In this paper, we examine the behavior of local government which is supposed to get not only local taxes but also some kinds of national grant and to spend them into both recurrent expenditure (e) and public investment (I). We divide public capital (k) into two types: one type is public capital for consumption (kc) and another is public capital for production (ki). Local government receives a non-matching grant (g) and a matching grant for local public investment (gi=αI) and for local recurrent expenditure (ge=βe). In Japan, as local government cannot receive national grant at face value, we introduce discount rates of national grant for each type grants: a matching grant for local public investment and local expenditure.
We build a dynamic model which is depending on these assumtions. We wil solve this model by applying maximum principle. At the long-run equilibrium point, we get a set of equilibrium values. Then we examine the effects of national grants.
