The plane is half empty yet the ticket price has risen

The price may have risen artificially to you because you have not cleared your browser cache. Flight operators (and others such as rail operators for example) will use cookies on your browser to attempt to identify how many times a person has searched for a particular flight.

If you repeatedly search for the price on a particular flight, this would suggest to the flight operator that you need to take the flight. By increasing the price to you specifically (using browser cookies to identify you) they encourage you to book the flight as it appears to you that it is getting more expensive.

Tip - clear your browser cache regularly when using travel websites.

The graphic you have displayed is not a good indicator that the flight is full; that is an indicator of how many people have pre-selected seats.

It is also normal for prices to increase as the date of departure nears - as you have to pay a premium for last minute tickets.

You are also arriving and departing the same day; which is normally an expensive itinerary.

Besides the other explanations given, the cheapest fares typically have advanced purchase restrictions such as being bought 7 days in advance of flight. As you approach the day of flight these fares start to become ineligible for purchase, and less restrictive, more expensive fares must be bought.

If the plane is half-empty, then it stands to reason that the airline wants to make as much money as possible from anyone who does now decide they need to take that flight. That way, they can attempt to recoup some of the "lost" revenue from those un-used seats.

You might be thinking that the airline should reduce the price of the seats, to encourage more people to help fill up the plane. However, people generally fly a specific flight for a specific reason, not just because some seats were cheaper than they used to be. Apparently, it's statistically more profitable to put the prices up for those who need to fly, than to put the prices down and hope enough people take the bait to make the same amount of extra money.

The airline has very good data and analytics to determine the best course of action in cases like these. You and I do not.

First, the seat map may not at all reflect the number of people booked on the flight. People may be booked but not have seats assigned yet for any number of reasons.

That said, airlines seek to maximize their profit, not to fill the plane. If someone is booking a flight at the last minute, there's a decent chance that particular flight is important to them, so they are willing to pay more. Last minute travelers might be bargain-hunting vacationers looking for a good deal, but they might also be business travelers who need to attend an important meeting and will do so at any remotely reasonable price.

As an example, the airline can make the same revenue (approximately, because of ancillary revenue from things like baggage fees) by selling 10 tickets for $100 or one ticket for $1,000. Which is easier: finding a single last-minute business traveler with limited budget constraints who absolutely needs to get to Istanbul or finding 10 bargain-hunters who are prepared to go to Istanbul at the last minute?

The airline's revenue management team has spent a lot of time answering this question, and they have decided that they think they can make more money trying to get a smaller number of passengers to pay more for this flight than if they tried to get a larger number of passengers to pay less. As such, they've raised the price.

And the airline may be more clever than that. They might sell the seat to the last-minute business traveler for $1,000, while offering a cheaper fare to a traveler who stays over the weekend, who is probably a vacationer with a more limited budget. Or, in some cases, they may sell the ticket for $1,000 normally, but offer it at a lower price through an opaque booking engine like Priceline or Hotwire to specifically target budget-conscious travelers. In this way, they can do their best to maximize revenue by having it both ways: sell seats at a low price to those who are price-sensitive, without cannibalizing their ability to sell seats at a higher price to those who are not.