Detail

Fake butter flavoring and yellow food coloring are clearly variable inputs since the theater only uses them when it makes more popcorn (we hope). So, an increase in their cost is an increase in the cost of a variable input. As shown above this shifts back the MC curve to MC₂ causing the profit maximizing firm to raise price and reduce output. 14. When you go to the movies, the theater is a monopoly vendor of popcorn while you're there (which is why it costs so much). Suppose that the cost to the theater of fake butter flavoring and yellow food coloring rise significantly, what will happen to the price and quantity of popcorn sold by the theater.

The price of popcorn will rise and the quantity sold will increase. This would require an increase in demand. Presumably when people make the decision to purchase popcorn they don't care about the cost of individual ingredients (though they may care what those ingredients are) they simply care about the total price of a tub of popcorn drenched in artificial ingredients. Thus, the demand for popcorn wouldn't change (though quantity demanded does as price changes).
The price of popcorn will rise and the quantity sold will fall.
The price of popcorn will remain unchanged and the quantity sold will remain unchanged. For this to be true only a fixed cost could have changed, or nothing at all.
The price of popcorn will fall and the quantity sold will fall. This would require a decrease in demand. Presumably when people make the decision to purchase popcorn they don't care about the cost of individual ingredients (though they may care what those ingredients are) they simply care about the total price of a tub of popcorn drenched in artificial ingredients. Thus, the demand for popcorn wouldn't change (though quantity demanded does as price changes).
The price of popcorn will fall and the quantity sold will increase. This would require a reduction in a variable cost, the opposite of what was stated.