Recently, I have purchased the book “Revenue Management and Pricing Analytics” written by Guillermo Gallego and Huseyin Topaloglu.

I have a question about the use of marginal analysis mentioned on page 6.

By using marginal analysis, it compares the anticipated marginal revenue of full fare to the expected marginal revenue of discounted fare. And it uses this comparison to indicate whether a company should accept the request for discounted fare or reject it. 

However, I have found this deduction a little jump, because the statement in the book implicitly assumes that the y units of capacity available to full fare can vary. That is to say, for each possible value of y, from 0 to c, we compare the anticipated marginal revenue of full fare to the expected marginal revenue of discounted fare. So, can you make this implicit assumption explicit?

Also, can you justify the use of marginal analysis, if the value of y is fixed? That is, when the value of y is fixed, can you justify that the marginal analysis is an appropriate method to derive an indicator or a criteria that can determine whether to accept or reject the request for discounted fare? When the value of y is fixed, the marginal analysis only considers the yth revenue. But how about the (y-1)th, the (y-2)th, the (y-n)th revenue?

Thanks!