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Additional resources for Behavioral Interactions, Markets, and Economic Dynamics: Topics in Behavioral Economics
11). hO u / sufficiently small. h/ D 1: If hO u is strictly higher than h2 , the child is perceived to be sufficiently mature and therefore the child’s rate of time preference is insensitive to the change in his or her level of human capital. Then, the lemma states that, starting from any initial h2 , the parent’s uncertainty decreases over time. Clearly, such an h2 must be larger if or is larger or if ı is smaller. hO u / is not less than 1, ˆ can be greater than 1. In fact, we can show that the following proposition holds: Proposition 1 Suppose that ct D exp.
HO t jt /2 ht2 C ! 11a). ht jt /2 . ht = 2t /C1 < 1. Since F 0 < 1 automatically implies the stability, for a divergence to occur, it is necessary to have F 0 > 1. hO t jt /: The question is whether there exists a combination of parameters with which there is a non-empty set of beliefs that can cause the expectation process to diverge. h/ D 1, be h1 and h2 , which exist if ct D exp. Áht / with Á > 0. 1 ı /2 /= 2 . h/ ! h/ ! C1. h1 ; h2 /; there exists a range of hO t jt , R. h1 ; h2 /, such that any value of hO t jt in R.
HO u / is not less than 1, ˆ can be greater than 1. In fact, we can show that the following proposition holds: Proposition 1 Suppose that ct D exp. h/> 1. Then, (i) there exists a combination of parameter values such that there exists a level of N 2 and the associated range of hO u , R. 1 ı /2 /= 2 / and any hO u 2 R. N 2 /, ˚ is greater than one, (ii) given an updated belief (hO u , h2 ) and the parameter values that satisfy the condition described in (i), the parent’s expectation process becomes divergent, and (iii) hL is decreasing and hH is increasing in N 2 .