If we are talking about government, no. If we are talking about individuals in voluntary exchange, yes.
To understand the free market you have to realize that it only exists by completely voluntary exchange and no coercion.
Why are no bid contracts by government not free market:
- Government taxes you.
- Taxation is coercion. Try not paying that tax if you are in disagreement with the procurement.
- No bid contracts to not provide best quality of service, or the best price.
- If this is a spec issue, how would you know if you are getting the best product without an open bid to see what other companies are doing.
- Most closed bid contracts are done because a contributor, to the purchasing government agent, paid as a perk to the government official.
Why are no bid contracts by individuals free market:
- You have your own money.
- You make the contact with your preferred service provider.
- If you chose to not look at other offerings, that is your choice to do what you want with your money.
There is a case where voluntary agreement is still not free market:
- If the government only allows certain people to compete for my business then that is not a free market.
- The best example is internet service providers. Most service providers have exclusive contracts with the cities that they are located in. And you wonder why the cost of the internet is so high.