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This is a question from a test: "A consumer with \$1000 income spends \$200 on good X per month. His income increases to \$1100, and price of good X increases 50%, with no other price changes. In his new equilibrium, he spends \$250 per month with X."

The correct alternative is "well-being increases to this individual". How such conclusion can be made without any information about this utility function? I've seen some explanations but they look too simplistic and I wanted to check if there is a more conclusive answer to this.

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First, the consumer cannot be worse of. If the consumer would want to buy the same consumption bundle, he could. Here, he does not.

Second, if you assume that there is a unique optimal consumption bundle, then any other consumption bundle that is affordable cannot be optimal, including the old one. So the old bundle must have been worse and the consumer must be strictly better off after the change.

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    $\begingroup$ He could have spent 300+800 to keep the same quantity of X, but instead he chooses 250+850, so this means an increase in well-being, is that it? $\endgroup$
    – calavera
    Commented Apr 12 at 1:08
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    $\begingroup$ Exactly. Though the strictly better off part requires unique optimal demands. This is implicit if one has a demand function. $\endgroup$
    – Michael Greinecker
    Commented Apr 12 at 7:50

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