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!


closed as off-topic by denesp, JoaoBotelho, Adam Bailey, Herr K., Maarten Punt May 17 '18 at 19:51

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  • "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – denesp, JoaoBotelho, Adam Bailey, Herr K., Maarten Punt

  • 3
    $\begingroup$ 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? $\endgroup$ – BB King Apr 29 '18 at 21:08

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!

  • $\begingroup$ Thank you so much! This has really helped me understand :) $\endgroup$ – G B Apr 30 '18 at 9:55

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