I'm trying to prove something small in economics using MVDT but can't seem to work it out:(adsbygoogle = window.adsbygoogle || []).push({});

So consider: S(x) and D(x) such that:

[itex] S' > 0 > D' [/itex]

[itex]S(x_{1}) = D(x_{1}) = Q_{1} [/itex]

[itex]S(x_{2}) + \epsilon = D(x_{2}) + \epsilon = Q_{2} [/itex]

Then can I prove the following?

[itex] x_{2} = x_{1} [/itex]

[itex] Q_{2} > Q_{1} [/itex]

I've tried to define a function that is the difference between S and D and then apply the mean value theorem, but it seems like I can't get where I want.

By the way there may not be an answer since I made the problem up. But instinct tells me this is doable, I just can't figure out how.

Thanks for your help.

BiP

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# MVDT Proof in economics

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