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# Decoding the problem of currency denomination, in 6 charts

## With ₹2,000 notes being withdrawn from circulation nearly seven years after being launched, cash transactions for large amounts will need more banknotes than before

The ongoing withdrawal of 2,000 banknotes from circulation leaves 500 as the highest currency denomination in India. In the absence of a 1,000 note, large cash transactions are set to become the toughest they have been in decades as we will need more spacious (read thicker) wallets. Barring that inconvenience, the disruption to our lives is much smaller than the one seen when the note was introduced after the 2016 demonetization, because notes of 2,000 were just 10.8% of all notes in circulation by value as of 31 March. How do denominations work in other economies, and how does the 2,000 withdrawal change India's currency dynamics?

## ‘Note’ the diversity

India’s currency (both coins and notes) comes in 11 denominations—one “sub-unit" (50 paise), the “base unit" ( 1) and nine “super-units" (from 2 to 2,000). Some other economies use more denominations; some are much tighter. South Korea and Indonesia no longer have sub-units; the latter also has a 100,000-rupiah note (but that doesn’t mean a great deal of money, given the rupiah’s exchange rate).

## What’s the coin change problem?

It’s a classic algorithmic problem where math-heads try to find the minimum number of coins/notes needed to build a given amount. For example, to clock 4,926 with India’s current set of notes, you need at least 15 notes: 9 x 500 + 2 x 200 + 2 x 10 + 1 x 5 + 1 x 1. (Or give 5,000 and take back 74, but we haven’t taken that into account since that relies too much on your payee!)

## Pile up the notes

The 2,000 note wasn’t too popular, given its difficulty of use for small transactions. But in theory, the period of its existence was the most convenient to put together large amounts in the classic “coin change problem" of currency economics. If 500 becomes the biggest unit, the task gets tougher than ever before. Look at the second chart below: this will be the most difficult phase in recent decades if you want to make large payments with the fewest banknotes possible (and if you’ve not gone digital yet!).

## Giant denominations

The 2,000 note made up just 3.3% of all banknotes even in its launch year, and its share kept reducing. By value, it averaged 19.2% in the last five years. The erstwhile 1,000 note had much wider demand, as it made up 39% of value in March 2016. Japan uses its highest-denomination note (10,000 yen) more often than others (93% share in total notes in circulation). The US’ \$100 bill has a nearly 81% share in the total value. If all 2,000 notes are replaced by 500 notes, the latter becomes the biggest denomination, and its share in value will jump from 77% to 88%.

## Share in economy

At 12.7%, India's currency-in-circulation (CiC)-to-GDP ratio for 2022-23 is slightly down from 2021-22. The demonetization year saw the ratio slump to 8.7%, but recovered after that, peaking at 14.4% in 2020-21 as a result of increased demand for cash and a contraction in GDP. CiC is the cash or currency of a country that is physically available to conduct transactions between consumers and businesses. In India, it comprises three components: banknotes, coins and the new digital rupee (e- ).

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Published: 28 Jun 2023, 12:34 AM IST
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