# Fundamental law of demand proof help

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Thread starter 5 days ago
#1
Proof:

x*(p) is a solution for u'(x*(p))=p, ∀ p.

Suppose a price rise, then p'>p. It follows u'(x*(p))<p'

Given for a quasi-linear utility function u(x), that u'(x)>0, u"(x)<0

Then: x*(p')<x*(p)

I follow the proof all the way up until the very last step. It seems logical that for higher prices there is less demand, but I don't know how from the proof the conclusion is that max{p'} will be less than max{p}? Because the bulk of the proof deals with the utility function?

I'd appreciate any help
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Thread starter 5 days ago
#2
Nevermind, I managed to get to an answer.

For anyone interested:

Because of the nature of u(x), it's a function e.g. u(x)=log(x). So, u'(x)=1/x, and the optimal condition is 1/x=p', so 1/p=x*(p'). So, a very small x means a very large p', which means the inequality holds as therefore, when we look at the inverse, x*(p')>x*(p) holds true, so higher prices means lower demand (demand is x, price is p').
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