Question: Explosive paths in the Samuelson overlapping-generations model. (Black, 1974; Brock, 1975; Calvo, 1978.) Consider the setup described in Problem 2.19. Assume that x is zero,

Explosive paths in the Samuelson overlapping-generations model. (Black, 1974; Brock, 1975; Calvo, 1978.) Consider the setup described in Problem 2.19.

Assume that x is zero, and assume that utility is constant-relative-risk-aversion with θ < 1 rather than logarithmic. Finally, assume for simplicity that n = 0.

(a) What is the behavior of an individual born at t as a function of Pt/Pt +1?

Show that the amount of his or her endowment that the individual sells for money is an increasing function of Pt/Pt +1 and approaches zero as this ratio approaches zero.

(b) Suppose P0/P1 < 1. How much of the good are the individuals born in period 0 planning to buy in period 1 from the individuals born then? What must P1/P2 be for the individuals born in period 1 to want to supply this amount?

(c) Iterating this reasoning forward, what is the qualitative behavior of Pt/Pt +1 over time? Does this represent an equilibrium path for the economy?

(d) Can there be an equilibrium path with P0/P1 > 1?

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