손실통제: 2기간 모형에서 비교정학분석을 중심으로
Self-insurance-cum-protection: Focusing on a Comparative Static Analysis in a Two-period Model
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초록
본 연구는 손실의 발생 시점과 최적 손실통제 (SICP)노력의 투입 시점을 분리한 2기간 세팅 하에서 예방적 SICP 노력의 특성을 살펴보고 있다. 비교정학분석을 수행한 결과는 다음과 같다. 첫째, 2기간 모형에서 효용함수의 오목성 증가로 인해 SICP 노력이 항상 증가하지는 않는다. 효용함수의 오목성 증가가 SICP노력이 증가하기 위해서는 (i) 1기의 노력으로 인한 비용 지출 이후 순 부의 수준이 2기 손실 발생 이후 순 부의 수준보다 높아야 하며, (ii) 2기의 손실 발생 이후 순 부의 수준의 특정값보다 높아야 한다. 둘째, 2기간 모형에서 위험회피성향의 변화를 정의하기 위해 Kihlstrom-Mirman 선호를 가정한 결과, 위험회피성향의 증가로 인해 SICP 노력이 항상 증가하는 것은 아니다. 위험회피성향의 증가가 SICP노력의 증가를 가져오기 위해서는 1기 비용 지출 이후 순 부의 수준 및 2기 손실 발생 이후 순 부의 수준이 모두 각각의 특정값보다 높아야 한다.
Abstract
This study examines characteristics of preventive self-insurance-cum- protection (SICP) efforts under intertemporal setting wherein the timings of paying SICP effort costs and loss occurrence are separated. The results of the comparative static analysis are as follows. First, an increase in the concavity of utility function in a two-period model does not guarantee an increase in SICP. If the following conditions hold, then an increase in concavity of utility function leads to an increase in SICP: (i) the level of net wealth after paying effort costs in the first period is higher than that of net wealth after loss occurrence, and (ii) the level of net wealth after loss occurrence is higher than the threshold. Second, it is assumed that an individual has Kihlstrom-Mirman preference to define the change in risk aversion. An increase in risk aversion does not always lead to an increase in SICP. In order for an increase in risk aversion to lead to an increase in SICP, both the level of net wealth after paying effort costs in the first period and that of net wealth after loss occurrence in the second period should exceed each threshold.
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