the budget constraint to be a natural $xP_x+yP_y \le I$  

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## 1 answers

### Answer by username_2 on 2016-08-18. Score: 1

First, your utility function is strictly increasing in both goods, so you know that your budget will bind so you can set $I=p\_xx+p\_yx$.

Second, your utility function is known as "quasilinear", where the good y is linear in your utility and the other good is there in some increasing function not connected to y. That's why the marginal utility for y is just a constant.

Finally, solve for x as you did, where x is a function of prices, then plug that into the budget constraint to solve for y. y should be a function of prices and income.


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