They do do this, and it is indeed called "price discrimination".
There has to be a reason for the buyer to pay the higher price. Your idea is based on time: first you sell the product for \$3 to everyone who's willing to pay \$3, then you decrease the price to \$2 and get some of the holdouts from when it was \$3, then you decrease it to \$1 and get more holdouts.
This does work and it's frequently done for products that are made all-at-once such as movies and video games. When the hit movie comes out it may cost \$30 to watch once at a theater; then eventually it comes out for \$20 on a DVD that you can watch as many times as you like (so a lower cost per watch); eventually the DVD price drops to \$5 and then \$3 in the bargain bin.
The reason for people to pay the higher price is so they can watch the movie (or play the game) sooner. This only works because there is an obvious moment when you can start the clock. You couldn't sell sugar like this, because even if you can charge lower prices to people who wait longer for their sugar, you have no way to tell who's buying sugar for the first time this week, versus who wanted it two weeks ago and waited until now. Even if I only just now decided that I wanted to bake a cake, I could pretend I wanted it two weeks ago, and get the two-week discount.
It also only works because there is monopoly power - only one firm gets to sell licenses to see that movie. Even if one firm were to start selling sugar in instalments (with a discount for buying January's sugar in February) the customers with the higher reservation price would simply buy their sugar at a normal price from a different brand that didn't employ such silly shenanigans. Customers with the lower reservation price would still buy the discounted sugar later. If the instalment sugar company was okay with that, they could sell their sugar for a lower price to begin with.
Another way to do price discrimination is to somehow guess the price the buyer will pay, and then only show them that price. They don't know that there are other prices, so they either pay the shown price or don't pay. If you get it right, they usually pay.
With computers this is possible, and airlines do it all the time, but you may also view old-school haggling as similar form of this. Student discounts and senior citizen discounts are coarse-grained forms of this - a child watching a movie still takes up a whole seat, but they pay less money for the ticket, because the movie theater thinks the parent won't watch the movie if they have to buy three adult tickets instead of one adult and two children.
Wikipedia lists several more types.
The study of market segmentation may help a producer think of ways to differentiate their consumers so they can sell different prices - commonly by packaging the same product in different packaging. It may be that all your salt comes from the sea, but packaging it as "Great Value Iodized Table Salt" for \$2 per bag and also as "Himalayan Luxury All-Natural Sea Salt" for \$5 per bag allows you to make more revenue (provided that "Himalayan" is merely a brand name and not a descriptor of the product).