Assume the following I The public holds no currency Il The r

Assume the following I. The public holds no currency. Il. The ratio of reserves to deposits is 0.08. III. The demand for money is given by: M SY(0.83- 2.9i) Initially, the monetary base is $90 billion, and nominal income is $5,300 billion. Calculate the demand function for central bank money: Hd ( .08 ) × ( 5300 × ( .83-2.9i ) Calculate the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money. The equlibrium interest rate is%. (Round your response to two decimal places.)

Solution

The monetary base is the supply of central bank money. Therefore the supply of central bank money is $90 billion

By equalizing the supply and demand we get

.08*5300*(.83-2.9i)=90

424*(.83-2.9i)=90

351.92-1229.6i=90

1229.6i=261.92

i=0.2130

or i=21.30%

Therefore the equilibrium interest rate is 21.30%