Example of standard indifference curve analysis, Microeconomics

Carmen, the Queen of Electra, is concerned over what she believes is an excessive consumption of electricity.  Consequently, she proposes an excise tax on electricity consumption which, if implemented, would add $500 per year to the taxes of the average Electran household.  An advisor to the Queen warns of a consumer backlash and suggests the following amendment-give the $500 back in the form of a tax rebate.  The Queen thinks this is the dumbest idea she's ever heard.  She reasons that such a plan would do nothing to reduce electricity consumption since the plan would take away $500 with one hand, but give it back with the other!       

Do you agree with the Queen or not?  Fully explain your answer using standard indifference curve analysis.

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