Question

Suppose that the money demand function takes the form $(M/P)^d=L(i,Y)=Y/(5i).$

1. If output grows at rate $g$ and the nominal interest rate is constant, at what rate will the demand for real balances grow?
2. What is the velocity of money in this economy?
3. If inflation and nominal interest rates are constant, at what rate, if any, will velocity grow?
4. How will a permanent (once-and-for-all) increase in the level of interest rates affect the level of velocity? How will it affect the subsequent growth rate of velocity?
5. If the central bank wants to achieve a long-run target inflation rate of $\pi$, at what rate should the money supply grow?

Answer 1

  
Tugowo (MIP) = Lli,4)u 51 This shows that moneu Dd has the reen with " (Olt) & inverse reen with i Ccinterest rate) are It y increases @ g and I it i (m|p) - (4+94) maggi! tornar = 4 + 9/4) maider sin tj: + wa (mlea + a(mp)9 milegir tence money od also increases by rate gusto The velocity of money refers to the number of times a unit of currency is circulated (used to per purchase goods & services) in the econonry Acc to Quantity Theory of honey (@TM), my=PY m= money stock during time period t. = velocity of money P₂ Price level at time to 42 Output level of time it', ATQ, Taking 1. Change on beth sides! Cf. Dinm) (1.Din V) =(1-DinP) (7. AinY) DM. OV = 1.04 qm . AU = .gy If interest rate is constant, growth rate of money (gn) is a constant; a gm. Duo Togg Du = growth rate of suspect.

Date: Page No. 1 If there is a permanent increase in interest rate ut reduces the real money stock in the econonry, as it becomes difficult to lend money, 1 On the other hand, money velocity increases when household spend on goods & services more freqreently, which will happen only if money is easily available to them. Hence if interest rate increases a velocity of money decreases . | When money supply increases at a rate faster than increase in output (gy), there is a rise in nominal Demand. In response to this increased demand, firms increases prices & hence inflation (II) u acheived.