Unformatted text preview: − ( r + s ) + rs = 1 − ( b + v ) + v = 1 − b and since 0 < b < 1, then 0 < (1 − r )(1 − s ) < 1. With both roots real and distinct, the general solution is Y t = c 1 r t + c 2 s t + Y ∗ where r is the larger of the two roots. The path of Y t is determined by the largest root, r > s . Since b > 0 and v > 0, then rs = v > 0 and so the roots must have the same sign. Furthermore, since r + s = b + v > 0, then both r and s must be positive. The path of income cannot oscillate. However, it will be damped if the largest root lies between zero and unity. Thus, a damped path occurs if 0 < s < r < 1, which arises if 0 < b < 1 and v < 1. Similarly, the path is explosive if the largest root exceeds unity, i.e., if r > s > 1, which implies 0 < b < 1 and rs = v > 1....
View Full Document
- Fall '11
- Economics, Complex number, Largest Root, Economic Dynamics, Real distinct roots