Let’s start with a little riddle. Milton is earning $20 an hour and pizzas cost $20, so Milton can buy one pizza for an hour of his time. Milton has worked for an hour and earned $20 but isn’t hungry right now. However, his friend Paul is hungry and offered to pay Milton 5 percent interest on a $20 pizza loan. How much interest will Milton earn when the loan comes due?
Should Paul pay Milton $21? That would be $20 for the principal and $1 for the interest. If there was no inflation and no innovation, Milton would earn 5 percent interest.
But what if inflation has increased the pizza price to $22? If Paul paid back $21, instead of earning 5 percent, Milton would be losing 4.5 percent. If money is purchasing power, shouldn’t Paul pay Milton $23.10? That would be $22 to replace the purchasing power and $1.10 for the interest.
Economists try to make the distinction between the nominal interest rate and the “real” interest rate with the following identity equation:
Nominal interest rate = Real interest rate + Rate of inflation
What if Milton bought the pizza and then loaned the pizza to Paul? Shouldn’t Paul pay back one pizza plus an additional 5 percent slice to cover the interest? (This is what my Muslim friends in Saudi Arabia do to avoid the forbidden “haram” of interest.)
But what if innovation has reduced the price to only $18? Would it be fair for Paul to pay Milton $21? If Paul paid back $21, wouldn’t he really be paying 16.7 percent interest instead of 5 percent ($3 divided by $18)? Shouldn’t Paul pay back $18.90? That would be $18 to replace the purchasing power and $0.90 for the interest.
Note that an economy can experience both inflation and innovation at the same time. Growth in monetary inflation can be offset by innovation. Calculating rates of return should take into consideration many things, including the purchasing power of time; the opportunity cost of that purchasing power when it has been converted to money; monetary inflation; and innovation. Interest rates should reflect both inflation and innovation. Therefore, a more descriptive equation should be:
Nominal interest rate = Real interest rate + Rate of inflation – Rate of innovation
The Time Value of Knowledge
We can measure innovation with time. We buy things with money, but we pay for them with our time. This means there are two prices: money prices and time prices. Money prices are expressed in dollars and cents while time prices are expressed in hours and minutes. Converting a money price to a time price is simple. Divide the money price of a product or service by hourly income, as with Milton’s pizza time price. The time price of pizza decreases if Milton’s income increases, or the money price decreases.
As long as hourly income is increasing faster than money prices, the time price will be decreasing. Time prices are an elegant and intuitive way to measure how much knowledge we are adding to an economy. It is the change in the time price over time that reveals the growth of knowledge and allows us to measure innovation and account for change in purchasing power per hour. Increases in innovation correspond to decreases in time prices. While it is good to think in dollars and cents, it can be much more valuable to think in hours and minutes.
Negative Nominal Interest Rates
Recognizing that nominal interest rates contain both inflation and innovation elements also explains why we could have negative nominal interest rates. If the real interest rate is 3 percent, and inflation is 4 percent, but innovation is 10 percent, the nominal interest rate would be negative 3 percent.