Apple - Can I install apps bought on the Mac App Store on multiple computers?
Yes. Just run the App Store app on the second Mac and go to the Purchases tab. You'll see a list of the apps you've already purchased, with an Install button next to each one - click the button to install on the second Mac.
Yes, you can install apps bought from the Mac App Store on any and every Mac that you personally own and use.
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Licenses and copy protection
Can I buy an app on one Mac for use on all my computers?
Yes, you can install apps bought from the Mac App Store on any and every Mac that you personally own and use.
What about the five-Mac restriction that I have with videos I bought from iTunes? Does that work for Apps too?
No. Apps don't check to see if you've using an iTunes-authorized Mac. They can ask you to verify your Apple ID and password, but that's a single check and it's just to verify you are who you say you are. Once your identity is verified, that's it. There's no authorizing or deauthorizing or counting of different Macs.
Does that mean I could buy one copy of an app and install it on every Mac in my business?
No, the license you agree to when you enter the Mac App Store says that app downloads are for Macs that you personally own, and that's a license for personal use. Apps that are intended for professional use are licensed for you or for a single computer used by several people. While there's no technical impediment to you installing them on multiple Macs at work, you'll be violating the license agreement. It's the same scenario as if you buy a single-user copy of iWork and install it on ten Macs at work—you can do it, but you're violating the license agreement, making the act ethically questionable.
There is no numerical limit, and you don't need to run App Store on every Mac. The App Store's own online Help document explains all this -- from App Store, open Help, then select Purchase Applications>Use Applications on Multiple Macs for details.
The only restriction on this is if your purchase was for commercial use and more than one person uses the apps. In that case the language of the license asks for one purchase per user or one purchase per computer.