How does left-digit bias affect price rigidity in firms?

I investigate how left-digit bias affects supply side decisions - in particular how it affects how rigid certain price-point endings are to cost increases. We construct a model of a profit-maximizing firm facing a left-digit biased demand curve and show that optimal prices are more rigid at 99-ending points - that is, the cost change required for the optimal price to change is greater. We then use Dominick's Dataset (data from a defunct grocery store that operated in the Chicago area) to examine whether 99 cent endings actually increase rigidity. We find significantly greater rigidity for 99-ending prices, and about half of the effect is present for 9-ending prices