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Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
ISBN: 9781337091985

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BuyFindarrow_forward

Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
ISBN: 9781337091985
Textbook Problem

Bank A has a leverage ratio of 10, while Bank B has a leverage ratio of 20. Similar losses on bank loans at the two banks cause the value of their assets to fall by 7 percent. Which bank shows a larger change in bank capital? Does either bank remain solvent? Explain.

To determine

The leverage ratio and the asset of the bank.

Explanation

The leverage ratio is the ratio of the bank’s total assets to the total capital of the bank. When the total assets of the bank decline by a given percentage, it will have the leverage ratio multiple times impact on the value of the capital of the bank. That is, the value of the capital of the bank declines by the percentage decline multiplied with the leverage ratio.

It is given that the decline in the value of the bank’s assets is by 7 percentages and the leverage ratio of bank A is 10 and that of bank B is 20. Thus, the decline in the capital of the banks can be calculated by multiplying the leverage ratio of each bank with the percentage decline, in order to calculate the percentage decline in the total capital of the bank as follows:

Decline in the total capitalBank A =Leverage ratioBank A×Percentage decline in asset=10×7=70

Thus, there will be a 70 percent decline in the total capital of bank A

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