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