Question

function of the nominal interest rate (i): 0 = 0.3-3i. 1. Suppose that bank reserves (8) The money multiplier (m) is m = (cr + 1)/(cr +0), where cr is the currency-deposit ratio. Initially, suppose the real interest rate (r) equals 0.03, the expected inflation rate (Pe) equals 0.03, and the currency-deposit ratio equals: cr = The real money demand function is L(Y, i) 0.8Y-1500i, where Y is the level of output. The monetary base equals 100. The price level equals 1.0 initially and will not change in the short run, but will adjust in the long a) Calculate the currency-deposit ratio, the reserve-deposit ratio, the money multiplier, the money supply, and the equilibrium level of output. Assume that this level of output equals full- employment output, so you are price level equal to 1.0. Show your work. b) Suppose financial innovation causes the reserve-deposit ratio to decline to e 0.2 3i Calculate the new currency-deposit ratio, the reserve-deposit ratio, the money multiplier, the money supply, and the equilibrium level of output in the short run, assuming a Keynesian model with the price level fixed in the short run. Show your work. c) Calculate the equilibrium price level in the long run. Show your work. are a 0.4 (10 x pe). run. assuming that the economy is in general equilibrium with the

Answer 1

As per the information given,

• 
  0.3-3
  
• 
  r=0.03
  
• 
  00= 2d
  
• Price level = 1.0
• Monetary base = 100
• As per Fisher's effect, Nominal interest rate is i = r + P ^e

1 a. Currency-deposit ratio is -

  

cr 0.4 (10 x Pe

Substituting value of we get ,

00= 2d

.
cr= 0.1

1 b. Nominal interest rate is

0.030.03 0.06

1 c. Reserve Deposit ratio

0.03 (3 x 0.06) 0.12

1 d. Money multiplier is given by -  

cr1 m cr

$\rightarrow m = \frac{0.1+1}{0.1+0.12} = 5$

1 e. Money Supply = Money multiplier x Monetary base

  

M.S. 5 x 100 500

1 f. In General Equilibrium, Output (Y) is determined when Money Supply = Money Demand.

Real Money Demand is given by -

M.D = 0.8Y 06-

0.8Y 90 =500(M.D= M.S

$\rightarrow Y = 737.5$ - This is the full employment level of Output.

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When reserve deposit ratio due to financial innovation declines to -   $\theta = 0.2-3i$ then,

2 a. Cr = 0.1 (no change)

2 b. Nominal interest rate i = 0.03+0.03 = 0.06 ( No change)

2 c. Reserve Deposit ratio $\theta = 0.2 -( 3\times 0.06) = 0.02$ ( decreases )

2 d. Money multiplier m = 1.1/ 0.12 = 9.17 ( increases)

2 e. Money Supply ( M.S) = 9.17 x 100 = 917 ( increases )

2 f. Output (Y) = 0.8 Y - 90 = 917

or, Y = 1258.75 (increases)

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3. To Calculate long term change in Price level we have to first calculate change in Price level due to financial innovation that causes bank reserves to decline.. For this we have -

$\Delta$ in Price level = $\Delta$ in short run Money Supply / $\Delta$ in Output (Aggregate Supply)

$\Delta$ in Price level =

917 500/1258.75 737.5

Therefore Price level in the long run

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