American Psycho

In 1987, wealthy New York investment banker Patrick Bateman's life revolves around dining at trendy restaurants while keeping up appearances for his fiancÃ©e Evelyn and for his circle of wealthy and shallow associates, most of whom he dislikes. Bateman describes the material accoutrements of his lifestyle, including his daily morning exercise and beautification routine. He also discusses his music collection, with performers such as Huey Lewis and the News, Phil Collins, and Whitney Houston. His focus on a lavish lifestyle is also evident by his taste in expensive designer clothing and his luxurious apartment.
Bateman and his associates flaunt their business cards in a display of vanity. Enraged by the superiority of co-worker Paul Allen's card, Bateman murders a homeless man and kills the man's dog. At a Christmas party, Bateman makes plans to have dinner with Paul, with Paul mistaking Bateman for another coworker, Marcus Halberstram. Bateman gets Paul drunk and lures him back to his apartment. While playing "Hip to Be Square" on the stereo, explaining to Paul his opinion and interpretation of the song, and while wearing a rain coat, Bateman ambushes Paul and murders him with an axe. He disposes of Paul's body, then goes to Paul's apartment to stage the situation so that others believe Paul has run off to London.
Bateman is later interviewed about Paul's disappearance in his office by private detective Donald Kimball, hired by Paul's family. During the night, Bateman takes two prostitutes, whom he names Christie and Sabrina, to his apartment and explains to them the improvement he saw in the band Genesis after they moved away from progressive rock toward a more pop rock sound beginning with the album Duke. After they have sex, Bateman tells them to stay, while taking out instruments he uses for torture. In the next scene, the prostitutes leave his apartment bruised and bloodied.
The next day, Bateman's colleague Luis Carruthers reveals his new business card. Bateman tries to kill Luis in the restroom of an expensive restaurant, but cannot bring himself to strangle him. Luis mistakes the attempted murder for a sexual advance and declares his love for Bateman, who flees in disgust. After murdering a model, Bateman invites his secretary, Jean, to dinner, suggesting she meet him at his apartment for drinks beforehand. When Jean arrives, Bateman, unbeknownst to her, holds a nailgun to the back of her head while the two converse. When he receives an answering machine message from his fiancÃ©e, he asks Jean to leave. Kimball meets Bateman for lunch and tells him he is not under suspicion.
Bateman has a threesome with his friend Elizabeth and Christie at Paul's apartment. Bateman kills Elizabeth during sex, and Christie runs, discovering multiple female corpses as she searches for an exit. She is chased by a naked Bateman wielding a chainsaw, and as she is running down the stairs of Paul's apartment building, is killed by the chainsaw which Bateman drops from several levels above her.
Bateman breaks off his engagement with Evelyn. That night, as he uses an ATM, he finds a stray kitten; the ATM displays the text "feed me a stray cat". As he prepares to shoot the cat, a woman sees him and tries to stop him; he shoots her and lets the cat go free. A police chase ensues, but Bateman destroys the police cars by shooting their gas tanks. Fleeing to his office, Bateman enters the wrong office building, where he murders a security guard and a janitor. In his office, Bateman calls his lawyer Harold and frantically leaves a lengthy confession on Harold's answering machine.
The following morning, Bateman visits Paul's apartment, expecting it to be full of decomposing bodies and in the middle of a police investigation, but it is vacant and for sale. The real estate broker tells him to leave. As Bateman goes to meet with his colleagues and lawyer for lunch, Jean finds detailed drawings of murder, mutilation, and rape in Bateman's office journal to her disgust and sympathy.
Bateman sees Harold at a restaurant and tries to convince him that he is a serial killer relating to the phone message he left the other night. Harold mistakes Bateman for another colleague and laughs off the phone message confession as a joke, saying he had dinner with Paul in London days earlier. A confused Bateman returns to his friends and in a final voice-over narration, he realizes he will continue to escape the punishment he deserves, that there has been no catharsis, and that his confession has meant nothing.

Question: Who kills Elizabeth?
Answer: Bateman; Bateman