One of the banking innovations in the 1960s was the payment of interest on certain types of demand deposits. Assume that interest is paid on money at the rate Rm, which equals (R-x), where x is exogenously determined in nominal terms by market structures and the cost of servicing deposits.
(i) Use the Baumol-Tobin transactions demand model to derive the demand function for money.
(ii) Generalizing the above demand function to md(y, R, x), show the behavior of the LM curve for shifts in x and P.
(iii) What is the effect of an increase in x on aggregate demand and the price level in the IS-LM model?
(iv) Assuming that both r and x always increase by the expected rate of in?ation, carry out (ii) and (iii) again.