Posted by **Jenney** on Thursday, March 13, 2014 at 3:49pm.

Consider the problem of a rational consumer with an experienced utility function given by 8*x^(1/2)+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 sx 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. Note that under the rebate policy, the consumer gets back $r for every unit that he purchases

QUESTION: What is the value of r (as a function of s) that leaves the consumer indifferent between the two situations?

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