If you are an ardent shopper you will be aware of the discount (% decrease) marketing strategy to produce the sale price. I began to wonder just how much mark-up (% increase) was added initially to an item in order to deliver the discounted sale price.

It was simple to construct a formula to convert one to the other.

For example a 30% (mark down) decrease in price required a 42.86% (mark up) to increase the price initially to Tag price. However when I started apply the formulae to a number of circumstances I noticed some very interesting circumstances associated with this relationship

For example a 99.999999% decrease is numerically equal to a 9,999,999,925% increase (huge ratio difference) while conversely a 0.1% decrease is numerically equal to a 0.10010010% increase (Infinitesimally small ratio difference) so the patterns appears logarithmic not linear.

However what really caught my attention was this pattern

See http://www.ozsmart.com/doc/percentage.htm

My questions is why does the decline in the ratio of increases in required mark up (%) price peak at 50 and 51% precisely and then expand again as the percentage move higher

Any explanation would be appreciated