I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the condition when it's true. Can you please help me with that?
A market is covered if all consumers will choose to buy from at least one of the firms at the prevailing prices.
For example, consider a standard Hotelling model with two firms who are located at opposite ends of the unit interval. Suppose that each firm charges that same price $p$ and that consumers are uniformly located on $[0, 1]$. Finally, suppose that every consumer has unit demand and the same utility function $u = v - tx - p$ where $v$ is their valuation for the good, $t$ is the cost of transportation and $x$ is the distance that they travel to the firm from which they buy. In this example, every consumer will choose to buy a good if and only if the consumer located in the centre chooses to buy the good (since she has the furthest distance to travel). This is equivalent to asserting that
$$ v - 0.5t - p \geq 0 \iff v \geq 0.5t + p .$$
That is, the market is covered when the valuations of the consumers are sufficiently high relative to the price and cost of transportation.
It is a market where firms compete for the marginal consumer.
It’s an opposite of having fully separated market where two firms do not compete for marginal customer.
An example of covered market would be market for bus rides where the departures are scheduled at the exactly same time - so there is competition for the marginal customer.
Example of separated marked would be when bus companies all schedule different times of departure so they don’t compete for the marginal customer.