How can I download he file with prices calculated by the recommendations?

From the application itself, we can generate several files: 

1) In the Dynamic Pricing tab:

2) In the Files tab: 

a) After creating and enabling the first rule, and generating the API key, a Repricing folder will appear: 

b) Past recommendations also appear in the historical report from the last 30 days:

The same files are also available via the API.