I am sorry to hear you are having trouble with your new HP printer. Before we do anything - did you remove the tape from the cartridge before you put it into the printer? A common error. Check this now.
The first thing to do is open your 1050 software (control panel/printers) and run a maintenance procedure. Search through the several tabs to get to the maintenance or cleaning cycles. After you perform the cleaning, print a test page. If there is no improvement in the print, go to the next step.
I suggest you delete the printer from your system and reinstall the driver. Here is how: First, go to www.hp.com/suppport
(you may have to select a country), find your device listing and download the latest drivers available for the Operating System you are using. Save to your desktop.
Open the Control Panel - find the printer folder - delete the 1050. Turn your computer off, unplug the printer data cord from your computer and unplug the printer power cord from the wall. Turn on your computer. Run the software you downloaded and follow the instructions which will appear on the screen. When you are instructed to plug the printer in ... remember to first plug the power cord in and wait for a minute before you plug in the data cord.
Thank you for your quesiton @ FixYa.com