Assignment
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) ≡ D? (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 ?d(t) in terms of a, g, and d(t)
(ii) Sketch ?d(t) as a function of d(t). Is this system stable?
(b) Suppose that the ratio of the primary deficit to output is constant and equal to a > 0. Thus the total deficit at t, δ(t), is given by δ(t) = aY(t) + r (t)D(t), where r (t) is the interest rate at t. Assume that r is an increasing function of the debt-to-output ratio:
r(t) = r(d(t)), where r'(•) >0. r''(•)>0, limd→∞ r(d) < g, limd→∞ r(d) > g.
(i) Find an expression for ?d(t) in terms of a, g, and d(t).
(ii) Sketch ?d(t) as a function of d(t). In the case where a is sufficiently small that ?d is negative for some values of d, what are the stability properties of the system? What about the case where a is sufficiently large that ?d is positive for all values of d?