Discount function

A discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility is time-separable, with the discount function f ( t ) {displaystyle f(t)} having a negative first derivative and with c t {displaystyle c_{t}} (or c ( t ) {displaystyle c(t)} in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by A discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility is time-separable, with the discount function f ( t ) {displaystyle f(t)} having a negative first derivative and with c t {displaystyle c_{t}} (or c ( t ) {displaystyle c(t)} in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by Total utility in the continuous-time case is given by