In the economy of Robberia, the monetary base is $2,000. People hold half of their money in the form of currency (and thus half as bank deposits). Banks hold a quarter of their deposits in reserve. If, in the face of this panic, the central bank wants to conduct an open-market operation to keep the money supply at its original level, does it buy or sell government bonds? Calculate, in dollars, how much central bank needs to transact. The central bank sells $ worth of bonds.

$500

Explanation:

Money supply at original level = [ currency deposit ratio + 1]* B / [ currency deposit ratio + reserve deposit ratio]  

currency deposit ratio = 1/2 = 0.5

reserve deposit ratio = 1/4 ( one quarter) = 0.25

Base ( B) = 2000

Money supply at original level = [ 0.5 + 1]*2000/ [0.5 + 0.25] = 4000

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To find the monetary base required to keep the money supply at its original level of $4000, substitute $4000 in the money supply equation and keep B variable

4000 = [new currency deposit ratio + 1]* B / [ new currency deposit ratio + reserve deposit ratio ]

4000 = [ 1+1]*B / [ 1+ 0.25]

4000 = 1.6B

B = 4000/1.6

B= 2500

Therefore the government should increase the monetary base by buying government bonds worth $500( = 2500-2000)