Is this East German visor cap authentic?

[Itani]

I recently encountered this DDR visor cap at an antique store. However, I didn't buy it as I was very skeptical about its authenticity.
On the inside of the cap, there's print that says, "Made in East Germany" in English. I know this doesn't make the cap fake, as some exporters do this, but it was still very suspicious to me.
The visor was also plastic, but I've done some research and it turns out that they are supposed to be plastic (I think?).
Everything else seemed to be okay. The cap was selling for 35 USD.
Is it real, and is $35 a fair price?