Economic theories of intertemporal consumption seek to explain people's preferences in relation to consumption and saving over the course of their lives. The earliest work on the subject was by Irving Fisher and Roy Harrod, who described 'hump saving', hypothesizing that savings would be highest in the middle years of a person's life as they saved for retirement. Economic theories of intertemporal consumption seek to explain people's preferences in relation to consumption and saving over the course of their lives. The earliest work on the subject was by Irving Fisher and Roy Harrod, who described 'hump saving', hypothesizing that savings would be highest in the middle years of a person's life as they saved for retirement. In the 1950s, more well-defined models built on discounted utility theory and approached the question of inter-temporal consumption as a lifetime income optimization problem. Solving this problem mathematically, assuming that individuals are rational and have access to complete markets, Modigliani & Brumberg (1954), Albert Ando, and Milton Friedman (1957) developed what became known as the life-cycle model. See Intertemporal choice:Modigliani's Life Cycle Income Hypothesis for details.