Tennis Serve Physics

On a kick serve, the racket meets the ball at high speed, with the ball literally sliding down on the racket strings for several inches before it leaves the racket. The strings themselves stretch for as much as an inch at the impact.

This is why there’s a ‘sleight-of-hand magic’ to the kick serve. The racket continues its path ‘beneath’ the ball, which at first has near-zero velocity; in slow motion, you can see that the racket head ‘moves ahead’ of the ball just immediately after impact. The server may get the feeling that he has caught the ball and is then ‘pulling the ball down’ as he continues with the serve’s follow through. (In fact, he has hit up on the ball, but with the racket on a circular path, which is why the follow-through is to the side, rather than forward.) The ball initially travels up and then arcs down because of gravity and spin.

All this happens because the body is sideways (not facing the net), and bent at the waist so that the swing path is left to right in relation to the body but ‘up and over’ in relation to an imaginary vertical line ending on the ground. The ‘up and over’ motion also reflects the ‘shoulder over shoulder’ rotation that creates the power for the serve.


From Popular Mechanics


Pancho Gonzalez’s serve on YouTube



Keynes, Macroeconomics, and Traffic

Orlando Roncesvalles (oroncesval4@gmail.com)

Back in 1936, a smart aleck named Keynes (John Maynard, or just Maynard) cooked up something he called The General Theory of Employment, Interest, and Money. He thought of unemployment as something to be solved, possibly in the same way that Albert (surname Einstein) thought “relativity” was the mystery to get fixated on. The parallels stop pretty much there despite the historical fact that failed mathematicians sought to infuse physics into economics, a project that took a long time to be discredited (not until 2008 anyway, when the Great Financial Crisis finally put paid to the misconception that physics and economics can mix, the latter having the muddle-like consistency of dirty motor oil and the former the empirical clarity of replicable experiments).

The genius of Keynes was in his insistence that the short run mattered more than the long run (when we would of course all have died). In that short run, slack in an economy (or unemployment) could be dealt with by public works. This idea was nothing new — even the Roman emperors knew that public spectacles kept people employed (even entertained). Keynes came up with the idea that in the short run, aggregate supply (or output, later standardized into GDP or gross domestic product) would have to adjust to what he called aggregate demand, whose components included consumption, investment, and government expenditure. Textbooks would later call this equality between aggregate demand and supply as “goods equilibrium.”

But Keynes then married the idea of goods equilibrium with something we might today call “asset equilibrium”— a situation wherein people are content to hold the quantity or amount of money in their pockets.

Asset equilibrium meant that peoples’ “liquidity preference” was satisfied through the movements of the interest rate as the price of credit and the opportunity cost of holding money. Money demand was driven by GDP and the interest rate, while money supply was a policy variable in the hands of the central bank. The equality of money demand with supply would be at the market-determined interest rate. Recognizing such an equilibrium was a way of bringing in the workings of the money and banking system into a fuller explanation of the gyrations of the business cycle. After all, the money markets determined interest rates, and these rates in turn drove business investment, which of course is a component of aggregate demand in the goods market.

The essence of Keynesian thinking was and remains the workhorse of macroeconomics (that specialty within economics that concerns itself with the short run determination of GDP and interest rates).

After Maynard, everyone then had a field day. The business-cycle savants focused on the confidence-based elements of aggregate demand (consumption and investment); the politicians latched on because government spending was their domain and Keynesian economics provided cover for influence and corruption; and the bankers were very much in on the act of determining interest rates. Macroeconomics caught on as the thing to know before one can say anything about the national or global economy.

It turns out that the apparatus of macroeconomics can be tweaked to help us understand the relationship between GDP and traffic.

Recently, a noted legislator reiterated the idea that prosperity (a growing GDP) was behind our traffic woes. I interpret what the legislator said to mean that without the heaven of a business boom, we wouldn’t have the hell of traffic. We should sit back and no more challenge him and his ilk to take public transportation because of course he already knew the answer: We are prosperous, so that we should just grin and bear it!

A critical but opposite view has nonetheless come forward. It is the idea that traffic is a brake on prosperity. The more severe the traffic, the less the GDP.

So, which is it? Is it a positive correlation between GDP and traffic? Or a negative one?

Keynes would likely scoff at the seeming contradiction. The negative correlation is the working of goods equilibrium if we realize that the severity of traffic negatively impacts aggregate demand. Bad traffic keeps consumers from traveling to malls, and smart businesses would likewise invest less if traffic drags down sales projections. Bad traffic kills GDP.

The positive correlation is something else. As GDP grows, the more we want to acquire transportation assets, such as cars and motorcycles. But in the short run, there is only so much roadway for all, and traffic problems arise.

The two disparate relationships – goods equilibrium and “traffic equilibrium” – are synthesized in the macroeconomics apparatus. Smart students will see that the thought experiment is the same as that of the infamous IS-LM apparatus of macroeconomics, where IS represents goods equilibrium and LM represents assets equilibrium; we now simply replace assets equilibrium with traffic equilibrium. Traffic equilibrium, by itself, reflects the positive influence of GDP on the severity of traffic problems, though it also suggests that the less the traffic, the more that people will demand transportation assets (this is the analog to the idea that the lower the interest rate, the more we would prefer liquidity or hold money).

What does all this mean? Can we now have a “clean” sorting out of the two disparate influences – the one of GDP on traffic and the other of traffic on GDP?

The answer is this. As an economy grows so of course does GDP. If the traffic infrastructure is left “as is,” traffic problems worsen, and governmental neglect is the culprit. This is because the traffic infrastructure (like monetary policy) is in the hands of the economic authorities. The infrastructure is in fact a public good. Still, the hapless citizens aren’t exactly helpless. They can move closer to where they work or work closer to where they live. They can drive less and consume less, and coincidentally lessen their carbon footprint. As a modern Marie Antoinette might say, let the travelers have their air-conditioned “me time.” Except that the peasants don’t eat cake or have their James (the proper name for chauffeurs of Rolls or Benz automobiles). Apparently there is no free lunch, and traffic is here to stay. Embrace it.

But if we were to solve the supply side of the transport asset equation, we reduce the severity of traffic, and the GDP boom continues or strengthens.

How to improve the traffic infrastructure is then the key. It is the magic but elusive password. Our legislators are perhaps simply not up to the challenge. Boot them, but don’t use the Denver boot. It won’t work because they’re too self-important. They’ve so far set things up so that they don’t suffer the inconvenience of public transport. Instead, they tell the ordinary citizen that it’s his fault because he enjoys a prosperous economy. Nuts.

That virus

by Orlando Roncesvalles, March 2020 (Letter from Dumaguete)

Extreme scenarios

The virus has us all riveted to our seats, watching the news, helplessly wondering what will happen next. Will we be “shut in” forcibly, as in China? Will we be more like Italy and Spain with draconian measures to keep almost all at home, not so much by force but by community efforts? Can we have something less drastic like Korea, where there is no lockdown but massive testing allows for infected people to be isolated early in the course of the epidemic? The answers are not easily found.

A thought experiment may point to how we might go about finding a reasonable approach. Suppose there were only two persons in an economy, and we cannot tell who is infected. But for sure, one of them is sick. If both go out and work, all get infected. Both die. And we have no more economy. This is the scenario if we did nothing at all to confront the virus.

If we don’t test, we can lockdown all at home, as we do now for Luzon. That effectively shuts down the economy. But at least the economy revives when a vaccine or cure is found. This means that lockdown is better than doing nothing. Lockdown at least keeps half the population alive while we wait for a vaccine or cure. Doing nothing is something like suicide, irreversible, or worse, a form of homicide.

For the duration of the virus problem, at least two policies have the same result of killing the economy. Again, we could achieve this by doing nothing at all, or by an absolute lockdown. However, the dichotomy here applies to the differing situations of Luzon and the rest of the country. Luzon is effectively on lockdown. The rest is still deciding what to do, which to some extent amounts to doing nothing (not yet anyway).

But doing nothing is not in the cards. We are neither that callous nor short-sighted, though perhaps early in the emergence of the disease there were officials who thought doing nothing was okay.

What else can be done?

If we test, we limit the economic damage to half. The healthy one goes to work; the sick stays at home.

If we’re unable or too poor to test, we could also “just take turns.” On odd days, one works; on even days, the other works. This also limits the damage to half of the economy.

This shows that the advantage of testing is not so large if somehow we can find a way to “take turns.” This requires a great deal of social cohesion because “taking turns” is pretty much the same as the much advised “social distancing” being promoted on the assumption that all are infected but asymptomatic. Still, no testing still means that half the economy is lost. What we really want is to limit the damage to much less.

And social distancing seems better than lockdown because the latter gives us a sense of helplessness, while the former at least calls upon us to go into a cooperative bayanihan spirit.

Admittedly, the above discussion is an extreme way of contrasting the various policies we might adopt. Still, doing nothing is “suicide”; the other — lockdown or social distancing — is “half a loaf.” Having said all that, can we get a better handle at “predicting” the near future?

Background facts on the epidemic

We summarize now what we think we know in terms of science and numbers. The key parameters are the rate of infection (called R) and the fatality rate (call this F).

R is defined as the average number of others that will be contaminated by an infected person. The important thing is that there is an initial number for R, known as Ro, which is the rate of infection that does not yet take into account policy or human interventions that would reduce R. Another important consideration is that so long as R>1, an epidemic outbreak will continue because the numbers of infected persons will continue to increase. Experts seem to think that Ro is 2.3; the actual R tends to fall, even if humans do nothing. This is just a mathematical thing. Once all are infected, R cannot go any higher. Any activity that breaks the infection chain, such as physical or social distancing, or a vaccine or cure, will cause R to decline. When R falls below 1, then the disease will sooner or later “peter out.”

F is the deadliness of the virus. The fatality rate is the probability that a person will die if he is infected. Various numbers have been given. WHO says it is 3.4%. In other words, an infected person has a 3.4% chance of dying from the virus (as opposed to other causes of death), though we also know that the number is an average. Young people have a lower F; so do women; so do healthier people. We might also think that F is a constant number. It is not. The experts say that F depends on whether the health care system is able to take care of the sick, through ventilators, intensive care, etc. F is higher for countries with fewer hospital beds (the Philippines ranks low in this regard, with one bed per thousamd of population, whereas advanced countries have something like 2-3 beds per thousand).

The important thing about F is that if we can “flatten the curve,” we reduce F. What does flattening the curve mean? The curve is the progression over time of infections. This depends on Ro and human interventions to reduce R. Thus, while F and R are different numbers, efforts to contain R also reduce F.

Two kinds of economic shocks

As an economist, I ask myself what economics has to offer to help solve the problem of the virus.

There is by now a consensus among economists that the virus is sufficiently problematic that they predict a major global economic recession. By historical standards, magnitudes of slowdown in global economic activity seen in 2008 (the Great Recession) seem to be applicable to the virus. Still, comparisons with the 1930s Great Depression, which was more severe, are not so far-fetched.

In the short run, economies are subject to supply and demand shocks.

A supply shock is something that disrupts the ability of firms to produce goods and services. The important thing about supply shocks is that there is little that public policy can do about it unless it was brought about by bad public policies to begin with. A freezing up of the banking system, which almost happened in 2008, is a supply shock that was partly solved by improvements in bank regulation. The supply shock of the virus arises when people get sick and can’t work, or if they’re on lockdown, or if social distancing reduces the productivity of workers. No one knows how large this supply shock is. In the mental experiment above, even if we did do something, the supply shock is a negative 50% as total output or GDP falls by half. The WHO estimate of F at 3.4% helps to set an upper bound on the size of the supply shock. If world population is lower by 3.4%, that’s a supply shock of that magnitude; but this is perhaps too high because not all are likely to be infected. But on the other hand, the supply shock can be higher because modern economies are specialized, and supply chains cut across several areas and countries affected by the virus. I would guess a supply shock of 5% to 7%.

But that’s not all. There is a demand shock that emerges when households recognize that their incomes are lower (through no fault of theirs) or when firms decide to invest less because they predict a bleaker economic outlook in the near future. The supply shock actually starts the demand shock going, but this is magnified by attempts of households to limit consumption in relation to income. Keynesian economists like to think of a multiplier on the demand side of 1.5 to 2. This means a fall in global output of 7% to 15% if governments did nothing on the economic front.

These shocks are mitigated by fiscal and monetary policies

The lessons from the Great Depression and the Great Recession are basically Keynesian. Governments have a duty to manage demand shocks, even if they can’t do much about supply shocks. A best-case scenario suggests that the demand shock is totally “absorbed.” The most common suggestions are “helicopter money,” or outright transfers to affected households. This is a combination of monetary and fiscal policies, since money has to be printed and the delivery of the money is through negative taxes, which typically require that governments go into debt. Under such a best case, the only thing that happens is the supply shock. That still means a global recession or decline in world output of 5% to 7%. This is, to emphasize, a best-guess scenario.

Guarded optimism

Forecasting isn’t a duty of economists, but we seem to demand that they do anyway. The easy way out is to pick a guess in between the worst and best cases. Governments impose a combination of testing, isolation, and lockdowns that reduce the supply shocks. They also enact fiscal and monetary policies that negate much of the demand shock. I would venture a guardedly optimistic forecast of global recession where output declines by 10%. Individual country experience will depend on how governments manage their policy responses to the demand shock.

Key lessons

What can be concluded? The cases of Korea and Singapore suggest that preparedness is important. This can limit the supply shocks in their economies, which nonetheless will be affected by what happens to their trading partners. This suggests that globalization has inherent risks that cannot be avoided when there are pandemics.

Regardless of how prepared a country is, social interventions matter. In the case of the virus, optimism is a public bad. It is better that people assume the worst (such as all are infected, if they’re not tested) and thereby voluntarily isolate themselves from each other. We know from the mental experiment that the worst case is when the infection rate is maintained by ignorance, and when this triggers an unanticipated demand on health care systems that increases the fatality rate.

In the interim, the deus ex machina is innovation. Malthus wrongly predicted doom because he did not foresee improvements in agricultural productivity. We can easily also predict doom if a vaccine or cure is not found; but we can hope that scientific breakthroughs would save the proverbial day.