106 LUCAS denoted by m, are not generally known (until next period) except to the extent that they are"revealed"to traders by the current period price level Similarly, the allocation variable 8 is unknown, except indirectly via price The development through time of the nominal moncy supply is governed =mx, (2.2) where x is a random variable Let x' denote next periods value of this ransfer variable, and let g be next period s allocation variable It is assumed that x and x are independent, with the common, continuous density function f on(0 ao). Similarly, 8 and 8 are independent, with the common, continuous symmetric density g on(0, 2) To summarize, the state of the economy in any period is entirely described by three variables m, x, and 8. The motion of the economy from state to state is independent of decisions made by individuals in the economy, and is given by (2.2)and the densities f and g of x and 8 3. PRETERENCES AND DEMAND FUNCTIONS We shall assume that the members of the older generation prefer mor consumption to less, other things equal, and attach no utility to the holding of money. As a result, they will supply their cash holdings, as augmented by transfers, inelastically. (Equivalently, they have a unit elastic demand or goods. The young, in contrast, have a nontrivial decision problem to which we now turn The objects of choice for a person of age 0 are his current consumption c, current labor supplied n, and future consumption, denoted by c. All individuals evaluate these goods according to the common utility function (c,n)+F{v()} (The distribution with respect to which the expactation in(3. 1)is taken will be specified later. )The function U is increasing in c, decreasing in n strictly concave, and continuously twice differentiable. In addition, current consumption and leisure are not inferior goods, or Un Unn<o and Ucc+ Uen <o The function V is increasing, strictly concave and continuously wIce106 LUCAS denoted by m’, are not generally known (until next period) except to the extent that they are “revealed” to traders by the current period price level. Similarly, the allocation variable 0 is unknown, except indirectly via price. The development through time of the nominal money supply is governed by m’ = mx, (2.2) where x is a random variable. Let x’ denote next period’s value of this transfer variable, and let 8’ be next period’s allocation variable. It is assumed that x and X’ are independent, with the common, continuous density functionf on (0, co). Similarly, 8 and 0’ are independent, with the common, continuous symmetric density g on (0, 2). To summarize, the state of the economy in any period is entirely described by three variables m, x, and 8. The motion of the economy from state to state is independent of decisions made by individuals in the economy, and is given by (2.2) and the densities f and g of x and 0. 3. PREFERENCES AND DEMAND FUNCTIONS We shall assume that the members of the older generation prefer more consumption to less, other things equal, and attach no utility to the holding of money. As a result, they will supply their cash holdings, as augmented by transfers, inelastically. (Equivalently, they have a unit elastic demand for goods.) The young, in contrast, have a nontrivial decision problem, to which we now turn. The objects of choice for a person of age 0 are his current consumption c, current labor supplied, n, and future consumption, denoted by c’. All individuals evaluate these goods according to the common utility function: WC, n> + JWV)). (3.1) (The distribution with respect to which the expactation in (3.1) is taken will be specified later.) The function U is increasing in c, decreasing in n, strictly concave, and continuously twice differentiable. In addition, current consumption and leisure are not inferior goods, or: UC, + u,, < 0 and UC, -+ u,, < 0. (3.2) The function V is increasing, strictly concave and continuously twice