Traditional pens contains of 100% polystyrene. Polystyrene is a cheap, mass produced plastic. The production of polystyrene releases chlorofluorocarbons (Schwarz, Leisewitz 1999) into the environment- gases that have roughly 1200 times the greenhouse effects of carbon dioxide.

• Calculation: 3.600.000.000.000.0 kg per year
• / 365 days
• = 98 630 136 986 KG per day
• /1440 minutes per day
• = 68 493 150 KG per minute
• 60 seconds per minute
• = 1 141 552 kg per second (baseline for our calucation)

Source: https://ourworldindata.org/co2-and-other-greenhouse-gas-emissions

Then you must consider that a huge quantity of these pens are manufactured in China, so you must also include the transport footprint too