Cash-in-advance constraint with status in a neoclassical growth model

In this paper, we assume that a cash-in-advance (CIA) constraint itself depends on relative income, which implies status. This constraint means that agents with higher income are more creditworthy and can make purchases with fewer money holdings. Under this assumption, we construct a one-sector neoclassical growth model and show that there exists a unique steady state that has saddle-path stability without specifying each function. Furthermore, we examine the effects of money growth on capital accumulation. If the status elasticity of CIA constraint is large, the Tobin effect can arise. In contrast, if it is small, the anti-Tobin effect can arise.