QUESTION 6 Consider an economy where banks keep 25% of deposits as reserves. Currency is 50...

QUESTION 6

Consider an economy where banks keep 25% of deposits as reserves. Currency is 50 billion pesos, which constitutes 10% of the monetary base.

    (a) Calculate the monetary base.
    (b) Calculate the money supply.
    (c) If the central bank requires a reserve-deposit ratio of at least 10%, calculate banks' excess reserves.
    (d) If the currency-deposit ratio increases by 3 percentage points, calculate the resulting money supply assuming that the monetary base and the reserve-deposit ratio stay the same.
    (e) In answering this question, assume that the change in the currency-deposit ratio described in (d) never happened. If the central bank buys 10 billion pesos worth of securities, calculate the percentage change in the monetary base and the percentage change in the money supply assuming that the currency-deposit ratio and the reserve-deposit ratio stay unchanged.

Solutions

Expert Solution

Answer 6:

Monetary Base=500 billion pesos.

Explanation: Given that the currency is 50 billion pesos and is 10% of monetary base. Monetary base is 10 times currency=10*50billion pesos.

Money supply=Currency+Deposits

where Deposits=4*Reserves.(Given that reserves are 25% of deposits)

Reserves=Monetary base-Currency=500 billion pesos-50 billion pesos=450 billion pesos.

Deposits=4*450 billion pesos=1800 billion pesos.

Money supply=50 billion pesos+1800 billion pesos=1850 billion pesos.

If required reserve ratio is 10%, then Bank's excess reserve=Actual reserve-Required reserve=450 billion pesos-(10%*1800 billion pesos)=450 billion pesos-180 billion pesos=270 billion pesos.

Present currency deposit ratio=50 billion pesos/1800 billion pesos*100=2.77%.

Currency deposit ratio after increase=2.77%+3%=5.77%.

Given that the monetary base and the reserve deposit ratio remains same,

Monetary base=Currency+Reserves=Currency+25% of deposits=500 billion pesos.

Currency/Deposits=5.77%. So, Deposits=Currency/5.77%

Currency+ 10%*Currency/5.77%=Currency[1+(25/5.77)] =500 billion pesos

Currency=500 billion pesos/[1+(25/5.77)]=94 billion pesos.

Deposit=Currency/5.77%=94 billion pesos/0.0577=1625 billion pesos.

Resulting money supply=94 billion pesos+1625 billion pesos=1719 billion peos.

Rahul Sunny answered 1 year ago

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