It's easy to make up excuses for why it might still be rational to go to the movie. Here's how to factor all that out and cut to the real issue:

Scenario 1: You bought a $10 non-refundable ticket to a show. (And note that you definitely would not have done so if the show cost $20.) As you get to the theater you realize you lost your ticket. Luckily, they have more available, still at $10. Do you buy another ticket?

Scenario 2: You didn't buy a ticket ahead of time. As you get to the theater you realize that $10 has fallen out of your pocket and is lost. Luckily, you still have enough to buy a ticket. Do you do so?

Everyone agrees on Scenario 2. Of course you do. No one's on such a tight budget that an unexpected change in wealth of $10 changes their utility for theater.

But many people refuse (I've checked) to see that Scenario 1 is fully equivalent. They can't bear to pay another $10 for a show they already paid $10 for. If Scenarios 1 and 2 don't feel fully equivalent, you're probably suffering from the sunk cost fallacy!