You don't necessarily need to do much
There are three factors at play here :
First, markets are all about balance between consumers and producers. As you told, your zombies only need the basic needs, meaning they will consume less. You need living beings at one point to have enough consumers so that you can still earn from having more products to sell. In other words, no one will have the use of 5 or 10 cars1, even at the price of one, so here's a economical limit.
Then, it looks like your undead are only capable of basic work. This will severely limit their use to give more complex products and services. Yes, it's kinda nice to have a semi-conscious worker for pennies, but it makes them relatively similar to today's automated machines. Pardon me the use of these words, but they'll still need "maintenance" like machines, without the advantage of an actual worker who can think and adapt.
Speaking of being akin to a machine, unless your culture is widely different from 20th and 21th's century, toying with corpses is something few enjoy. Worse, it's very unlikely you'll easily agree your boyfriend, father or mother is used by someone till death. Why? Well, first, it's likely a cultural concept coming from before zombies were invented. Then and most importantly, it's tied deeply in our construction as social, living beings : relationships are forged slowly but last through time2. In our world, people come by their relative tombstones even years and years after, and would be horrified if they learned the corpse was removed even to be used as compost. This principle is really not easily destroyed. To sum up, it will be hard to convince the majority it's morally OK to give away their relatives, even when knowing the benefits.
Ensuring it with laws
That being said, let's give people some tools to protect this cultural identity. After all, there are people who have little to no morale compass who need to be regulated. Like frauds, the solution will most likely come from laws and governemental services specialized in this topic.
First the law, give the right of the body to the family, exactly like property inheritance3. To give more control to the future zombie, you can also -and even- give the right to refuse any necromancy on your own body, exactly like you can allow or disallow the use of your corpse as a science subject, organ donor or any equivalent in most countries in the real world.
To ensure the law is followed, you'll need specific authorities. It's not technically possible to prevent any sort of corruption, but if you create complementary authorities, and prepare enough administrative laws this should limit the risk. It will be akin to occupational medicine nowadays, minus every zombie will have an appointed legal guardian to speak in their name.
1 : Without needing much market knowledge, The Asterix & Obelix "Obelix and Co." comic book is a good -and parodic- showcase of why having too much products vs not enough consumers is bad economically. Read it if you can, it's quite fun :).
2 : An excellent example of lasting relationship lies in the Hachikô : Until the end of his life, this dog waited for his master at the railway station.
3 : Of course, don't give the body's rights to someone if they killed the recently deceased. You should not be rewarded for your crimes.