Long-term equilibrium price inelastic? I have doubts about some
economic interpretation:
Why is the long-term equilibrium price inelastic?
But in the short run, the equilibrium price is not necessarily inelastic. What is the economic interpretation of it?
For starters, elasticity is the percentage change in quantity (demanded or supplied, depending on what we're looking at) due to a one percent change in price. Or more vaguely: elasticity measures the sensitivity to price of behavior. From this definition it is clear that stating that a 'price is elastic' is nonsense. Trivially, the elasticity of price with respect to price is one.
That being said, I think I know what you mean. The long run supply curve is perfectly elastic. That is: the long run price is set in stone. It is insensitive to some changes. In a diagram as seen below this means a horizontal supply curve, with price being the same for all output levels. Why is this? Firms are often assumed to have some kind of efficient scale at which the average cost is at its minimum. That is: there is some particular quantity $q^*$ such that $AC(q^*)=\min\{AC(q)|q \geq0\}$. In the long run it seems reasonable to assume that every firm $i$ will produce exactly $q_i=q^*$. With number of firms operating such that in fact price will be equal to $P=AC(q^*)$. Define $P^*=AC(q^*)$,  formally the equilibrium would be such that: $nq^*=Q^d(P^*)$ (supply equals demand). So price will always be the same, namely $P^*$, with $n$ and thus $Q^S=nq^*$ changing in response to changes in demand. All this is long run.

Now  why does this theory make sense? Well, suppose at some moment the price in the market is below $P^*$, then every firm loses money, so it can't persist since firms can just stop operations. Suppose price is above $P^*$: a firm operating at the efficient scale can come in, undercut the market price by a small margin and sell at a profit.