Consider the following situation in the Canadian banking system: • The Bank of Canada purchases $5 million worth of government securities
From an investment dealer with a cheque drawn on the Bank of Canada.
• The dealer deposits this cheque at Bank XYZ,a commercial bank.
• The target reserve ratio for all commercial banks is 25%.
• All commercial banks operate with no excess reserves.
• There is no cash drain.
TABLE 26-4
Refer to Table 26-4.If Bank XYZ increases its loans to the maximum extent possible with its new excess reserves,the second-generation banks will be able to expand their loans by

Question

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When the Bank of Canada purchases government securities for $5 million and the cheque is deposited at Bank XYZ, the initial increase in reserves is $5 million. With a reserve ratio of 25%, Bank XYZ must keep $1.25 million (25% of $5 million) as reserves and can loan out the remaining $3.75 million. This $3.75 million, when deposited in second-generation banks, also faces a 25% reserve requirement, allowing these banks to loan out 75% of that amount. The process continues with each generation of banks lending out 75% of the funds deposited from the previous round of lending. This creates a geometric series with the sum given by the initial amount times the multiplier effect, where the multiplier is 1/(Reserve Ratio) = 1/0.25 = 4. The total increase in loans is the initial increase in loans ($3.75 million) times the multiplier (4) minus the initial loan amount, which equals $15 million - $3.75 million = $11.25 million. However, the question asks for the loans that second-generation banks can expand by, which is the initial loan amount of $3.75 million times 75% (since they can only loan out 75% of any new deposits they receive), which equals $2.81 million.

Consider the Following Situation in the Canadian Banking System: •