I don’t own a law firm, neither am I distinctly related to it. But coming to your question, I don’t think (freelance) marketing writers have any different pricing model for law firms. Majority of them would treat you like just any other client.
Usually, the cost to you will depend on the writer you choose. Some would agree to work for you at meager 0.20ppw. Others could charge as high as 1ppw. You have to make the decision here, which must be shaped around the quality you want and the budget you have.
A general marketing writer (who writes on virtually every topic) would charge you much less. The one who specializes in your niche (law), they will comparatively charge higher. Also, a lot will depend on the technical aspect. Do you want the writer to write you technical copies? In that case, the marketing writer must also have fluency in penning technical copies. So, they will charge you higher.
In addition, the pricing will vary on the kind of project you’re offering. Is it a one-time work? In that case, you would be charged slightly higher. If it’s a long-term, consistent work, the pricing will be discounted.
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Now note, all the above details are from a freelancer’s view.
If you’re planning to hire an agency to write you marketing copies, the pricing will be higher as compared to a freelancer. It will cost even more if you’re going for marketing agencies who specialize in dealing with law firms. Again, the pricing will depend from agency to agency, the kind of project you have, and the negotiation skills you have.
All in all, a cost for marketing writers for a law firm is almost the same for any kind of company or niche. If you’re hiring generalized writer/agency, the pay will be lower. If hiring a specialized writer/agency, you will have to pay more.
My opinion is that if the project is one-time, go with the freelancers. If it’s for the long-term, agencies are the ideal choice. Similarly, if the work is strictly limited to the marketing copies, hire general writer/agency. If the work is more technical that requires some knowledge about law, opt for the specialized writer/agency.
Upwork is a good platform to find out how much writers are charging for project like yours.