# How to estimate signifcance of price difference?

I am trying to estimate how significant is a difference between two prices.

# Preface

It seems to not be percentage, as price difference of \$0.10 vs \$0.09 wouldn't make me go for the cheaper shop while \$10000 vs \$9000 is a 10% price difference that I care about and would surely choose the shop that is cheaper.

On the other hand, the absolute value also is not the key - if two shops offer the same thing for \$0.50 and \$5.50, I'd go for the cheaper shop. If it's a big thing and the price is \$9995 vs \$10000, I'd rather go for the shop that somehow seems better or more respectable...

It seems to me that the actual significance of price difference for a rational customer would compare the price difference to costs of choosing the cheaper shop - increased risk, decreased prestige, commuting costs to physically choose the other shop etc. But can this be aproximately estimated?

# Main question

Have some researchers worked on quantitavely estimating this? Is there any function that assigns a "signifcant difference" margin to a price? Or directly estimates the significance of the price difference.

I understand that such significance of difference will probably be dependant on customer and currency, I have no objections to involvement of coefficients etc.

# My attempt

I will display you my attempts at estimating what I'm looking for - it might help to better understand what I'm interested in if my previous explanations were too muddy.

By some numerical experiments it seems that the significance of price difference is monotonously dependant (and somewhat proportional) on inverse of logarithm of price. I arrived (experimentally) at such formula that somewhat estimates what change seems acceptable in price:

$$\text{Acceptable change} = \text{Price} \frac{1}{10 \log( \text{Price})}$$

From this I can conclude that \$9-\$11 is similar \$10 while similar prices to \$100 are \$95-\$105.