Check you are signed in the the Google account you used to purchase the app (you should see it listing in your app purchases)
Order History:
https://support.google.com/googlepla.../2850369?hl=en

Here is Google's help information for installing/downloading:
https://support.google.com/googlepla.../7513003?hl=en
Sometimes clearing the caches works if it is asking (incorrectly) for payment.