Este parece ser o The Price of Life , um curta-metragem de 1987 produzido pela Chanticleer Films e originalmente exibido no canal a cabo norte-americano Showtime.
Embora não tenha uma entrada própria da Wikipédia, mas uma breve descrição é encontrada em “ Obras semelhantes ”seção do artigo para o filme de 2011 In Time . A ênfase abaixo é minha.
The Price of Life was a 38-minute short film (story by Stephen Tolkin and Michel Monteaux) in which a time account is physically linked to every infant at birth, with death automatic when the balance drops to zero. An elite upper-class is portrayed as living hundreds of years or more. The protagonist is given a certain amount of time as an infant, and as a young boy adds days and years to his time account by buying valuables from people and selling them to visiting tourists from the rich enclave. After his sister dies after gambling away her time, the protagonist (now a young man) sets out on a journey to the enclave of "the Old Ones" in order to save the life of his mother, who is (literally) running out of time. He gets there and meets a beautiful older woman who co-opts him into the immortal lifestyle.
O filme completo pode ser encontrado aqui , no Vimeo.