NEUTRALITY OF MONEY differentiable. The function v(c)c is increasing, with an elasticity bounded away from unity, or v"(c)c'+v(c)>0, (33) c'(c) ≤-a<0 (34) ondition(3. 3)essentially insures that a rise in the price of future goods will, ceteris paribus, induce an increase in current consumption or that the substitution effect of such a price change will dominate its income effect The strict concavity requirement imposed on V implies that the left term of (3.4)be negative, so that(3. 4)is a slight strengthening of concavity Finally we require that the marginal utility of future consumption be high enough to justify at least the first unit of labor expended, and ultimately tend to zero im V'(c)=0 (3.6) Future consumption, c, cannot be purchased directly by an age 0 individual. Instead, a known quantity of nominal balances A is acquired in exchange for goods. If next period's price level (dollars per unit of ouptut) is p and if next period's transfer is x', these balances will then purchase x'mlp' units of future consumption. 6 Although it is purely formal at this point, it is convenient to have some notation for the distribution function of (x', p), conditioned on the information currently available to the 6 The restrictions(3. 2)and (3.3)are similar to those utilized in an econometric study of the labor market conducted by Rapping and myself, [5]. Their function here is the same as it was in [5]: to assure that the Phillips curve slopes the"right way. " 6 There is a question as to whether cash balances in this scheme are "transactions balances"or a"store of value i think it is clear that the model under discussion is not rich enough to permit an interesting discussion of the distinctions between these, or other, motives for holding money. On the other hand all motives for holding money require that it be held for a positive time interval before being spent there is no reason o use money (as opposed to barter) if it is to be received for goods and then instan- ' yields utility. "Certainly the answer in this context is yes, in the sense that ir ey aneously exchanged for other goods. There is also the question of whether m imposes on an individual the constraint that he cannot hold cash, his utility under ar ptimal policy is lower than it will be if this constraint is removed. It should be equally lear, however, that this argument does not imply that real or nominal balances should be included as an argument in the individual preference functions. The distinction the familiar one between the utility function and the alue of this function under aNEUTRALITY OF MONEY 107 differentiable. The function V’(c’)c’ is increasing, with an elasticity bounded away from unity, or: vyc’) c’ + V’(c’) > 0, (3.3) c’ V”(c’) ~ < -a < 0. V(d) (3.4) Condition (3.3) essentially insures that a rise in the price of future goods will, ceteris paribus, induce an increase in current consumption or that the substitution effect of such a price change will dominate its income effect.5 The strict concavity requirement imposed on V implies that the left term of (3.4) be negative, so that (3.4) is a slight strengthening of concavity. Finally, we require that the marginal utility of future consumption be high enough to justify at least the first unit of labor expended, and ultimately tend to zero: lim V(c’) = +co, C’--0 (3.5) lim v’(c’) = 0. c’+m (3.6) Future consumption, c’, cannot be purchased directly by an age 0 individual. Instead, a known quantity of nominal balances X is acquired in exchange for goods. If next period’s price level (dollars per unit of ouptut) is p’ and if next period’s transfer is x’, these balances will then purchase x’h/p’ units of future consumption.6 Although it is purely formal at this point, it is convenient to have some notation for the distribution function of (x’, p’), conditioned on the information currently available to the 6 The restrictions (3.2) and (3.3) are similar to those utilized in an econometric study of the labor market conducted by Rapping and myself, [5]. Their function here is the same as it was in [5]: to assure that the Phillips curve slopes the “right way.” e There is a question as to whether cash balances in this scheme are “transactions balances” or a “store of value.” I think it is clear that the model under discussion is not rich enough to permit an interesting discussion of the distinctions between these, or other, motives for holding money. On the other hand, all motives for holding money require that it be held for a positive time interval before being spent: there is no reason to use money (as opposed to barter) if it is to be received for goods and then instun￾taneously exchanged for other goods. There is also the question of whether money “yields utility.” Certainly the answer in this context is yes, in the sense that if one imposes on an individual the constraint that he cannot hold cash, his utility under an optimal policy is lower than it will be if this constraint is removed. It should be equally clear, however, that this argument does ll~t imply that real or nominal balances should be included as an argument in the individual preference functions. The distinction is the familiar one between the utility function and the value of this function under a particular set of choices