The R0 value, or the reproduction number, is a key statistic recorded for contagious diseases. In Layman’s terms, it is the number of individuals that each diseased will infect during their sickness. The total number of cases with each generation can double with an R0 of just 2.
So, with an estimated R0 of up to 18, measles can really be quite a handful.
This is exponential growth, and can just as easily become exponential decay when the R0 falls below 1. Without paying close attention, the changing outputs of an exponential function can catch you by surprise.
For the same reason that exponential growth can turn a contagious disease into a global crisis, it is gifting graduates with unassailable debt while turning shrewd investors into millionaires. I followed the data and observed three reasons why you should care about the R0 and exponential growth.
University degrees, by definition, provide education. Perhaps more importantly though, they are a signal to employers of quality – that the graduate is a valuable good in the market for labour. Depending on the course, the university and the employer themselves, this stamp of approval can be of varying standards.
Unfortunately, in the United Kingdom, this stamp does not come cheaply.
The nuances of interest accumulation and debt repayment on tuition loans is complicated at best and at worst, well, it hurts the brain. Simplified, it is £9250 per year (e.g. for three years), where interest accrues at between the RPI and the RPI + 3%, depending on your earnings. Graduates on plan 2 loans only begin to repay this loan at 9% of annual earnings above £26575.
Much of this is simply lots of words that make your ears bleed and the tears start rolling – at least mine do anyway. Yet those yearly percentages mean one thing and one thing only, exponential growth.
The R0 of the amount to be repaid is only between 1.024 and 1.054 (based on current UK RPI of 2.4), yet starting at almost £30000 means annual interest is significant from the start. In our chart, only those with the highest salaries manage to pay off their tuition loan, and no one who earns less than £50000 per year manage to ever pay more back than the interest accrued.
Worse, a graduate who earns between £31-60k over the 30 years will pay almost as much as those with slightly higher salaries, yet still have almost £30000 of student debt.
As their degree has not provided those with the lowest salaries with much added value, they pay back less, if any at all. However, exponential growth here highlights the dangers of being someone in that middle bracket, paying back the most in this current system.
My £60000 of student debt is looking scarier by the minute.
Exponential growth is perhaps one of the greatest driving forces in the economy. Investment yields, economic growth, inflation – each of these measured in % growth due to the power of exponentials. Take the United Kingdom’s current inflation rate of 1.94%. In other words, the price of goods and services in the UK economy effectively has an annual R0 of 1.0194.
It only takes one look at the changing share value of Apple Inc. to know that it is exponential growth that facilitates the wealth of businesses and individuals.
Not everyone can invest in Apple during its infancy, however. At least no one can anymore.
Instead, ISAs and other fixed rate investment schemes provide a stable mechanism of investing money over long periods of time. This is where relevance to the reproduction number is most prominent. 9 times out of 10 you will effectively be told the R0 before you even sign up.
This is the interest rate. Just as with R0, the effects of different interest rates are profound. Investing in an account with a 10% interest rate compounded monthly compared to one with a 2% interest rate will provide almost 13 times as much returns over 20 years.
The earlier the money is invested, the more the rewards of exponential growth you will reap. With a 10% interest rate, more money is accrued in the final 6 years than in the entire first 14.
In 1965, when even my parents were little and computers enormous, the CEO of Intel predicted that the number of components per integrated unit would double each year. Whilst growth like this is unpredictable, Gordon Moore recognised early the power exponential growth had in technological innovation.
He may have missed the mark slightly, but computing power has still doubled every 18 months since 1975.
It almost feels alien to me coming from Generation Z, but there was a time 15 years ago that mobile phones were getting smaller. Functionality was still low so the size of the mobile was optimised for portability. This was Moore’s Law acting exponentially. Moore’s Law means your laptop is getting thinner, your computing is getting faster and television manufacturers are running out of characters to put in front of 4K Ultra-HD.
This pattern may be predicted to slow, but for 50 years it has dragged human society forward.
Exponentials are important. I hope that has been made abundantly clear. We can see from tuition loans that even the slightest deviation above 1 has significant impacts on everyday people.
The same goes in a pandemic. We must act responsibly to ensure R0 remains below 1, else the second wave will be upon us before we know it.
Sources: Wikipedia, gov.uk, macrotrends