GOVERNMENT BONDS IIo5 be written in the indirect form U=f3*[(1-r)A where(1-r)A2- B now determines the endowment for members of generation 3. Since generation 2 no longer pays off the government debt principal, its budget equation is modified from the form of equation(12)to +(1-r)A-B=以+(1-r)c2+(1-r)[(1-r)A2-B For given values of w, r, and the net bequest from generation I (1-r)Ai-B, generation 2 would select an optimal value of the net bequest to generation 3,(1-r)A2-B. This net bequest would be invariant with B as long as the solution for A? were interior. Assuming that this solution is interior, the attainable utility of generation 2 can be written in the indirect form U2=f2*[(1-r)AB-B,,] which coincides in form with equation(13). The situation has therefore been reduced to the previous case in which marginal changes in B led solely to changes in Ai which kept(I-r)Ai- B constant without affecting any values of consumption or attained util The three-generation results generalize to the case in which taxes are levied on m generations, with the mth generation paying off the principal By starting with generation m and progressing backward, it can be shown for all 2si m-I that, if Ao is interior, U can be written in an direct form as a function of (1-r)4% BAs long all inhe hoices are interior(as anticipated by current generations), shifts in B ply fully compensating shifts in bequest values of consumption and attained utility 12 Intuitively, if this condition is violated for some generations, the impact of these olations on current behavior should be less important the further in the future the tually paid off is crucial. If the amor standing government debt were constant, the impact of the principal on current would become negligible for large m as long as r >0. However, a difficulty ar when B is allowed to grow over time. Suppose that the growth of B were limited to the in turn on the growth of real income. Suppose that the growth rate of realineepends growth of the governments collateral in the sense of its taxing capacity, which do equal to n, which can be viewed as the combined effects of population gre of the In that case the pres which n> r applies is inefficient in that it is associated with a capital stock in excess the golden rule level(see, e.g., Diamond 1965, p, 1129). It is possible in Dia model (p. 1135) that the competitive equilibrium ca in this However, this situation is not possible in growth models where individuals lived and utility is discounted(see, e. g, Koopmans 1965). As long as intergenerati transfers are operative, the overlapping-generations model would seem to be equivalent to the infinite- life model in this re nat is, the possibility of inefficiency in Diamond,'s model seems to hinge on finite lives with inoperative intergenerational transfers. Henc when these transfers are operative, n< r would be guaranteed, and the possibility of perpetual government finance by new debt issue could then be ruled out