Problem of a rational consumer with an utility function

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Consider the problem of a rational consumer with an experienced utility function given by 8√x+m. Let p=$1 p/unit denote the market price of good x.
Suppose that, initially, the firm selling the good matches his purchases as follows: for every x units that he buys, he gets an additional $x units for free.
Based on customer feedback, the firm is considering eliminating the matching policy and introducing instead a price rebate of size r per-unit purchased.

What is the value of r that leaves the consumer indifferent between the two situations

Reference no: EM13191065

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