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"the PBoC said it would keep interest rates below the nominal GDP growth rate as a way of maintaining debt sustainability. But this only makes debt "sustainable" by implicitly allocating part of the debt-servicing cost to net savers (i.e. households)."

I read this on a Twitter thread. I don't understand it fully. Please explain this to me as if I am a 5 year old

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Annual revenue is the value of all that is sold in a year by a particular business. Nominal GDP in a year is the spending in the entire economy in a year. If a business' annual revenue, R, grows at the same rate as nominal GDP, then revenue increases by N * R where N is the rate of nominal GDP growth.

Thus deltaR = N * R.

Suppose the business is a borrower. Suppose the average business has debt, D equal to annual revenue. Thus D = R. There is no such thing as the average business and some businesses are much more indebted than others but just go with it.

From the foregoing, deltaR = N * D.

Suppose the cost of earning that incremental revenue is zero. This is unrealistic but it can be a real world approximation if you can get workers to "go the extra mile" without asking for anything in return other than making it a little more likely that they keep their jobs. Material input costs incurred to earn that incremental revenue are not realistically zero but suppose the business can find a way to stretch their materials.

If labour and materials can both be stretched in this way then all the incremental revenue can be incremental operating profit.

deltaO = deltaR

From the foregoing, deltaO = N * D.

Let i be the interest rate. So the debt grows by i*D each year.

Let deltaD = i * D.

If the Peoples' Bank of China keeps interest rate i less than N, then deltaD will be less than deltaO. This means the incremental operating profit is enough to cover incremental interest so that the debt does not grow. Thus the debt is sustained.

Households deposit money in banks to earn interest at a rate not the same as but related to i. If the PBoC suppresses i it is suppressing what households earn so it is as if the households are forced to sustain business debt.

Since there are certain assumptions in the foregoing, to the degree the assumptions are quantitatively misstated, it cannot be said that i < N is a threshold for debt sustainability so what the PBoC said is not much different from saying that it will suppress i to help businesses, but comparing i to the nominal GDP growth rate gives a clue about the PBoC's thinking.

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  • $\begingroup$ Thanks, that's very helpful $\endgroup$
    – qinnairen
    Jun 3, 2023 at 23:21
  • $\begingroup$ @qinnairen Please select my answer. $\endgroup$
    – H2ONaCl
    Jul 28, 2023 at 12:05

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