Foundations and Properties of Time Discount Functions

A critical element in all discounted utility models is the specification of a discount function. We introduce three functions: the delay, speedup and generating functions. Each can be uniquely elicited from behaviour. The delay function determines stationary and the common difference effect. The speedup function determines impatience. Additivity is jointly determined by the delay and speedup functions. The speedup and generating functions jointly determine a unique discount function. Conversely, a continuous discount function determines unique speedup and generating functions.