Universal Basic Income: Indexation and Inflation

Question

Let’s assume a monthly Universal Basic Income (UBI) payment of \$1,000 and an annual inflation rate of 2%. I would like to understand what would happen to the real value of this UBI (its purchasing power) in terms of year-zero prices each year for say 20 years. Namely, how much the original \$1,000 worth after 5,10, and 20 years? This is the link to a google spreadsheet - I hope that I did the calculations right.

My questions are: How to calculate the real value of the UBI in each year in terms of year-zero prices if there is NO INDEXATION? Obviously, the real value must decrease due to inflation, but I would like to see what is left from the original purchasing power of $1,000 in years-zero every year for 20 years.

This is what I have done in the Excel file attached:

The Column “Real Value” represents the purchasing power of the nominal (NOT indexed) UBI of 1,000 dollars. Is it correct?

The Column “Inflated Value” represents the INDEXED UBI, namely the UBI than would maintain the real purchasing power of the original $1,000 despite inflation. It is correct?

If the calculations are correct, why then the loss to inflation is lower (and decreasing) than the amount of yearly compensation by indexation which is also increasing? What is the logic and intuition behind this?

Thanks a lot!

Answer 1

Your real value column is wrong, but only slightly. You are decreasing it by 2% per year, but inflation of 2% doesn't cause real value to decrease by quite 2%. If there is 2% inflation, real value doesn't decrease by 2%; it decreases by 1 - 1/1.02 which is approximately 1.961% .

This is just the way percentages work. Since they are multiplicative, the inverse is different in magnitude:

• If you lose 80% of an investment you have to gain 400% to break even.
• If you lose 50% of an investment you have to gain 100% to break even.
• If you lose 20% of an investment you have to gain 25% to break even.
• If you lose about 1.961% of an investment you have to gain 2% to break even.

If you change your real value formula to =F6/(1+$F$4) you will get the correct values. You can also calculate the real value column by just calculating what portion of the buying power is left (1000/H26) and multiplying it by the nominal value: =1000*1000/H26. Both methods will give you the same result.

Answer 2

I don’t entirely follow what you are asking. The answer appears straightforward, and does not need a spreadsheet.

• If there is no indexation, the real value drops in value by the inflation rate (2%/year). Divide through by $\frac{1}{(1.02)^n}$ to get real value in year n.
• If indexed, the payment grows at the rate of inflation, and the real value is constant.

The only technical issue is that in the real world, indexation is done with a lag, and there are deviations in real value if the inflation rate is not constant.