This depends on what model of perfect competition we are talking about.
In a 101 textbook perfect competition firms do not decide on what prices are but prices are determined by the market. Firms simply decide what quantity to supply to the market given the market prices. They do not set up or experiment with the prices, their choice variable is quantity not price.
In perfect competition supply curve will be given as a horizontal sum of marginal costs of firms in the industry so there will be some supply curve, for example it could be:
On market there will be some demand lets say:
$$q_d = 100-p$$
$p$ is found by intersecting $q_s=q_d$, so in this example:
$$10+p = 100-p \implies p=45$$
If technology would change marginal costs of a firm then that would change the supply curve which is again horizontal sum of marginal costs. For example, if some technology makes production easier new marginal costs could be given by:
So new price would be found using:
$$5+2p=100-p \implies p=36.66$$
Note both after and before change to costs function $MR=MC$, $MR$ for a perfectly competitive firm is $p$. For a single firm $MR$ is constant (horizontal line) but the market price $p$ is not constant.
In slightly more advanced 101 model that you can find in textbooks there will also be entry of new firms that imposes lower price and in short run firms can actually earn profit if marginal costs decrease. There are also various other models where firms also can set prices and so on but these do not appear in undergraduate materials.
So this is how the standard model works. The price is determined by demand-supply interaction, firm's then take the price determined by the market as given and do not experiment with it.