comparative/superlative usage - English Language & Usage

The technically correct answer is A.

This is subtle, and a little nitpicky. The price is the number of dollars you pay for something, and that number has the property of being higher (or lower) than something else. The dress, on the other hand, has the property of expensiveness, and can be more (or less) expensive than something else.

So we say that "The dress is more expensive than the jacket" and "the price of the dress is higher than the jacket" because the dress has a higher price. We do not say "The price of the dress is more expensive". If we said "The price of the dress is more expensive" it would technically mean "I can buy the price for some dollar value, and that dollar value is higher than something else". This could only be true in a situation where finding out the price of the dress cost you some money.

In reality, "The price of the dress is more expensive" is frequently used, and most people are not going to think twice about it.

"the higher" is wrong because straight comparatives don't take articles. (except "the higher of" two things).