Metropolis National Bank is holding 2% of its deposits as excess reserves. Assume that no banks in the economy want to maintain holdings of excess reserves and that people only hold deposits and no currency. The Fed makes open market purchases of $10,000. The person who sold bonds to the Fed deposits all the funds in Metropolis National Bank. If the bank now loans out all its excess reserves, by how much will the money supply increase

Increase in money supply = $200,000

Explanation:

Note: The given question is incomplete, missing part is as follow:

                    Metropolis National Bank

                            Balance sheet

Assets                                              Liabilities

Reserves     $60,000                Deposits          $500,000

Loans           $440,000                                                          

Computation:

Excess reserve hold = 2% × Deposits  

Excess reserve hold = 2% × $500,000

Excess reserve hold = $10,000

Required reserve =  Reserves - Excess reserve hold

Required reserve = $60,000 - $10,000

Required reserve = $50,000

So,

Required reserve ratio = [$50,000 / $500,000]100 = 10%

Multiplier(K) = 1 / Required reserve ratio

Multiplier(K) = 1 / 10%

Multiplier(K) = 10

Total Money = Person deposit +  Excess reserve hold

Total Money = $10,000 + $10,000

Total Money = $20,000

Increase in money supply = Total Money × Multiplier(K)

Increase in money supply = $20,000 × 10

Increase in money supply = $200,000

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