A NOTE ON THE INTEREST ELASTICITY OF THE TRANSACTIONS DEMAND FOR CASH*

Abstract

SASTRY I [5] has examined the effect of credit on an individual's transactionsdemand for cash-balances by amending the basic inventory-theoretic transactions-demand model to permit short-term borrowing. Wrightman and Terninko W-T [7] since have argued that Sastry's opportunity-cost formulation is incorrect and Litzenberger [4] has criticized Sastry's assumption that the individual's (or firm's) short-term borrowing C2, is constant with respect to changes in its short-term lending i. In incorporating Litzenberger's [4] comments, however, Sastry II [6] has ignored W-T's criticism, and as a result, Sastry's II revised results concerning the interest elasticity of the demand for money are incorrect. In this note, selected results of Sastry II are rederived under a corrected formulation equivalent to W-T. In particular, Sastry II understates the possibility of a positive interest elasticity of the demand for (average) cash balances, a result of special interest given the low elasticities in empirical demand for currency equations (Lewis-Breen [3], Goldfeld [1]) and the general interest in the size and sign of the interest-rate coefficient in the demand-formoney literature. Second, Sastry's entire formulation is valid only under the assumption that the borrowing C2, is a penalty rate, greater than i. The basic Sastry framework assumes the individual receives A dollars at the beginning of the period to be spent at a uniform rate over the period. The individual buys securities at the beginning of the period (at a rate of i per the period) and retains a starting cash balance of S. Once the S has been spent, the individual has the option of liquidating some securities to replenish cash balances or acquiring goods on credit, at an interest rate of C2 per period. Eventually the individual will liquidate M of his securities, subject to a fixed conversion cost of C1, to repay his indebtedness and possibly to reacquire cash balances.' Given the above notation, several simple algebraic results derived in Sastry I [ 5 ] and W-T [ 7 ] follow: