Does a web design agency write the copy? Usually not, unless the quote says so in plain words. Most studios design and build. The words on the page are yours, a copywriter's, or a named line in the scope. Find out which before you sign. Missing copy is among the most common reasons a website build stalls.
Here is why. A designer lays out a page around the words that will sit on it. One copywriter makes this argument (so she has a stake in it) and tells of a designer who left room for a one line headline when the copy needed three. Small, but it is the whole problem. The layout was a guess, and the guess was wrong.
Filler text hides the same thing. Nielsen Norman Group notes that placeholder copy such as Lorem Ipsum is convenient early in a design, but it can cause trouble when the real content differs in length, density or structure. The layout you approve in week two is provisional. It becomes real when the words arrive.
So who writes them? There are three honest answers. You do, which works if you know the business cold and can hold to a date, though writing for a page is a different skill from explaining your company across a table. A specialist copywriter does, ideally after the messaging is settled. Or the studio does, which is fine when it is a named part of the scope with a price and a deadline, and a problem when both sides assume it.
What are you aiming for? Plain, short and factual. In Nielsen Norman Group's 1997 studies, 15 of 19 participants always scanned unfamiliar web text before reading it. Against a promotional style control, a concise version scored 58% higher on measured usability, a scannable one 47% higher, and an objective one 27% higher. All three together scored 124% higher. The studies are old and the numbers are directional, but people still skim, and they still distrust hype.
Copy moves the price and the timeline too, though we won't put a number on it. We have no reliable one to give. The designers in that same copywriter's community said finished copy means fewer rounds of revisions, which keeps their prices down. That is anecdote from an interested source, not a study. The logic holds, though. Late copy means placeholders, then rework, then a project sitting idle.
The order that tends to work is strategy and messaging first, then brand, then copy, then the website design. Copy can run alongside brand work once the messaging is clear.
Ask the studio five things. Who writes the words? When are they due? What happens to the schedule if they are late? How many rounds of revisions cover the copy? Who signs it off?
Before you ask anyone for a quote, write down who owns the words and by what date. Bring that to the first call and watch how the studio answers.