Abstract: 

We study how altruism networks affect the demand for formal insurance. Agents with CARA utilities are connected through a network of altruistic relationships. Incomes are subject to a common shock and to a large individual shock, generating heterogeneous damages. Agents can buy formal insurance to cover the common shock, up to a coverage cap. We find that ex-post altruistic transfers induce interdependence in ex-ante formal insurance decisions. We characterize the Nash equilibria of the insurance game and show that agents act as if they are trying to maximize the expected utility of a representative agent with average damages. Altruism thus tends to increase demand of low-damage agents and to decrease demand of high-damage agents. Its aggregate impact depends on the interplay between demand homogenization, the zero lower bound and the coverage cap. We find that aggregate demand is higher with altruism than without altruism at low prices and lower at high prices. Nash equilibria are constrained Pareto efficient.

This paper examines the influence of formal insurance on the configuration of risk-sharing networks. When facing idiosyncratic risks, agents can choose between forming costly risk-sharing links and purchasing formal insurance. I find that formal insurance and risk-sharing networks are substitutes. Moreover, the price of formal insurance determines how agents' incentives to form links vary with the number of agents they are connected to. For some price levels, there is multiplicity in the structure of stable networks. When the linking cost is high, the unraveling of the risk-sharing network is gradual, and the number of components in a stable network decreases weakly and progressively as the price of insurance decreases. When the linking cost is low, the unraveling is abrupt and agents go from being connected to the entire community to relying only on the formal insurance.