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I have a utility function (logit) that is kinda weird and hard to work with given the constraints mentioned in the problem.

I’m trying to derive the marshallian demand for $x_0$, but I'm not sure how to. Thought of doing a transformation such that it looks like a Cobb-Douglas (however w. a e{$x_0$} in the beginning of the expression). Can’t get further than that.

I have posted the problem and my take on the problem, but I don't think my solution is correct as I don't see how this helps me realize that I can find the demand beforehand. The question is framed such that it should be obvious and trivial to find the demand. Can someone maybe help me with a hint or a solution? Thanks in advance!

The problem

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My take on the problem

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InanimateBeing
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Patrick Nodi
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Aug 20 '22 at 14:00
  • Thanks for the heads up. I have now tried to clarify the problem and my take on it. – Patrick Nodi Aug 20 '22 at 15:19

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