In my research project, the focus is on the roles of capital vintages in the overlapping-generations models (hereafter, OLG models). The assumption of durable capital goods distinguishes my OLG model from the standard one. Even in the single good good model, the price of consumption good is not necessarily equal to the price of capital good because of incomplete depreciation.
More closely, I set up the following problems :
(1)Introduction of vintage capital into the OLG model and definition of competitive equilibria,
(2)Vintage composition of capital goods in competitive equilibria,
(3)derivation of a necessary and sufficient condition for production efficiency (Extension of Cass(1972)).
For (1), I modify the standard treatment of capital goods so that the capital stock, K_t, at the t-th period is given by
K_t=a_0k_t+a_1k_<t-1>+a_2k_<t-2>+... ; a_t>0(t=0, 1, 2, ...).
As a result, my feasibility condition is formalized as c_t=f(K_t)-k_t>0, (t=0, 1, 2, ...), where c_t, k_t, and f(.) are, respectively, the consumption and investment in the t-th period, and a production function.
For (2), it has become clear that the vintage composition crucially depends upon both the no arbitrary condition and the coefficients, a1, which reflect
For (3), it is shown that competitive equilibrium paths are production efficient if the value of capital stock at infinity is finite : lim_<1**>p_tK_t<+*.