Difference between currency notes and coins

[Milan Gupta]

I was reading an article on the concept of Seigniorage. Segniorage is defined differently for coins and currency notes:

• For coins: Seigniorage is a tax that is added to the cost of the coin, which is then the price of the coin. For example if a Rs. 2 coin costs the govt. Re 1, then the difference of 1 rupee is the siegniorage.
• For currency notes: For currency notes the seigniorage is the difference between the interest on the securities bought in exchange of currency notes, and the cost of producing and distributing those notes. Suppose the government buys Rs.100 worth of securities-----exchanging currency notes for security. Suppose over one year, the government increases the money supply by Rs.10 for every 100 rupees in the market. This means that now, what was 100 rupees bought is is now bought by 110 rupees. 110 rupees of currency spent by the consumer buy security originally worth 100 rupees from the government. The government thereby earns a tax of 10 rupees at the cost of printing only notes of 10 rupees, when it buys back the currency(by selling the security). Increasing the money supply increases inflation, although it helps the govt. earn tax. Is this why seigniorage is called inflation tax?

One thing that these definitions indicate that the relation of coins and currency with respect to central bank are different. The central bank is under obligation to buy back the currency in exchange for securities, but no such obligation exists for coins. Is that correct? Also is my understanding of the concept of Seigniorage correct?

[Nishi Dixit]

In the above example, are we saying that Rs.10 is the segniorage? So is 110  the amount which includes the cost of producing and distributing these notes?

Also why doesn't the government handle the coins in the same way as the currency notes? 

[Milan Gupta]

If the cost of printing and distributing the new supply of Rs.10 is Re.1, then the seigniorage is 10-1=9 rupees.

I think the reason why coins are handled differently from currency notes is in their historical differences. Earlier the face value of the coin was equal to its material value---for example when gold used to be the currency. Because gold prices may increase over time, resulting in material value of coin being more than the face value of the coin, this may be misused by forgers who would melt the coin to extract its material value. This led the government to replace gold by a less valuable material, such that the face value of the coin was much greater than the material value. The difference between these two values is the tax or the seigniorage. So when you buy the coin you are paying for the material and the tax on it. But when you buy currency you are lending the government securities which you have a right to buy back any time, theoretically that is.