CALCULUS ECONOMICS
posted by Jenney .
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 perunit 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?

I have never taken business economics. I hope there is someone here who has but have not run into them.