Abstract
We build a simple two-period general equilibrium model with incomplete markets which incorporates reverse market mortgages without appealing to the complicated framework required by the infinite horizon models. Two types of agents are considered: elderly agents and investors. The former are owners of physical assets (for instance housing) who will want to sell them to investors. For that end the elderly agents, who are assumed to not have any bequest motive, issue claims against physical assets they own. One of the claims issued will be interpreted as reverse mortgage (loan for seniors) and the other one as a call option written on the value of housing equity. By assuming that both the elderly agents and the investors are price takers, and by applying the generalized game approach, we show that the equilibrium in this economy always exists, providing the usual conditions on utilities and initial endowments are satisfied. We end with a remark on efficiency of the quilibrium.
Highlights
One of the great problems that many countries’ social security systems faces is how to sustain the elderly people who are ageing later than in previous generations
In Brazil, reverse mortgages are offered as forms of investments which are sold as options to fund retirements
We will give sufficient conditions which guarantee the existence of equilibrium for an economy with reverse mortgage
Summary
One of the great problems that many countries’ social security systems faces is how to sustain the elderly people who are ageing later than in previous generations. When an elderly homeowner receives cash flows due to the reverse mortgage, it is as if they were spending some portion of their housing equity (wealth product from their past), increasing the net worth of the household. In this sense, a reverse mortgage is a dissavings scheme, and for many elderly persons it is the main vehicle for life-cycle consumption-health financing. There exists a competitive general equilibrium in an economy in which the elderly people engage in reverse mortgages in order to fund their consumption. We demonstrate that equilibrium for the generalized game corresponds to equilibrium for our original economy
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