Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 1)

So by now I’m sure you’ve heard about the semiconductor shortage of 2021. For a few complicated reasons, demand is greater than supply, and not everybody who wants to buy integrated circuits can do so. Today we’re going to try to answer some hard questions:

• Why are we in the middle of a semiconductor shortage?
• Why is it taking so long to get my [insert part number here]?
• Did this shortage suddenly sneak up on everybody? If not, what were the signs, and why weren’t we able to prevent it?
• Who or what is to blame?
• Is it really a shortage of all semiconductors, or is there a specific kind of semiconductor in short supply?
• Why is this semiconductor shortage different from all other semiconductor shortages?
• What kind of steps can we take to avoid a semiconductor shortage again? Or are we just doomed to this kind of pain and suffering in the future?

I say “try to answer” because it’s a tough situation to understand, because semiconductor manufacturers are somewhat secretive, and because, quite honestly, the general news media isn’t helping to enlighten us much. Oh, sure, there’s a locust-plague of articles stating that there is a shortage, or that it should be over soon, or maybe in mid-2022, or not until 2023, or that company X is handling the shortage better than company Y, or that company X should have known better, or companies X and Y are never going to let this happen again, or that the government wants to fix the shortage, or that it’s that… that… you know, we have supply chain problems. Supply chain. Yes. And company X took a \$234 million charge this quarter because of the shortage. But insight about how we really got into this mess? Hmmm. I just don’t see a lot of good media coverage, beyond a few needles in the haystack that I’ll point out. The usual attempts at an explanation involve some variation of “Trade war then COVID, so auto manufacturers cancel orders, but now everyone is working from home and then bitcoin mining and container ships, so oops now we can’t buy anything and by the way fabs are expensive.” — with some glitzy stock photos of integrated circuits being made, or integrated circuits on a printed circuit board. The better articles are the ones that talk about 200mm vs. 300mm wafers at the foundries, or refer to “mature process nodes”. Well then… and you expect me to provide some answers? I’m just a guy writing a blog in my spare time; I can’t even afford the stock photos. But let’s see what we can do.

Prologue: The chip shortage is so bad.... (HOW BAD IS IT?)

As I write this, it seems so hard to summarize the situation and get across how bad it is this year, without engaging in cliché — “it’s a perfect storm!” — or hyperbole of the sort you find in movies, like 1984’s Ghostbusters:

VENKMAN: …or you could accept the fact that this city is headed for a disaster of biblical proportions.

MAYOR: What do you mean, “biblical”?

STANTZ: What he means is Old Testament, Mr. Mayor. Real Wrath-of-God type stuff!

VENKMAN: Exactly.

STANTZ: Fire and brimstone coming down from the skies! Rivers and seas boiling!

SPENGLER: 40 years of darkness! Earthquakes, volcanoes!

ZEDDEMORE: The dead rising from the grave!

VENKMAN: Human sacrifice, dogs and cats living together, mass hysteria!

Instead, we’ll just have to turn to hard facts. The biggest symptom in the news this year is probably the announcements from automotive manufacturers that they have suspended production lines or otherwise reduced production due to shortages of semiconductors. We’re not talking about one company; we’re talking about practically all of them:

• BMW
• Daimler
• Ford
• General Motors
• Honda
• Hyundai-Kia
• Jaguar Land Rover
• Renault - Nissan - Mitsubishi
• Stellantis (= Chrysler/Fiat/Peugeot/etc., in case you’ve slept through the last few years)
• Tesla
• Toyota
• Volkswagen

It’s so bad that in mid-November, General Motors announced that it would be removing heated seats as a option from many of its vehicles, along with heated steering wheels. GM later backpedaled a bit and salvaged some good news: within a week, the automaker said that a retrofit was possible for the heated seats, and by December 3 had announced a similar retrofit for heated steering wheels. As the Detroit Free Press put it:

General Motors pulled a multimillion-dollar rabbit out of its hat Friday, telling its dealers it has figured out a way to resume offering two popular features on its vehicles. The move could keep some of Cadillac, Chevrolet, Buick and GMC’s most loyal and affluent buyers from defecting to other automakers.

Starting in the first half of 2022, the automaker’s dealers will be able to activate heated and ventilated front seats on vehicles built without the features due to a shortage of the computer chips that control them.

Now hang on… let’s just wait for that to sink in. Heated seats.

Forget for a moment about whether seat warmers are a necessity, or that they are apparently the most desired optional feature, according to the market research firm AutoPacific — instead, think about the circuit elements that are needed for today’s heated seats. You’d need a heating element (resistor) and a thermistor (NTC resistor) as a temperature-sensing safety mechanism to avoid burns, and a power switch to connect the resistor across the 12V DC bus, and probably a microcontroller to check the thermistor temperature and control the power switch. In days of yore before microcontrollers, this would just have been a relay and thermostat, or maybe some analog circuitry, but nowadays it makes sense to add a microcontroller to reduce the wiring harness costs: send the 12V bus and a LIN bus everywhere, maybe a 5V or 3.3V control power line too, and you no longer have to send zillions of wires in an expensive-to-build-and-replace bundle around the auto chassis. OK, so we’re probably — and I’m just guessing here — talking about a MOSFET and a shortage of some microcontroller with an analog input for the thermistor(s) and a LIN transceiver and a couple of digital I/O pins and that’s about it. It’s hard to find out much tangible information about GM’s heated seat control modules beyond some general DIY troubleshooting schematics. Teardowns for iPods, yes; teardowns for automotive electronics modules, no, not interesting enough. And there are probably dozens of different microcontrollers that could be substituted for the one that was presumably in short supply.

But here we are, things got so dire that GM announced it might not be able to provide heated seats.

We had a hint of this sort of crisis ten years ago, during the Fukushima earthquake in March 2011, which the New York Times proclaimed as a “Stress Test for the Global Supply Chain”; DRAM prices rose a bit in the first half of 2011, but the bigger issue was the presence of pinch points in the supply chain for wafers and specialty semiconductors from Japanese manufacturers. (No worries! Renesas brought its Naka plant back online in only three months! How bad could it be?) Then in October 2011, floods hit southern Thailand and shut down a big chunk of the world’s production of hard drives, leading to a shortage that drove up prices.

This year’s semiconductor crisis is much worse, and is prevalent throughout the world, instead of a localized issue that affected one particular region.

Another data point, this one closer to the electrical engineer’s perspective, has to do with lead times. Suppose you’re on the team that’s designing the Magic Happy Mobile Blender and you want to buy some parts from Digi-Key. If Digi-Key has some inventory in stock for some prototyping… well, that’s great! They have 372 of the op-amps you want in stock, and you only need 20, so you place an order and two days later they’re on your desk. Later you need more of them, for a 2000-piece build, but now they’re out of stock. You check to see when they’ll have more… and it looks like it’ll be another 12 weeks. That’s the lead time. Moral of the story: you can’t just expect to buy electronic components whenever you feel like it. Purchasers in the field of electronics have to prepare in advance and take lead times into account when planning for product builds.

I seem to remember typical lead times for semiconductors were in the 8-16 week range, maybe a little more for certain manufacturers (looking at you, Maxim Integrated and Linear Technology)… and sometimes they crept up a little higher in a hot business cycle. This year, however, lead times have skyrocketed, and it’s common to see more than 26 weeks. Some cases in point:

Yikes!

Supply Chain Games for the Impatient

So how did we get here? I’m going to take a roundabout tour of the economics of semiconductors and the dynamics of supply chains to show you, in my own way. If you’re looking for a quick answer, this article isn’t for you. But there are some good articles on the subject:

• BBC, “Why is there a chip shortage?”
• The Conversation, “How the world ran out of semiconductors”
• CNET, “The chip shortage is boosting US manufacturing: What you need to know”
• Electronic Design, “The Global Chip Shortage, Explained” (click on the slide show to read more of the article)
• Forbes, Willy Shih’s “Toilet Paper Surplus, Ketchup And Semiconductor Chip Shortages — Supply Chain Forecasting Is Hard”
• Forbes, Willy Shih’s “About That White House Meeting To Discuss The Semiconductor Supply Chain”
• The Verge, “Why the Global Chip Shortage Is Making It So Hard to Buy a PS5 (Interview with Willy Shih)”
• CNBC, “The global chip shortage will probably hit your everyday life” (Beyond the Valley Podcast, interview with Peter Hanbury)
• Fusion Worldwide, “The Global Chip Shortage: A Timeline of Unfortunate Events”
• Wall Street Journal, “How Car Makers Collided With a Global Chip Shortage”
• Wired, “Why the Chip Shortage Drags On and On… and On”

Here’s my two minute summary, if you really want one:

• As of early 2020, there were several factors that influenced the reduction of manufacturing output in the semiconductor industry, most notably COVID-19 — but also a considerable decline in semiconductor sales in 2019 and poor worldwide automotive demand in 2018-2019, both amid US-China trade wars.

• COVID-19 was a major catalyst of the chip shortage, but it wasn’t an underlying cause any more than Gavrilo Princip caused the First World War, or Mrs. O’Leary’s cow caused the Great Chicago Fire of 1871. In the case of COVID-19, there was a widespread fear of economic calamity, followed by a surge in stay-at-home demand:

  • Early 2020 started expectations of a second poor year of semiconductor sales after 2019: for example, IC Insights revised its economic forecast downward in April 2020.

  • The automotive industry was in a rather dire situation, to say the least. The consulting firm Accenture published a glossy presentation in April 2020 titled “Impact on the Automotive Industry: Navigating the Human and Business Impact of COVID-19” quoting an IHS Markit forecast of another 12% sales drop from 2019, and citing the fact that automotive OEMs had median operating cash to support two months of operating expenses. (Accenture summarized their answer to this crisis as an alliterative easy-to-remember slogan: Respond, Reset, Renew!)

  • Fear drives corporations to be conservative, and take steps to ride out a possible economic catastrophe. Perhaps the best example in 2020 was that rental car companies were so desperate to avoid going out of business, that they sold large portions of their fleets. Semiconductor companies have to decide how much product to manufacture based on demand forecasts, which at the time were conservative. Fortune Magazine cited an automotive expert who claimed the drop in European automotive demand would persist for ten years. Automotive OEMs, amid the COVID situation and dismal sales forecasts, canceled orders.

  • Economic stimulus packages were crafted, in the United States and internationally.

  • All of a sudden people had some more money to spend, and no place to go. Oh, and they needed more computers to work from home. And things to entertain themselves. As Paul Krugman put it in a July 2021 New York Times column:

    So why are we facing a semiconductor shortage? Part of the answer is that the pandemic created a weird business cycle. People couldn’t go out to eat, so they remodeled their kitchens, and they couldn’t go to the gym, so they bought Pelotons. So demand for services is still depressed, while demand for goods has soared. And as I said, practically every physical good now has a chip in it.

  • Sudden, unexpected increases in demand for consumer electronics, and the chips inside them, outpaced the industry’s ability to ramp back up production, and the automotive OEMs had to get back in line and compete for scarce supply. In early December 2020, Volkswagen and Germany-based suppliers Continental AG and Bosch were forecasting capacity problems based on a lack of available chips. By February, the chip shortage was mainstream news.

  And here we are, with crazy lead times everywhere. Is that a satisfying explanation? Probably not — after all, why is it taking so long? It’s been over a year since Reuters broke the VW/Continental/Bosch story, and still supply is scarce enough that GM can’t deliver heated seats.

  Just keep repeating this to yourself: COVID was the catalyst, not the cause. COVID was the catalyst, not the cause....

• To make matters slightly worse, the semiconductor industry saw a few other minor regional crises:

  • a Nittobo Group factory fire in Fukushima, Japan disrupted the supply of glass fiber material to manufacturers of Ajinomoto Build-up Film. (If this doesn’t make much sense to you, you’re not alone; it’s a component used as a substrate in IC packages with high-density I/O, like microprocessors. Chip manufacturing requires a lot more than just silicon.)

  • a fire damaged the Asahi Kasei Microdevices fab in Nobeoka, Japan.

  • Renesas’s Naka fab — the same one that was rebuilt after the 2011 Fukushima earthquake — got shutdown twice in 2021: first for about a week by an earthquake and then a few weeks later by a fire that broke out in the factory.

  • a winter storm in Texas overloaded the state’s power grid, forcing fab shutdowns at Samsung, NXP and Infineon.

  The list goes on; you can read for yourself, while you keep repeating: The catalyst, not the cause… the catalyst, not the cause… Hi ho the derry-o, the catalyst, not the cause.... These sorts of events do happen, and in a normal year we might hardly notice, but in a dire shortage, every bit of bad news becomes part of the slings and arrows of outrageous fortune.

• Many articles refer to “the chip shortage”, as though it is one monolithic phenomenon; when it is really a group of shortages happening in different market segments. (SNV’s policy brief, “Understanding the global chip shortages” is one of a few publications that gets this right.)

• Semiconductor manufacturing is subject to numerous, inherent production delays. It takes months to build a new manufacturing plant or re-equip an old plant. It takes weeks to manufacture and package the chips themselves. In normal times you aren’t aware of these delays, because — like the memory caches in your computer or mobile phone which speed up access to information — supply chain inventory acts as a reservoir for short-term demand. Unfortunately, large transient imbalances between supply and demand can exceed the capacity of inventory and lead to lengthy shortages or surpluses.

• One consequence of the lengthy delays of semiconductor supply chain is that it becomes vulnerable to the bullwhip effect, which can amplify demand uncertainty from downstream customers, and make it very difficult for manufacturers to respond quickly to situations like the automotive chip shortage.

• Portions of the semiconductor market (notably automotive ICs and microcontrollers) are manufactured on so-called “mature nodes” in older 200mm wafer fabs, that have been running low on spare capacity for several years prior to COVID-19, and despite the occasional warning in a trade journal, and some increases in capacity, the 200mm capacity shortage still exists.

  But why do we have the “mature node” problem, anyway, and what should we do about it? The economics of semiconductor manufacturing is just weird. Totally bizarre. As I’ve been researching this article, I feel like I’ve fallen down the rabbit hole, and every time I think I can wrap my head around how it works, I run across some new curve ball. There are economic and engineering reasons that new chips are being designed today on 10- or 20-year old fabrication processes — but it’s hard to wrap it up in a quick sound bite.

That’s the short answer (aside from this last point), and if that’s enough for you, by all means, stop here. Otherwise, buckle your seatbelts and get ready for a ride through the craziness.

I feel like we need some mood music here, maybe some Velvet Underground. If you listen very carefully, you might be able to hear Lou Reed arch an eyebrow. And mayyyyyybe you’re reading this as a plain old consumer, and continue to wait — perhaps even patiently — while the rest of us in Semiconductor-land sort this one out....

There are problems in these times
But ooh! none of them are mine
Oh baby, I’m beginning to see the light

Disclaimers

A few disclaimers before we start:

I am not an economist. I am also not directly involved in the semiconductor manufacturing process. So take my “wisdom” with a grain of salt. I have made reasonable attempts to understand some of the nuances of the semiconductor industry that are relevant to the situation, but I expect that understanding is imperfect. At any rate, I would appreciate any feedback to correct errors in this series of articles.

Though I work for Microchip Technology, Inc. as an application engineer, the views and opinions expressed in this article are my own and are not representative of my employer. Furthermore, although from time to time I do have some exposure to internal financial and operations details of a semiconductor manufacturer, that exposure is minimal and outside my normal job responsibilities, and I have taken great care in this article not to reveal what little proprietary business information I do know. Any specific financial or strategic information I mention about Microchip in these articles is specifically cited from public financial statements or press releases.

Okay, here we go!

Supply Chain Games, 2020: Good Toilet Paper Is Hard To Find, and Hoarders Are To Blame

Anyone remember this?

I took this picture on March 25, 2020. It was notable because it was the first time in a couple of weeks that I had seen anything other than empty shelves in the toilet paper aisle of the grocery store, and I had to pause just to make sure I was seeing anything there at all. Admittedly, the only toilet paper available that day was a small 4-roll single-ply store brand, and the store was limiting sales to two packages per person. Very frustrating. Where were all the missing rolls going? Hoarders!

“I heard about it on the news,” said Mrs. Paul McCoy of Houston, “so I bought an extra 15 rolls.”

In Seattle, one store owner, ordered an extra 21 cases of toilet paper. When he received only three cases, he became worried and rationed his supply. That prompted more buying, even at increased prices.

When Mrs. Clare Clark of Jenkintown, Pa., gave a party, guests asked what they could bring. “I told them toilet paper,” she said.

Oh, wait — that’s not from 2020; that was from the Great Shortage of Toilet Paper of 1974. This was an odd little quirk of history that had started in late 1973, but really took off only after Johnny Carson mentioned it on The Tonight Show.

And it was a shortage that need never have been. For the toilet paper shortage was a rumor run wild in a nation that has recently become geared to expect shortages in items considered absolute necessities.

Dozens of interviews seeking to reconstruct this latest shortage have uncovered what seems to be a developing “shortage psychology,” almost an eagerness among many Americans to anticipate the next shortage. Such an attitude, brought on by shortages of gasoline, electricity and, for a time, even onions, seems to assure no future shortage of shortage rumors.

Fears of a possible bathroom tissue shortage, which continue in some areas as the result of abnormal buying and hoarding, seem to have sprouted last November, when news agencies carried articles about a shortage in Japan.

In early March 2020 we had more toilet paper hoarding, after COVID-19 cases began spreading across the world. News articles began trying to explain the psychology behind hoarding.

Several countries have already imposed mass quarantines. People buying up toilet paper and other household supplies may be preparing for the same thing in their city, said Baruch Fischhoff, a psychologist and professor in the Department of Engineering and Public Policy and the Institute for Politics and Strategy at Carnegie Mellon University

“Unless people have seen… official promises that everyone will be taken care of, they are left to guess at the probability of needing the extra toilet paper, sooner rather than later,” he told CNN. “The fact that there are no official promises might increase those probabilities.”

Other articles covered personality studies of those most prone to hoarding:

When the researchers analyzed their data, they found that people were more likely to hoard if they were especially frightened by COVID-19. They also were likely to stockpile if they scored high in emotionality — that is, they tended to be more fearful, anxious, dependent and sentimental — and/or high in conscientiousness — folks who are organized, diligent, perfectionistic and prudent.

And while the study only focused on toilet paper purchases, stockpiling likely wasn’t limited to that, Toppe said in an email. “From our point of view, it seems plausible that our pattern of results — more threat goes along with more stockpiling — exists for other commodities,” he said.

This behavior caused us to run out of toilet paper, the media told us — despite the fact that, according to another article, production was fairly normal:

A majority of the industry’s manufacturing facilities are located in remote areas with low population densities, meaning employees are less likely to transmit the virus, miss work and cause production delays. In fact, all toilet paper manufacturing facilities in the U.S. are currently fully operational.

However, because grocery stores and other retailers usually only keep several weeks’ worth of toilet paper in their warehouses, the sudden increase in demand — largely fueled by panic-buying and hoarding — has quickly depleted stocks.

“Consumers are experiencing nervousness and they are buying more than they should, depleting inventories of an industry that is very lean,” Gonzalez said. “It will take a couple of weeks for people to understand they have enough, and the inventories will increase on the shelves.”

We did get back to normal, eventually… but hoarding wasn’t the only issue — at least that’s what some experts stated. The assertion was that with so many people working from home, they would need to use additional toilet paper that they would ordinarily be getting from their work environment:

Another reason for the sudden increase in demand is that people actually do need more toilet paper during the pandemic. The hygiene paper industry is divided into two markets: consumer (the kind of toilet paper you use at home) and commercial (bulky rolls of thin paper that you find in public restrooms, offices, restaurants and hospitals).

With people staying at home because of business closings and shelter-in-place orders, the demand for consumer toilet paper has skyrocketed while the demand for commercial toilet paper has decreased.

Data from Georgia-Pacific, maker of the Angel Soft and Quilted Northern brands, shows that the average American household — 2.6 people — uses about 409 rolls of toilet paper a year. The company estimates that people will use about 40% more toilet paper than usual if they spend all their time at home during the pandemic.

But why couldn’t the suppliers just make more consumer toilet paper to respond to this crisis? It would take time for the supply chain to catch up to this demand:

In theory, some of the mills that make commercial toilet paper could try to redirect some of that supply to the consumer market. People desperate for toilet paper probably wouldn’t turn up their noses at it. But the industry can’t just flip a switch. Shifting to retail channels would require new relationships and contracts between suppliers, distributors, and stores; different formats for packaging and shipping; new trucking routes — all for a bulky product with lean profit margins.

Because toilet paper is high volume but low value, the industry runs on extreme efficiency, with mills built to work at full capacity around the clock even in normal times. That works only because demand is typically so steady. If toilet paper manufacturers spend a bunch of money now to refocus on the retail channel, they’ll face the same problem in reverse once people head back to work again.

“The normal distribution system is like a well-orchestrated ballet,” said Willy Shih, a professor at Harvard Business School. “If you make a delivery to a Walmart distribution center, they give you a half-hour window, and your truck has to show up then.” The changes wrought by the coronavirus, he said, “have thrown the whole thing out of balance, and everything has to readjust.”

Aha, there’s Willy Shih’s name popping up again. He’s a great writer on this topic of supply chains, making the subject very accessible to the nontechnical reader, and had his own article in early March 2020 in Forbes, about the toilet paper shortage, when it had first hit some of the Far East countries and Australia in advance of the crisis in the US.

The second important characteristic of this market is that demand is stable. It is not seasonal, and consumption should be roughly in line with the population and shouldn’t vary that much. As a consequence, manufacturers optimize their supply chains with these assumptions. I was talking to an alumnus and former student of mine last summer. She was the buyer for paper products at a large regional grocery chain, and we got to talking about the velocity with which paper products, and toilet paper specifically, moved through their distribution centers. She was amazed at the volume that moved through every day, but it was a well-oiled system designed for stable demand.

So what happens when shoppers scoop up all that toilet paper and hoard it? It sends a demand signal through the supply chain to produce more. If producers do ramp up capacity (which is hard to do instantaneously), they might eventually send more product into the distribution channel. Meanwhile, as the crisis passes, consumers can then burn off their “pantry inventory” — and that burn down will take time, depressing demand for an extended period. This of course will lead to overstock in the stores, and signals to cut production. In our operations management class at HBS, we teach this as the bullwhip effect.

Will this actually happen in the toilet paper supply chain? I’m actually guardedly optimistic because producers know that demand is stable year-over-year, and that this is a temporary spike. If I were a plant manager, it would take a lot of convincing for me to add manufacturing capacity right now. The best thing to do is to put retailers on allocation, who would likely limit purchases so that shoppers can’t buy themselves a five year supply anymore, at least until this crisis passes.

Professor Shih is right on the money here. And to some extent, you can substitute “semiconductors” for “toilet paper”; the same patterns occur. I am not sure, however, that all of what he says is self-evident, or if the implications of it sink in. So we’ll come back to some of the business-school assertions about the supply chain later. Let’s rewind a few decades.

Supply Chain Games, 1983: What Supply Chain?

If you attended public school in the United States in the 1980s, chances were very high that your school had a computer lab with Apple II computers, and you played Oregon Trail and Lemonade Stand at some point. Lemonade Stand was an economics game where you sold lemonade in the town of — wait for it… — Lemonsville. Each day you were greeted by the bleeping and tweeting noises of the weather forecast: a few bars of Gershwin’s Summertime for hot and dry weather, or a shrill version of the pastoral Call to the Cows section of Rossini’s William Tell Overture for sunny weather. Once the day began, you had to figure out how many glasses of lemonade to sell, at what price, and how many advertising signs to buy. Then at the end of the day the computer told you how many glasses of lemonade you sold. Maybe you made a few dollars profit. Then the process repeated, day after day — at least until there was a thunderstorm that destroyed everything, or until the other kids in your class got impatient and it was their turn.

If you have not had this experience — well, I’m sorry; anyway, now you can just play Lemonade Stand in an in-browser emulator to see for yourself.

There was some variation in the weather (hot and dry, sunny, or cloudy with a chance of thunderstorms) and occasionally the street department was working with the result that you lost traffic, but otherwise your sales was a deterministic function of price and advertising. Your cost of goods was initially 2 cents a glass, but after a few days it stabilized at 5 cents a glass; advertising signs were 15 cents each, and could boost sales, with diminishing returns: sales approached double their advertising-less figures with infinitely many signs. So it was possible to optimize the price after a lot of experimentation — or if you stopped the game and deciphered the source code. Here’s what the demand curves looked like for sunny days:

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

import math

def lemonade_sales(signs, price, weather):
    p9 = 10.0 # optimal price in most cases
    s3 = 0.15 # price per sign
    s2 = 30   # some base number of glasses?
    c9 = 0.5  # scaling factor?
    c2 = 1    # another scaling factor?
    g  = 1    # normally 1, except 0 in thunderstorms
    if price >= p9:
        n1 = (p9**2)*s2 / (price**2)
    else:
        n1 = (p9 - price)/p9 * 0.8 * s2 + s2
    w = -signs * c9
    v = 1 - math.exp(w) * c2
    if weather == 'sunny':
        r1 = 1
    elif weather == 'hot':
        r1 = 2
    elif weather == 'cloudy':
        r1 = 0.3
    else:
        raise ValueError('weather must be sunny, hot, or cloudy')
    n2 = r1 * (n1 + (n1 * v))
    return int(n2 * g)
    
price = np.arange(5,15.1)
signs = np.arange(0,5.1)
sales = np.array([[lemonade_sales(s,p,'sunny') for s in signs] for p in price])
profit = ((sales.T * (price - 5)).T - signs*15) * 0.01

fig = plt.figure(figsize=(7,9))
axes = [fig.add_subplot(2,1,k+1) for k in range(2)]
ax=axes[0]
ax.plot(price, sales,'.-')
ax.set_ylabel('Demand (glasses)')

ax=axes[1]
ax.plot(price, profit, '.-')
ax.set_ylabel('Net profit (dollars)')

for ax in axes:
    ax.set_xlim(5,15)
    ax.set_xticks(price)
    ax.set_xlabel('Price (cents)')
    ax.legend(['signs=%d' % s for s in signs],
             loc='best', labelspacing=0)

print ("Max profit = $%.2f" % profit.max())

Max profit = $2.20

Like most real-world demand curves, demand decreases monotonically with increasing price — which makes sense; why would I be more likely to buy something if the price goes up? — so although you might be able to sell more glasses at lower cost, or get more profit per glass at higher cost, neither extreme gets you very far, and there’s a sweet spot in the middle.

Profit shown here assumes that you prepare exactly the number of glasses to meet demand, based on a devious and careful analysis of the math: the upshot is that you maximize profits on sunny days at \$2.20 if you buy three signs and set the price at 10 cents a glass.

The rules of Lemonade Stand are fairly primitive and do not permit or include any of the following factors that might be more realistic:

• indefinite expansion, forming an empire of lemonade franchises (suck it up: instead, the best you can do is to earn the lofty sum of \$2.20 on sunny days and \$5.00 on hot and dry days)
• the possibility of other competing lemonade stands
• desperately thirsty customers willing to pay more when supplies are low
• any kind of variation over time (maybe there are passing fads for Zima or Irn-Bru instead? Or tax credits for young entrepreneurs?)
• dependence of customer behavior on your past history
• labor costs
• shortages in ingredients

Oh, well, it’s only a simple game that exposes kids to the excitement of entrepreneurship — at least it did, at a time when smartphones and the World Wide Web were nonexistent, and all the other competing forms of electronic entertainment were based on 8-bit processors with limited graphics.

Wrapup

What, that’s it?! Toilet paper and a 40-year-old lemonade stand game? How is that going to help? There are some takeaways here:

• Games can be an effective method of learning how systems work. The traditional approaches of teaching economic concepts involve graphs or equations — both of which can provide abstract descriptions of a demand curve — or static case studies. Games allow the player to experience behavior directly, in an interactive setting. Yes, even the Lemonade Stand game. People let down their guard with games — you might just learn something, even if you don’t realize it! — whereas mathematics sometimes makes people put barriers in front of their own brains. Whoever thought that Angry Birds would be teaching millions about the physics of projectile motion? (Shhh! Don’t tell anybody!) The experiential aspect of games can complement traditional learning.

  

• Demand curves are monotonically decreasing. Lower the cost of something, and sales are likely to go up.

• Consumers and producers interact via pricing and sales. Yes, it’s possible for a group of people to walk into a store and tell the owner, “Five of us will each buy one of these things at a price of \$7.50, but if you drop the price to \$6.00, ten of us will buy them.” But rather unlikely: regular people are probably just going to buy or not buy or shop around, rather than giving details of their demand curves; and sometimes what people say they’re going to do doesn’t match their actual behavior. Large corporate purchases can be just as vague. At any rate, consumer purchasing is influenced by price, and producers adjust their prices and production levels based on purchasing patterns to maximize their profits, so we have a feedback loop even if no one says anything.

• Toilet paper underwent a supply disruption when large numbers of consumers started working from home. Demand moved from commercial-grade to consumer-grade toilet paper, which come from different supplies. The supply chain takes time to react.

• Increasing inventory is a common reaction to supply uncertainty. In other words: people hoard more when they fear they may not be able to get something. This exacerbates supply shortages, because of an artificial demand increase.

We covered a number of reasons that the chip shortages started in late 2020 — the catalyst, not the cause… the catalyst, not the cause — most notably the demand shocks of COVID-19 first reducing sales, and then increasing sales of consumer electronics as millions of people adapted to working from home, leaving automotive suppliers in a tight spot, as they had to compete for scarce supply. The semiconductor industry has long inherent lead times that are obscured normally by inventory caches throughout the supply chain, just as in the case of toilet paper.

Given sufficient capacity, this supply-demand imbalance will work its way out of the system. But there’s the rub: right now there still isn’t sufficient capacity for some chips, and there are a few nuances in the semiconductor market that make this situation somewhat interesting. One important aspect is that the market has more than one segment — and different types of ICs are manufactured on different equipment (again, like the toilet paper situation) so there is really a group of shortages rather than just one, and they will likely have different durations and severities.

We’ll talk about some of those nuances in Part 2, as we take a look more closely at the semiconductor industry, starting with a “retro” view, and then with another game that can help us understand some of the challenges of being a producer in a dynamically-changing market.

In the meantime, here’s wishing you all a Happy New Year!

© 2021 Jason M. Sachs, all rights reserved.