Observation equivalence holds in the hyperbolic discounting models such as Laibson (1996), Barro (1999), and Krusell et al (2002). We study a hyperbolic discounting model where the policy function cannot be replicated by a geometric discounting model. Under the logarithmic utility and Cobb-Douglas production, we obtain the explicit solution for consumer's consumption-saving decision. Different from the literatures of exponential discounting, our model shows that the habit persistence affects consumer''s consumption-saving decision. Therefore, observational equivalence does not hold in our hyperbolic discounting model.
Lake eutrophication caused by excess phosphorus (P) loading from point sources (PS) and nonpoint sources (NPS) is a persistent and serious ecological problem in China. A phosphorus budget, based on material flow analysis(MFA) and system dynamic (SD), is proposed and applied for the agriculture-dominated Qionghai Lake watershed located in southwestern China. The MFA-SD approach will not only cover the transporting process of P in the lake-watershed ecosystems, but also can deal with the changes of P budget due to the dynamics of watershed. P inflows include the fertilizer for agricultural croplands, soil losses, domestic sewage discharges, and the atmospheric disposition such as precipitation and dust sinking. Outflows are consisted of hydrologic export, water resources development, fishery and aquatic plants harvesting. The internal P recycling processes are also considered in this paper. From 1988 to 2015, the total P inflows for Lake Qionghai are in a rapid increase from 35.65 to 78.73 t/a, which results in the rising of P concentration in the lake. Among the total P load 2015, agricultural loss and domestic sewage account for 70.60% and 17.27% respectively, directly related to the rapid social-economic development and the swift urbanization. Future management programs designed to reduce P inputs must be put into practices in the coming years to ensure the ecosystem health in the watershed.