THE TUPY-POOLEY FRAMEWORK
MEASURING THE GROWTH OF KNOWLEDGE WITH TIME

How can we measure whether resources are getting more abundant or less abundant? Historically, many people have done so by estimating the quantity of a resource, such as crude oil, and dividing that estimate by the rate of consumption of that resource. If known reserves of a resource grew at a slower rate than the consumption rate, statisticians could predict the time when a resource were to run out. Or so they thought. This kind of a measurement has to be faulty, for despite millennia of economic activity and hundreds of years of observations and prognostications, humanity has never run out of a single nonrenewable resource. Don’t believe us? Try to think of one.

There are many reasons why the measurement of quantities does not yield expected results. First, quantities are often not directly observable. We really have no idea how much oil and gas, for example, we have. That’s because we do not have the know-how to measure the total supply of any given resource on the planet in a cost-effective way. Second, there is a large range of quality, grades, and concentration levels of resources. That makes the costs of discovery, extraction, and refinement of resources highly subjective. Third, because it is so expensive to perform surveys of resource reserves, those surveys usually end up having little or no value. To give an example, after more than a century of the intensive use of fossil fuels, we have more known deposits today of oil and gas than ever before. Fourth, we often don’t know where to look for resources. Although survey technology is improving, the location of new deposits often come as a surprise. Fifth, quantities do not account for substitutes and recycling. History suggests that many substitutes for current resources and ways to recycle those resources are yet to be discovered. Sixth, we can’t predict future discoveries of new deposits of resources and improved extractive technologies that may increase the supply of resources. Seventh, surveyors of resources face asymmetrical costs. If they overestimate resource reserves, companies lose money in a very visible way. If surveyors underestimate resource reserves, exploration does not take place, and the cost to companies is invisible. Finally, the surveyors may also want to underestimate resource reserves to increase their budgets and, consequently, their status.

Prices, we believe, are a much better way of ascertaining the relative abundance or scarcity of resources. If prices go up, resources are getting scarcer. If they go down, they are getting more abundant. Where do prices come from? In a free economy, nobody sets prices. They emerge spontaneously through the revealed preferences of individual buyers and sellers. Every time you buy a cup of coffee on the way to work, for example, you incrementally increase the price of coffee beans. Every time you fail to buy your usual morning cup of coffee, you decrease the price of coffee beans by a tiny amount. If everyone stopped buying coffee, the price of coffee beans would collapse. The movement of prices informs both producers and owners of capital about the goods and services that ought to be produced (cars and smartphones) and goods and services that ought to be discontinued (horse-drawn carriages and the telegraph). So the market is a mechanism (or, really, a process) for the gathering and exchange of information. Individual decisions made by billions of buyers and sellers generate useful knowledge that ensures the relatively smooth functioning of an economy (no permanent shortages of desired goods or permanent stockpiles of undesired goods) and the continued generation of wealth.

However, note that there are different kinds of prices. The simplest kind of price is the “nominal,” or current price, which you see in the shop when you buy a loaf of bread or fill up your car at the gas station. A more sophisticated, or “real” kind of price, is adjusted for inflation, which accounts for the well-known fact that in the era of fiat currency or government-issued currency, the dollars in your pocket get less valuable every year (i.e., the government tends to print more money than is necessary, thereby lowering the value of the currency relative to the total amount of goods and services in the economy). The real price, therefore, subtracts from the nominal price the rate of inflation, thus making it possible to compare prices or abundance of resources across time. What’s missing from both kinds of prices is the amount of dollars in your wallet. How often have you heard your grandparents complain that a gallon of gas cost 50 cents and a loaf of bread 5 cents “back in the good old days”? “True, Grandma and Grandad,” ought to be your response, “but what happened to your incomes over your working lives?”

Typically, though not always, individual incomes increase at a higher rate than inflation. That’s because people tend to grow more productive (i.e., they use new knowledge or inventions to generate more value per input, such as an hour of work, an acre of land, and amount of capital available) over their lifetimes and across time. Just think of the economic output or productivity of a worker with a shovel versus that of a driver of a giant excavator. It is that productivity growth that has resulted in our incomes today being much higher than that of our grandparents (adjusted for inflation, the real median personal income in the United States rose from $25,326 in 1974 to $35,805 in 2020). To correct for the problem of the missing wage increases, we have come up with the concept of “time prices.” Whereas nominal and real prices are measured in dollars and cents, time prices are measured in hours and minutes. To calculate a time price, all you need to do is to divide the nominal price of a good or service by your nominal hourly income. That tells you how long you must work to afford something. So long as your nominal hourly income increases at a faster pace than nominal prices do, goods and services get more abundant.

There are at least four reasons why time prices are better at measuring abundance than money prices. First, as mentioned, time prices contain more information than money prices do. Since new knowledge, which is to say innovation or productivity, both lowers prices and increases wages, time prices more fully capture the benefits of that new knowledge. To just look at prices, without also looking at wages, only tells half of the story. Time prices make it easier to see the whole picture. Second, time prices transcend the complications associated with converting nominal prices to real prices. They avoid subjective and disputed adjustments such as the consumer price index (CPI), the GDP deflator, and the purchasing power parity (PPP). Time prices use the nominal price and the nominal hourly income at each point in time, so inflation adjustments are not necessary. Third, time prices can be calculated for any product in any currency at any time and in any place. That means you can compare the time price of bread in France in 1850 to the time price of bread in New York in 2022. Fourth, time is an objective and universal constant. The International System of Units has established seven key metrics, six of which are bounded in one way or another by the passage of time. As the only irreducible element in the universe, time cannot be inflated or counterfeited. With 24 hours in a day, everyone has perfect equality of time. These four reasons make using time prices superior to using money prices for measuring resource abundance. Time prices are elegant, intuitive, and simple. They are the true prices we pay for the things that we buy in life.

Our analytical framework was inspired by the works of the late University of Maryland economist Julian Simon, Stanford University’s Hoover Institution economist Thomas Sowell, and the American bestselling author and economist George Gilder. Simon was a rigorous empiricist who found that, in the long run, resource prices declined; he postulated that the ultimate resource is the minds of free-thinking people. Sowell argued that economic growth is not about the quantity of atoms, which are finite, but about the increase in human knowledge, which is infinite. As he put it, “The cavemen had the same natural resources at their disposal as we have today, and the difference between their standard of living and ours is a difference between the knowledge they could bring to bear on those resources and the knowledge used today.” Finally, Gilder offers three propositions: wealth is knowledge, growth is learning, and money is time. From these propositions we derived a theorem, which states that the growth in knowledge can and should be measured with time. This measurement can be performed at individual and global levels. Let us show you how.

The Framework