Question

Question 4 (a) The above table has the demand for money schedule. Quantity of Interest rate money demanded (percent per year) (trillions of 2015 dollars) 0.7 0.9 1.1 1.3 (1) If the Fed supplies $1.1 trillion dollars, what is the equilibrium interest rate? (ii) Discuss how equilibrium is restored if the interest rate is greater than the equilibrium rate found in part (i). (b) Explain how a currency drain affects the size of the money multiplier. In your explanation, suppose that a bank gains $1 million in new deposits and reserves. Further suppose that the desired reserve ratio is 10 percent and the currency drain is 50 percent.

Answer 1

i) If the money supply is $1.1 trillion, the equilibrium interest rate occurs at a point where money demanded equals money supplied. Hence, the equilibrium interest rate is 4 per cent per year.

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ii) if the interest rate is greater than the equilibrium interest rate of 4 %, then money supply exceeds the money demanded. This is because at higher interest rate banks are willing to provide more loans than what is demanded.

How this happens- When interest rate is higher. people will like to keep more in interest bearing deposits and hold less in cash. This increases the supply of loanable funds with the banks. This accompanied with constant loan demands, causes the interest rate to fall. With falling interest rate the demand for money starts to rise. This happens till the equilibrium is restored at at a point where money demanded again equals money supplied.

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iii) Money Multiplier = money supply / monetary base

Money supply = Deposits (D) + Currency (C)

Monetary Base = Reserves (R) + Currency (C)

  $Money Multiplier = \frac{D + C}{R + C}$

or

$Money Multiplier = \frac{1 + C/D}{R/D + C/D}$......... (1)

as given C/D = 0.5 and R/D = 0.1

$Money Multiplier = \frac{1 + 0.5}{0.1 + 0.5}$

$Money Multiplier = \frac{1.5}{0.6}$

$Money Multiplier = 2.5$

This means that $1 million gain in new deposits and reserves would increase the money supply by 2.5 * 1000000 = $2500000.

The size of the currency drainage negatively  impacts the money multiplier. The larger the currency drainage the lesser amount is available for providing loans in the next period. Hence, it reduces the money multiplier.

Money multiplier without currency drainage is given by 1/ (R/D) as against (1) with currency drainage. Suppose there is zero currency drainage, the money multiplier would have been 10. this implies that all the new deposits and reserves will be loaned out.

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