The stability of fiscal policy. (Blinder and Solow, 1973.) By definition, the budget deficit equals the rate of change of the amount of debt outstanding: δ(t)=?(t). Define d(t) to be the ratio of debt to output: d(t)=D(t)Y(t). Assume that Y(t) grows at a constant rate g>0.
(a) Suppose that the deficit-to-output ratio is constant: δ(t)Y(t)=a, where a>0.
(i) Find an expression for ?(t) in terms of a, g, and d(t).