Introduction to Modern Economic Growth The only difference from the standard budget constraint is the additional term, zi (t), which reflects transfers to the individual The reason why these transfers are introduced is as follows: since individuals face an uncertain time of death, there may be “accidental bequests” In particular, individuals will typically come to the end of their lives while their asset positions are positive When this happens, one possibility is that the accidental bequests might be collected by the government and redistributed equally across all households in the economy In this case, zi (t) would represent these receipts for individual i However, this would require that we impose a constraint of the form (t) ≥ 0, in order to prevent individuals from accumulating debts by the time their life comes to an end An alternative, which avoids this additional constraint and makes the model more tractable, has been proposed and studied by Menahem Yaari and Olivier Blanchard This alternative involves introducing life-insurance or annuity markets, where competitive life insurance firms make payments to individuals (as a function of their asset levels) in return for receiving their positive assets when they die The term z (t) captures these annuity payments In particular, imagine the following type of life insurance contract: a company would make a payment equal to z (a (t)) to an individual as a function of his asset holdings during every period in which he is alive.2 When the individual dies, all his assets go to the insurance company The fact that the payment level z (a (t)) depends only on the asset holdings of the individual and not on his age is a consequence of the perpetual youth assumption–conditional expectation of further life is independent of when the individual was born and in fact, it is independent of everything else in the model The profits of a particular insurance company contracting with an individual with asset holding equal to a (t), at time t will be π (a, t) = − (1 − ν) z (a) + νa With free entry, insurance companies should make zero expected profits (in terms of net present discounted value), which requires that π (a (t) , t) = for all t and a, 2The reader might note that this is the opposite of the most common type of life insurance contract where individuals make payments in order for their families to receive payments after their death These types of insurance contracts are not useful in the current model, since individuals not have offsprings or are not altruistic towards them 442