Require password for each application to install
Apps that are free don't have to be purchased -> no purchase means no password prompt. 

I see two possibilities for you:


Delete your Google account from the device. Google apps usually sync everything to the cloud, therefore by re-adding the account everything will be restored.
If the device has the possibility to create a guest user account set a difficult password on your primary account and create a guest user. Guest users aren't allowed to install new apps, however they can use every app that is already installed and the app data is stored in a separate directory therefore the guest can use the apps but don't access your app data.