<p>as you see that is a Cobb Douglas function(Monotonous transformation), I will assume you already know how to get the X* and Y* Marshallian . "w" is the wealth of the consumer. In case you dont know how to get the marshallians you have to maximize the utility ( "U = log(x) + log (y)") subject to the constrain budget (w = Xpx+Ypy)</p>

<p>$ X(*) = w/2px $ </p>

<p>$ Y(*) = w/2py $</p>

<p>So let's start with the income elasticity, we want to know how the consumption of X will change when the income//price of x (own-price) //   (cross price )price of y changes, but we want it in terms of percentage/relative ( that's why we want elasticities ) . </p>

<p>So the income elasticity is :</p>

<p>$(\frac{\partial X}{\partial w})*(\frac{w}{X}) =(\frac{1}{2px} )(\frac{w}{\frac{w}{2px}})\ = 1 $ </p>

<p>cross price elasticity:</p>

<p>$(\frac{\partial X}{\partial py})*(\frac{py}{X}) =(0)(\frac{py}{\frac{w}{2px}}) = 0 $</p>

<p>own price elasticity :</p>

<p>$ (\frac{\partial X}{\partial px})*(\frac{px}{X}) =(\frac{-w}{2px^{2}} )(\frac{px}{\frac{w}{2px}}) = -1 $</p>

<p>I will let you search what means that numbers! :D </p>

<p>Hope this helps you!</p>

CC BY-SA 3.0
2018-04-30T09:55:56.573Z
Thank you so much! This has really helped me understand :)
G Brads
CC BY-SA 3.0
2018-04-29T22:47:06.567Z
2018-04-29T22:47:06.567Z
Miguel Gutierrez
<p>I am stuck on a multiple choice question that came up on a Micro university past papers.</p>

<p>The question is: </p>

<blockquote>
  <p>Marshallian demand curves derived from utility function: $U = log(x) +
log (y)$. What is the own price elasticity, cross price elasticity,
  and income elasticity?</p>
</blockquote>

<p>The answers are -1, 0, and 1 respectively, yet I don't understand how.</p>

<p>Many thanks!</p>

CC BY-SA 3.0
2018-04-29T21:08:33.150Z
You increase your chances of an (appropriate) answer if you show us what you tried.Could you find the demand curves? Do you know the formulas for elasticities? What did not work out?
BB King
<elasticity>
Marshallian demand curve elasticities
G Brads
# Marshallian demand curve elasticities

(Asked by: username_0 on 2018-04-29)

I am stuck on a multiple choice question that came up on a Micro university past papers.

The question is:

> Marshallian demand curves derived from utility function: $U = log(x) +
> log (y)$. What is the own price elasticity, cross price elasticity,
> and income elasticity?

The answers are -1, 0, and 1 respectively, yet I don't understand how.

Many thanks!

**Tags:** elasticity

> **Comments:**
> **username_1**: You increase your chances of an (appropriate) answer if you show us what you tried.Could you find the demand curves? Do you know the formulas for elasticities? What did not work out?  

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## 1 answers

### Answer by username_2 on 2018-04-29. Score: 1

as you see that is a Cobb Douglas function(Monotonous transformation), I will assume you already know how to get the X\* and Y\* Marshallian . "w" is the wealth of the consumer. In case you dont know how to get the marshallians you have to maximize the utility ( "U = log(x) + log (y)") subject to the constrain budget (w = Xpx+Ypy)

$ X(\*) = w/2px $

$ Y(\*) = w/2py $

So let's start with the income elasticity, we want to know how the consumption of X will change when the income//price of x (own-price) // (cross price )price of y changes, but we want it in terms of percentage/relative ( that's why we want elasticities ) .

So the income elasticity is :

$(\frac{\partial X}{\partial w})\*(\frac{w}{X}) =(\frac{1}{2px} )(\frac{w}{\frac{w}{2px}})\ = 1 $

cross price elasticity:

$(\frac{\partial X}{\partial py})\*(\frac{py}{X}) =(0)(\frac{py}{\frac{w}{2px}}) = 0 $

own price elasticity :

$ (\frac{\partial X}{\partial px})\*(\frac{px}{X}) =(\frac{-w}{2px^{2}} )(\frac{px}{\frac{w}{2px}}) = -1 $

I will let you search what means that numbers! :D

Hope this helps you!

> **Comments:**
> **username_0**: Thank you so much! This has really helped me understand :)  

---

