Cost determines the Lower Limit for Price, I think

A Google Scholar search for "cost-push inflation in ancient Rome" (without quotes) turned up something I wasn't looking for: Flaws and Ceilings: Price Controls and the Damage They Cause. It's a Google book with a 48-page preview, and as it happened, the 48 pages included a page I could use. Here's part of page 37:

They say the cost-push idea is "based on a simple mistake." And, unbelievably, they suggest that "increases in wages" do not cause corresponding increases in prices. They argue that the increase in wages puts no upward pressure on the price level.

They say:

Costs do not determine the prices of consumption goods; rather it is the value attributed to a consumption good that determines its price.

Yes and no, I think. If the consumer values a product at a value higher than cost-plus-profit, then yes, the price will soon rise to the higher value. But if the consumer values the product at a value lower than cost-plus-profit, soon the product will not be sold at all.

To get rid of that first batch of low-valued goods, the store will mark down the prices repeatedly until the whole batch is sold. But you'll never see that product in that store again. No one who is in it for the money buys products to sell them at a loss.

There are exceptions, no doubt. The store might run a special and sell selected items at a loss for a week, to bring new customers in. But that is a special situation.

Of course the store will sell their stuff for the most they can get, with some big-picture exceptions like running a special. But no store can long exist if its standard practice is to sell everything at a loss. Costs may not "determine the prices of consumption goods." But costs surely do establish minimum prices. The argument made in Flaws and Ceilings is nonsense.

Therefore, I reject their view that there is no such thing as cost-push inflation. I reject their view that because cost is not the sole determinant of price, cost-push inflation is impossible. Prices, perhaps, seldom come down when costs come down. But surely, prices almost always go up when costs go up.

This view that they hold, I have seen it before, and I simply cannot accept it. Is my thinking flawed? 

Note: I am only disputing the argument put forth in the paragraph from Flaws and Ceilings. I am not disputing the inflation-is-always-a-monetary-phenomenon argument.