Problem? What Problem?

A mathematical problem should be difficult to entice us, yet not completely inaccessible. It should be a guidepost on the mazy paths to hidden truths. – David Hilbert

In a space-limited outdoor diner we visited a while ago, we observed the seating arrangement in A. They had two tables for two and ten for four. Seven of the four-place tables had parties of two. So, I wondered – is the setup they had the best for the crowd they faced?

A report I found (see below) noted that restaurant parties of two outnumber four-person parties by over two to one. On average, there should be more tables set up for couples than for larger groups.

But the average condition may not be the usual one. Or the one they faced.

What to do?

Suppose the four left-most tables were modular. The establishment could separate them into eight two-place setups. Then they could seat all seven of their two-person parties and put a two-top in storage. Their capacity would go down by two (at least temporarily), but, in the case shown, occupancy could go up by 30%, as we see in B.

Restaurants make money through occupancy, not capacity. It’s important to know what problem you need to solve.

#sales #demand #restaurants #business #success #management #problemsolving

Restaurant Math

“I was at this restaurant. The sign said ‘Breakfast Anytime.’ So I ordered French Toast in the Renaissance.”
Steven Wright

Forget about ordering off the menu; first, you have to get a seat. That’s not a given anymore.

It was never a slam dunk to get into our preferred local eatery. Once COVID-19 forced all patrons outside with social distancing, it was harder still. As we sat waiting for some seats for the third weekend in a row, we began to fidget. What to do? In an era where restrictions abound, sometimes it’s hard to see the options.

Happily, we knew the owner and every boss in the place. I pulled our most-beloved manager aside and asked her if she would be willing to rearrange the furniture and make more money. I explained to her that smaller parties were crowding out larger ones. Why not go from the arrangement you have (which was A) to one with several smaller tables (which became B), I asked? If you track the revenue changes, you’ll be pleasantly surprised.

As shown below, she did just that. Revenue went up by over 25%. Unlike A, Setup B recognizes they face a Demand Curve, with more parties of one or two people than groups of five or more.

#demand #demandanalysis #restaurant #restaurantmath #profits #revenue

A Sufficient Condition

For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled
Richard P. Feynman

Feynman’s observation about truth is one that can move past physics, where he won the Nobel prize.

It happens that in all markets, we collectively form relationships about how we respond to product features and prices. It is our Nature.

As we build, say, a helicopter for the President of the United States (A), we might be inclined to keep adding to it: unprecedented speed, a larger cabin, extra defensive systems. After all, we might tell ourselves; there won’t be a more important thing in the sky. It is a necessary condition to protect it and everyone inside.

The bonus features drive an increase in Value – and Price.
But at a group-induced limit we call the Demand Frontier, sales stop. We do not have any more monies to buy more of the product in question past the points on that line. Trying to exceed the Demand Frontier is a sufficient condition to stop any program.

In the case of the VH-71, USG requirements creep let it become untenable. All of that could have been avoided by analyzing the market as in B.

Doing a market analysis is hard.

Losing $4.2 billion is harder.

#innovation #demand #marketanalysis #business

 

Bounding Problems

In countless games, the parameters, once set, never vary. There are only a given number of spaces on the chessboard. American football always uses an elliptical spheroid built to strict specifications. All NBA basketball rims are the same diameter, ten feet in the air.

Markets seem different. They don’t have instruction manuals. At first glance, it would seem you could do anything you want in them.

Still, they have rules. Not understanding them can sink a project.

In addition to DeLorean not understanding the value of horsepower (see the last post), they also failed to appreciate the Demand Frontier they faced in 1981. As A shows us, DeLorean thought they could exceed that limit by nearly two standard deviations, despite no one else beating it by half that much.

In this and many other markets, Product Market Demand Curves form. Always flatter than the overall Demand Frontier they build, they describe the product price limits as quantities sold increase. These curves set boundaries producers must consider before they enter any market. Ignoring them can have disastrous consequences.

How do Product Market Demand Curves compare to their Learning Curves? Look to the next post for answers.

#markets #demand #pricing #boundary #innovation #business

Demand By Proxy

You can’t always get what you want…

Finding data can be hard. Say you needed to model demand for Japanese bullet train travel, or the London to Paris run. Ideally, both firms would post these figures, and you could reduce that to insight. While you can locate that information for NYC cab data (see one of my previous posts), you won’t for The Shinkansen or the Chunnel. What to do?

Let’s suppose train operators match the number of seats offered by class to their demand. Why wouldn’t they? If they had too many high-priced seats open, they’d either drop the price or change the seating arrangement. Eventually, they would come to a configuration that works most of the time.

Below, we see the number of seats by price for Japanese (A) and European (B) high-speed rail services. By themselves, neither has enough data to form a viable study. Together, in (C), they reveal collective thinking from different sides of the planet – and it’s much the same. Yes, that’s only two routes. More would be better. But this shows us we can gain an understanding of a market using the files we have instead of the ones we want.

…If you try sometimes, you just might find…you get what you need (Mick Jagger/Keith Richards).

#innovation #demand #markets #marketanalysis #strategy

Cannabis Laffer Curve Expanded:
The Netherlands Sparked North American Interest

In an earlier post, we examined the recreational pot tax structure.  Using US-only data, we discovered that at its frontier, a Laffer Curve formed that described the maximum amount of tax revenues possible given specific tax rates.

Here we entertain other authorities taxing legal recreational pot.  Added to the blue points forming a limit is another describing the tax rate and revenue per user for The Netherlands (NL) in 2008 (adjusted for inflation).  Through these blue points, the Laffer Curve explains 90% of their variation and is highly negative (power exponent -1.61).

Also considered now but not part of the Laffer Curve is the recent experience of British Columbia (BL 2019).  Observe it registered minuscule tax revenues.

At least 3 factors influence cannabis tax receipts: 1) Ease of legal access: BC, OR, and CA lag far behind their better-organized counterparts in making legal recreational marijuana sufficiently available.  2) Tax rate: From 15.3% (NV 2019) to 108% (WA 2014), revenues go up as tax percentages go down.  3) The proximity of lower-cost options: some would-be CA or CA tourist receipts or go to NV or black markets.

#laffercurve #market #marketanalysis #price #taxpolicy #demand #tax

Missing Price Targets

Businesses frequently set price goals. What does it mean not to hit them?

In A, we predict 1, the price of a barrel of oil. When the forecast date arises, the actual price, 2, varies, resulting in a one-dimension Error Line. We know by how much we missed, but nothing else.

B shows us what it means to be off-target in archery. If we aim at 1 and land on 2, we create an Error Triangle. That’s a two-dimensional error, in elevation (up and down) and azimuth (left to right).

In C, where every blue diamond stands for a business jet, we propose a new one. We set our target quantity and price, as 1, on the Demand Frontier, the line through the market’s outermost quantity-price points, in yellow. If we can’t put in enough features to support that price, we’d make a plane fetching less money, as 2. Moving from 1 to 2, we make a Demand Error Triangle.

But, in D, we find as prices fall, we might be able to sell more models. Analysts should find the Demand Frontier Slope to ascertain the amount of revenue available at market limits. That will be the areas under the curves, the green rectangle for 1, the orange one for 2.

What does it mean to miss price targets in Value Space? Find out in my next post.

#prices #demand #demandplanning #demandforecasting

Real Demand Curves In Action

The rock star Meatloaf tells us that “Two out of three ain’t bad.”

But, when it comes to, say, selling your new supersonic jet, it can be.

One can adequately estimate a product’s Cost and Value (as a sustainable price for the first business jet to go over 1,000 miles per hour) only run afoul of its market’s Demand Frontier.

Below, we find Aerion offers a credible development Cost target for its supersonic AS2 (see A), and offline there is evidence its $120 million Price works for the market. Their problem lies with Demand. They forecast a market of 500 models, with 300 in a decade. But in the ten years studied in B, their forecast exceeded the limit of the Upper Demand Frontier (P-Value 4.91E-04). Five years later, in C, the Demand Frontier (P-Value 5.39E-05) shifted only slightly. As of January 2020, the company still only has the 20 orders they received in 2015. Currently, its chances of selling 300 units at $120 million in a decade are less than 25%.

COVID-19 or other forces may increase business jet demand, moving the Demand Frontier where Aerion would like it to be.

Failing that, the company likely got Cost and Price right, but missed Demand.

In business, two out of three is bad.

#demand #demandforecasting #marketanalysis #prices

What Supports Currency Prices?

Several factors determine the price of any given country’s currency.  A 4D analysis helps you visualize those influences.  Here, we examine what held up those values on July 12, 2019.

As the red Demand Plane shows us, as the amount of currency issued increases, its price generally falls.

We can (and, in this case, must – we can’t get a functional equation without it) use this influence with others to predict sustainable currency prices in USD.  In the left Value Space, the plane running through the data indicates currency value goes up with added Foreign Exchange Reserves and down with Volume.  The P-Value for this equation is 3.30E-12.  The chance it accidentally predicts the data is that low.

The case manifests The Law Of Value And Demand, which states:

  1. Features determine Value
  2. Value affects Price
  3. Price influences Quantity sold and
  4. Quantity sold is a feature.

The equation explaining the plane in Value Space uses the Prime Rate, set to 2%.  What happens if we set the Prime Rate to 63%?  Check the next post for the answer.

#demand #currency #prices #markets #currencytrading

Cryptocurrency Demand Shift

We’ve all heard about a shift in demand.  Not all of us see it in action.  With a dynamic market, we can.  The one for cryptocurrencies fits the bill.

Last August, the top 100 cryptocurrencies had quantities and prices indicated by the white circles in the figure.  Those with a red dot in the center of them formed their red Demand Frontier as of August 1, 2019 (with a P-Value, the chance this equation came about by chance, of 1.28E-04).

Then things changed.

On Friday, March 20, 2020, 94 cryptocurrencies (we lost some), with blue squares for their quantities and prices, reflecting a downward and inward shift in demand.  Each of the Demand Frontier points shifted down (the corralled ordered pairs), except for Tether (which grew slightly) and Ripple (which went down and in).  The result was a shift in the cryptocurrency Demand Frontier to the one in blue, which is steeper (the slope was -1.47, is -1.57) and more highly correlated (R2 was 92.6%, is 96.8%, with P-Value falling to 9.92E-06).  Though the log scaling tends to disguise it, the market lost over 40% of its market capitalization.

What holds up currency prices?  We’ll look at that next time.

#cryptocurrencies #bitcoin #currency #crypto #cryptocurrency #demand