<p>Just compare the utilities of these three bundles: <span class="math-container">$\left(\frac{M}{p_X}, 0, 0\right)$</span>, <span class="math-container">$\left(0, \frac{M}{p_Y}, 0\right)$</span> and <span class="math-container">$\left(0,0, \frac{M}{p_Z}\right)$</span> and consume the one that yields highest utility.</p>

CC BY-SA 4.0
2019-12-14T01:28:51.177Z
Is this because it will be a corner solution?
Brennan
CC BY-SA 4.0
2019-12-14T01:32:20.610Z
It'll be a corner solution because the utility function is strictly quasi convex.
Amit
CC BY-SA 4.0
2019-12-14T01:07:58.050Z
2019-12-14T01:07:58.050Z
Amit
<p>Consider the utility function <span class="math-container">$u(x)=x+y^2+2z^2$</span>. How to derive Marshallian demand for a consumer with these preferences?</p>

CC BY-SA 4.0
2019-12-13T02:04:44.297Z
Just construct the Lagrangean using the budget constraint $$M = p_{x}x + p_{y}y + p_{z}z$$ and take the first order conditions and solve each. The result will be the Marshallian demand.
Brennan
CC BY-SA 4.0
2019-12-13T05:36:59.923Z
@Brennan Does the **convexity** of this function not matter at all, are you sure first order conditions are sufficient?
Giskard
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2019-12-13T09:02:25.743Z
That's why I'm asking, I can't get far with the usual interior conditions.
econ86
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2019-12-13T17:52:56.577Z
@Giskard very good point that I overlooked
Brennan
<consumer-theory>
How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$?
econ86
# How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$?

(Asked by: username_0 on 2019-12-12)

Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?

**Tags:** consumer-theory

> **Comments:**
> **username_1**: Just construct the Lagrangean using the budget constraint $$M = p_{x}x + p_{y}y + p_{z}z$$ and take the first order conditions and solve each. The result will be the Marshallian demand.  
> **username_2**: @username_1 Does the **convexity** of this function not matter at all, are you sure first order conditions are sufficient?  
> **username_0**: That's why I'm asking, I can't get far with the usual interior conditions.  
> **username_1**: @username_2 very good point that I overlooked  

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## 1 answers

### Answer by username_3 on 2019-12-14. Score: 3

Just compare the utilities of these three bundles: $\left(\frac{M}{p\_X}, 0, 0\right)$, $\left(0, \frac{M}{p\_Y}, 0\right)$ and $\left(0,0, \frac{M}{p\_Z}\right)$ and consume the one that yields highest utility.

> **Comments:**
> **username_1**: Is this because it will be a corner solution?  
> **username_3**: It'll be a corner solution because the utility function is strictly quasi convex.  

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