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The City of Lone Tree, Colorado ( http://www.lone-tree.org ), a small suburb of Denver, has privatized all of their municipal services, including planning.
Then again, consider how much a planner makes in the public sector (about $20 an hour or so, plus benefits), and the functions they perform (i.e. a lot if it's a one person department) versus private sector planning services ($75/hour rate, plus expenses)
Whitewater. Our staff does quite a bit of planning and all of the hands-on development work, but we contract with a private consultant to do long-range planning and for some site review work (with plenty of input from all city staff).
It is very common for smaller communities to contract with consultants. I used to do it myself, I just interviewed one such planner in the Traverse Bay area, Michigan, and have run across it in a number of places over the years. It is also very common for smaller communities in some states to contract with a regional council of governments for planning services. The quality of the work obtained in this setting ranges from excellent to shaky, but it is often the only choice. Dan's per hour comparison is inaccurate: if you hire a staff planner you have to provide office space, equipment, benefits, etc. that make the cost of an in-house planner much closer to that of a consultant when everything is accounted for. The main reason to go in-house is not cost per planner, although you may save some money. It is because your local workload is high and/or because local officials want people who will be totally committed and responsive to the community.