In recessions, the stock market falls more than in proportion to corporate profit. The discount rate implicit in the stock market rises. All types of investment fall, including employers’ investment in job creation. According to the leading view of unemployment—the Diamond-Mortensen-Pissarides model—when the incentive for job creation rises, the labor market tightens and unemployment falls. Emp...

It is widely recognized that the economics of distant-future events, like climate change, is critically dependent upon the choice of a discount rate. Unfortunately, it is unclear how to discount distant-future events when the future discount rate itself is unknown. In previous work, an analytically-tractable approach called ‘‘gamma discounting’’ was proposed, which gave a declining discount rat...

Excessively devaluing delayed reinforcers co-occurs with a wide variety of clinical conditions such as drug dependence, obesity, and excessive gambling. If excessive delay discounting is a trans-disease process that underlies the choice behavior leading to these and other negative health conditions, efforts to change an individual's discount rate are arguably important. Although discount rate i...

This paper considers optimal social insurance in a dynamic moral hazard economy. The existing literature has focussed on environments in which a planner and a population agents share the same discount factor. A key finding is that agents are almost surely immiserated: their welfare is driven to its lowest bound. We show that this immiseration result does not hold when the planner’s discount fac...

Schur's partition theorem states that the number of partitions of n into distinct parts ≡ 1, 2 (mod 3) equals the number of partitions of n into parts which differ by 3, where the inequality is strict if a part is a multiple of 3. We establish a double bounded refined version of this theorem by imposing one bound on the parts ≡ 0, 1 (mod 3) and another on the parts ≡ 2(mod 3), and by keeping tr...