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I read the following explanation for debt deflation in my textbook:

To better understand how this decline in net worth occurs, consider what happens if a firm in 2018 has assets of 100 million (in 2018 dollars) and 90 million of long-term liabilities, so that it has 10 million in net worth (the difference between the value of assets and liabilities). If the price level falls by 10% in 2019, the real value of the liabilities would rise to 99 million in 2018 dollars, while the real value of the assets would likely remain unchanged at 100 million. The result would be that real net worth in 2018 dollars would fall from 10 million to 1 million (100 million minus $99 million)

I don't get how the fall in prices raises the real value of liabilities from 90 to 99 instead of 100 dollars because 90/price level = 90/(1-0.10) = 100. Could anyone clarify?

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Liabilities in 2018: \$90 million
Liabilities in 2019: \$90 million

Price level falls 10% from 2018 to 2019, implies 1 2019 dollar is worth 1.1 2018 dollars.
"exchange rate": 1.1 2018D/2019D

\$90 million 2019D * \$1.1 2018D/2019D = \$99 million 2018D

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As pointed out by James Wattam, it is possible to interpret

price level falls 10% in 2019

as $$ \frac{P_{2018}}{P_{2019}} = 100\% + 10\%. $$

I agree with you that the interpretation $$ \frac{P_{2019}}{P_{2018}} = 100\%-10\% $$ makes more sense. The question comes down to what the writer of the text considers the base year.

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