lower production costs translate into lower sales costs
Not as such, because you're looking at the total budget for making a movie and all the copies of it needed to distribute and show it many, many times. "The latest iPhone" cost a lot more in total to research, design and manufacture all the units, than my house did. But my house is a lot more expensive than an iPhone, because the iPhone has lots of buyers sharing the costs, and my house had only one. So there is no such direct relation between the total budget of bringing a new product to market, and the per-unit retail price of the product. All else being equal there would be, but all else is not equal.
The price you have to charge to cover costs depends on development costs per unit sold, not just the total budget, plus marginal costs of production. The marginal cost of providing a cinema seat is basically the same regardless of what film is showing (assuming the same kind of projection and sound). So that's a large chunk of the ticket price that not only has nothing to do with the budget on which the movie was made (which in any case as BKay says is a sunk cost), but doesn't even feed into the calculation in advance of whether it's worthwhile making a movie with a particular budget and particular expected audience size.
To plan for your movie to cover its development costs you have two options: charge more per viewer or find more viewers. Big-budget movies aggressively pursue the latter option and therefore (they hope) don't need to do the former. Meanwhile, movies with a smaller expected audience are constrained, by the fact that there's only so much they can charge per ticket, to lower budgets.
In fact, since prices don't vary much by by movie, we can very roughly (and with caution due to some of the "clever" accounting that goes on around movies) compare how much movies cost to make per seat by looking at the ratio between its budget and its box office. We see plenty of big-budget movies with decently high ratios (which therefore, to cover costs, could actually have charged less per seat than they actually did), and we see plenty of mid- and low-budget movies that make a loss and therefore achieved a ratio of less than one (and therefore, to cover costs, would have had to charge more than they actually did). I don't know what direction the correlation ends up being, if any, but it's clearly not the case that by all charging the same prices big-budget movies are uniformly under-charging and/or low-budget movies are uniformly over-charging. If that was the case then low-budget movies would be consistently more profitable (by this rough metric) than big-budget movies, and they aren't.
On the demand side, a viewer chooses what movie they want to watch partly on price and partly on the value to them of seeing the movie. BKay's answer goes into some detail of why it's undesirable for the movie-makers or the cinemas to do too much by way of varying prices. I hope I've explained why it is that they can actually achieve that without the difference in movie budgets getting in the way.
You ask in a comment:
in a saturated, competitive market suppliers can compete by lowering
their prices. A reduction in production cost means they can do so
without reducing margins. Are you saying this intuition is incorrect more
times than not?
Not "more times than not", just "not in the case of movies". Taking two arbitrary examples of science-fiction movies, there is no price point, not even 0, at which "Under the Skin" (budget 13 million USD, and which made a loss at the box office) could have achieved the same number of bums on seats as "The Force Awakens" (budget 200 million, box office north of 1.5 billion and still counting). The former is either a niche product, or an inferior product, or both, and if you could draw up the demand curves of the two movies they'd be drawing on completely different demand: these aren't "the same goods". Further, you would not find a strategy by which either of them gets anything much out of competing with each other on price. Not that they were even in the cinema at the same time, but even if they had been they are too distinct to use a simple model of a customer looking at both and picking the cheaper, despite the fact that individual customers do frequently find themselves in a cinema picking a movie. If there was a means by which "Under the Skin" could satisfy all that "Force Awakens" demand, then sure, it would seriously look into it, but they aren't fungible commodities.
On a loosely-related topic, note that cinemas in any case try to cater to a lot of price sensitivity among customers, by giving them the opportunity to drop a heap of cash on food and drink. Therefore (within a certain range) customers who might be tempted to see a cheaper movie than the average are in fact already in the door. They just aren't having popcorn.