Vertex operator for the non-autonomous ultradiscrete KP equation

We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.Comment: 9 page

Habit Formation, Parents' Education Spending, and Growth

This paper investigates the impact of habits on economic growth in an overlapping generations (OLG) economy with physical and human capital in which altruistic parents finance the education of their children. Habit formation interacts with the role of human capital as an engine of growth by reducing education spending in the short run and by increasing the wage rate and decreasing the interest rate in the long run. When relative risk aversion (RRA) lies around unity, or when the RRA is no less than one and production is physical capital intensive and the level of the total production factor is large or the strength of habits are large, the effect of increasing the wage rate dominates the other effects and, therefore, the desired level of human capital investment increases in the long run, with habits. As a result, compared with a case with time-separable utility, the stationary growth rate implied by a model with habits is higher.economic growth