Fuzzy little things that I find interesting.

Political musings from someone who thinks the S-D curve is more important to politics than politicians.

“These violent delights have violent ends.”

I’m convinced the most creative visual story telling is now talking place for Television, not movies. Movies have gotten themselves in a blockbuster rut, and while there are some very good movies out there (Doctor Strange comes to mind), the have to be, in a very real way, predictable, structured carefully, and ultimately like very good roller coaster rides: unique, but doing more or less the same thing.

Television, on the other hand, has become a far more creative outlet exploring interesting themes and ideas, unpredictable, and interesting.

And one of the best examples of this is the HBO series Westworld..

Which begs one of the most scariest questions I’ve heard contemplated in a very long time:

Which is scarier: a computer which passes the Turing Test?

Or a computer smart enough to lie and deliberately fail the Turing Test?

Comments on the supply/demand curve.

Generally when I read a discussion of the supply and demand curve I see something that goes like this:

If we plot price and quantity, supply is this vague curve sloping upwards, demand is this vague curve sloping downwards, and at some point where they meet that intersection point is the balance where supply and demand meet.

The thing that has always bothered me about this representation, however, is that the curves representing supply and demand are always these vague representations, arbitrarily drawn on the chalkboard. There is never an effort to quantify what those curves should look like before we launch into discussions of things like increasing demand for lower-priced goods or what happens when price controls are put into place.

But we can quantify these things to some extent.

In all of the graphs below, I preserve the convention of price along the Y axis and quantity along the X axis, so some of this may seem “sideways.”

First, let’s look at the demand curve.

Let’s suppose we’re selling a thing, and people want one of these things. The question we ask of that population of people is “how much should that thing cost?”

Of course the question is a complex one, but to first order we may expect that overall the answer to that question becomes a bell curve centered around the most expected price for that thing:

Bell Curve

Again, note the convention: price is along the Y axis, quantity is along the X axis. This is a bell curve centered around the price B with about 1/3rd of B being the standard deviation in the price people are willing to pay. The equation representing this curve is given by:

Bell Curve Equation

The demand curve would then be the integral from +∞ to y; that is, as the price declines more people buy–and the total amount of product sold would be the area under the curve from price y to infinity.

Demand Curve

(I’ve scaled the X axis to fit in our graph.)

What this graph represents is what we intuitively already know: that as the price gets cheaper–as we drop down on the Y axis–the amount of product we can sell–that is, the number of people who are willing to buy our product–increases. But also notice a few features at the extreme ends of the curve: there is a point where we won’t sell very much product at all: if our product is priced way out of our audience’s reach, dropping the price a little bit just won’t move stuff off the shelves. And at the other extreme, if we’ve reached market saturation, dropping our price more just won’t move more product–because we’ve reached market saturation.

The equation for this curve is given by:


Where the function erf is the error function.

Now let’s add the supply curve. We can use a similar argument as with the demand curve: if we have a whole bunch of suppliers and they believe they can bring in a price at a given price point, our supply bell curve looks very similar to the demand curve. However, the number of people who are willing to sell at a given price winds up being the integral above, except from -∞ to y. Plotting this on our graph:


There are some interesting things to note here.

First, let’s suppose that our suppliers are able to bring the cost of production down. We get the classic plot showing the supply curve shifting to stimulate demand:

Supply Stimulus

As prices fall because suppliers determine a cheaper way to make their products, demand rises, and in this case they rise considerably.

But, as was noted before, if we are at either extreme: if, for example, we’ve reached market saturation, then the curve simply does not bend that much. We’ve reached saturation–and the incremental effort to sell to the remaining few who haven’t purchased a product can be rather considerable.

The same thing happens at the other end of the curve: if a product is just too far out of the price range of the vast majority of people, dropping the price a little bit just isn’t going to move the needle. You’re not going to sell a lot more $300,000 Ferraris if you drop the price to $290,000.

We can also use this graph to describe price ceilings and price floors.

Suppose, for example, we’re describing raising minimum wages. In this case, “supply” are the workers who are willing to work a given job at a given price, and “demand” is the willingness of employers to employ people at a given price.

So what happens at a given minimum wage?

Well, that depends on if the minimum wage is raised above the natural price given by the supply/demand curve.

Suppose our proposed minimum wage is below the crossing point of our supply and demand curves:


Then our price floor–minimum wage–doesn’t affect things very much at all. If currently workers for a given job are being paid more than the proposed floor, everyone’s going to ignore that floor because already prevailing wages are above the floor.

This is, in fact, the situation in most areas of software development: for me personally you could raise minimum wage to $30/hour and it won’t make a significant impact on my own take-home pay. (It may make some change, because remember: the above graph really represents a narrow slice of the supply/demand curve in a particular profession for a particular market. And as the minimum wage is raised, the shape of the overall market changes, which then affects people’s budgets and that may make them reallocate where they spend money–just as if a sudden sale on steak may make you rethink buying chicken.)

It’s not to say that at this level the minimum wage doesn’t serve a useful social function. In fact, it does: there are undoubtedly employers who are assholes who are trying to convince people to work for nothing–and a minimum wage floor gives those employees another legal tool to prevent abuse. This social function, however, is not really relevant to the economic discussion.

Now, on the other hand, suppose the price floor is raised above the natural supply/demand curve. (I’ve taken the liberty to label the supply and demand curves for what they represent: the willingness of employers to hire at a given wage verses the willingness of people to work at a given wage.)


What happens is simple: as wages go up, more people want to make money at that given wage. However, as wages go up, employers are less likely to want to hire at that wage. And that leads to a gap–a gap between the number of people who want to work and the number of employers willing to hire.

And that is, by definition, unemployment.

Similar arguments can be said about price floors and price ceilings in other economic arenas. For example, the long lines and rationing that had to take place in the 1970’s during the gas shortage came from the government imposing price ceilings. A ceiling then creates a gap between the amount of stuff someone can sell, and the amount of stuff people want to buy–which creates shortages:


And people react to shortages by being willing to stand in long lines; the line becomes an added “price” people are willing to pay.

Now let’s do something completely different.

Suppose I’m a company which makes widgets. I mass manufacture those widgets.

Mass manufacturing is interesting in that it entails a setup cost and a per-product cost. Meaning that, for example, if I’m making chairs using plastic injected moulding, then I have to pay a large setup cost to set up the mould, and then I pay a per-chair charge for the plastic for each chair.

That is, the total price it costs me to make n chairs is:


where n is the number of chairs I’m making, s is my setup cost (such as the cost of the mould), and c is the per-chair cost (such as the cost of the plastic).

Now if I make x chairs and sell them at a price y, this means that I have xy amount of money to make chairs. Subtract out the setup price s, divide by the per-chair cost and this gives me the number of chairs I can make at a given price:


We can solve for the quantity x and the price y to give me the number of chairs I am, as a manufacturer, able to sell at a given price:


Plugging our final formula into our graph for given values of s and c, and we get a completely different curve than we’re used to seeing when drawing supply/demand curves:


Note that our supply curve, instead of sloping upwards from lower-left to upper-right, instead, curves downwards; as we ship more product we can lower our per-product price.

And notice our supply curve intersects our demand curve in two places–at a high price/low quantity point, and at a low price/high quantity point.

In many ways this models very well something many manufacturers do, when they take a high-price premium “luxury” item (at the upper-left) and move it downstream towards the low-price mass-produced point (at the lower-right). As the setup charge pays for itself in the luxury market arena, it becomes easier to then make the product in larger quantities for the mass market arena by reusing the same mould or jigs or manufacturing tools, and cranking the assembly line wide open for the mass market.

Of course, the problem with consumers is that if you sell too many luxury items as mass-manufactured items, it becomes tougher to sell upscale products.

You can tackle this problem one of two ways: either (a) through branding (by having a luxury brand and a mass-manufactured brand, such as Toyota and Lexus), or (b) by simply deciding to sell all your products at the upper-left corner (as Bang-Olufsen does) or the lower-right corner of the curve (as Apple does).

Now we can also use this to explain why certain technologies suddenly “appear”; that is, we can easily describe what happens when some technology waiting in the wings suddenly explodes on the scene:

Suppose we have a new technology, and our setup costs are high and our per-item charge is high–because it’s an all new technology. Perhaps tinkerers play with the technology or it’s something that floats around in the labs–but to get it out there would cost a lot of money.

Then we may see a supply curve that looks like this:


Note the curves never cross.

At no price point does the supply curve ever cross the demand curve, because the item simply cannot be made at a price that anyone would want it at.

This is far different than the traditional supply/demand curve we looked at where we model the supply of something as a gaussian curve; that gaussian assumed a large number of suppliers who could supply a good, and a few could create a handful of items at a high price point.


Using the old supply/demand curve, what happens when the price drops a little bit is what we would expect:


We get a tiny gain in the population willing to buy a product.

But if we use our equation describing the actual manufacturing costs we don’t just get an incremental number of adopters buying a luxury product. Instead, for a small drop in manufacturing price we get an explosion of demand:


This explains how we went from just a handful of mobile smart phones in 2006 to nearly everyone carrying an iPhone less than a decade later. As manufacturing costs dropped, it intersected the demand curve–and suddenly we went to a world were nearly everyone had one. And it wasn’t like the price to manufacture smart phones radically dropped in order to stimulate demand, as would be suggested if we used the traditional supply curve.

I really don’t have a point to all of the above, except to note that some rather interesting things come out of the traditional supply/demand curve if you attempt to actually model what the supply curve actually looks like and what the demand curve actually looks like, rather than just gesturing at the chalk board and drawing an upward and downward sloping line.

I’m sure if a more generalized treatment of the demand curve was done–for example, if we have a population where half are willing to jump on at one price, and the other at a second price, we’d see some other interesting things jump out of the graph. Just as I’m sure if we could model the additional dimensions behind the supply/demand curve, such as the different values different employees have for a corporation, or we could model businesses which use loss leaders to make a profit–we’d get a much deeper insight into how the economy works.

Finally bought the airplane.

So I finally purchased the airplane.

The final tally (for those interested in how much it costs to buy an airplane): $62,500 for the aircraft. Escrow and title was $550, of which I paid half. I paid another $182 to have the oil changed, and another $70 to fuel it up to fly it home.

The hanger is running me around $450/month at RDU through Landmark; this was because I paid a full year in advance, a lump sum of around $5400 or so. Insurance is costing me $1,250 per year.

My wife and I picked up the airplane; we drove down to South Carolina, and I picked up the airplane, flew it to Johnson County (to refuel), then to RDU. (Refueled in Johnson County because avgas there is sooooo much cheaper.) My wife drove to RDU, we flew around for a little bit, then came back and parked it in the hanger.

The annual is due in June, and I suspect my first annual will be several thousand; from what I hear each mechanic has their own list of things they look for, and things they let go–and so switching mechanics means a bunch of new things get found and fixed the other mechanic was missing. (This is not an inditement on mechanics; some people see a frayed wire and think nothing of it; another wants to rip out all the wiring to be safe.)

And so, I now own a Piper Arrow II.

Buying an airplane: escrow and hangers and stuff.

Just last week I finally came to an agreement with the seller of the airplane I’m looking to buy. It’s a nice Piper Arrow from 1974, complete with speed mods, a 430 (not WAAS), and an AM radio. (Okay, technically an ADF receiver.) It also has a nice 3-blade prop and the engine compressions in the logs seem to be excellent.

So we came to an agreement. The price we settled on was $62,500, and perhaps $1500 to $2500 more than I wanted to pay for the airplane–but then, I’ve never one to allow perfect to get in the way of good enough. There are a couple of minor niggles, naturally, for a 1974 airplane: the step is rusted (and I’ve already asked for it to be repaired or replaced), and the trim where the door meets the fuselage doesn’t look all that great. But by and large the airplane looks like it’s in great shape and has been well cared for (if the logs are to be believed) as well as hangered.

So yesterday I arranged a hanger at RDU, and dropped off a check and the paperwork for a TSA background check so I can actually drive onto the airport. The background check takes approximately 3 to 5 working days, so I should have a badge next week.

As to the hanger, it’s a very nice large hanger from Landmark Aviation, and the going rate is $490/month. (I got a discount by paying the entire first year’s rent all at once.)

Escrow and title was opened with AIC Title, which was recommended by one of the insurance companies I talked to. Their cost is around 1% of the purchase price of the airplane: around $625 in this case.

Now transferring title of the airplane–beyond money and a title search and title transfer, as well as registration in the great state of North Carolina, ‘natch–essentially requires the buyer to fill out form AC 8050-1, a tiny little carbon-paper based form which must be obtained in person from an FSDO (or can be mailed to you from an escrow company), which asks for the new owner’s name and signature, and form AC 8050-2, a bill of sale from the current owner, signed in ink.

Of course I’m getting the title search done; while everyone I’ve dealt with have been the nicest people I’ve encountered–trust but verify.

And of course the different airplane and purchase price (and hull value) means my insurance is slightly larger: it works out to be $1,250/year.

So on Friday I drive down to South Carolina for a second time to do the pre-buy inspection. I’ve opted to do an owner-assisted pre-buy inspection, which is where I get to spend an afternoon with the mechanic as we pour through everything with the airplane itself. I opted for this because I wanted to spend time looking at the aircraft and understanding it for myself.

And hopefully if the weather is good I’ll get a chance to actually fly the aircraft as well, as one of the conditions of sale. (To make sure the airplane flies true.)

And if all goes well, I plan to take posession of the airplane the following week, and arrange for a CFI in South Carolina to fly the airplane back to RDU, and I’ll give him a ride in my airplane (!) back to South Carolina.

Another airplane, but this one is very nice.

Of course you’re buying a 40 year old airplane, so “very nice” is relative: it’s not perfect, it wasn’t owned by someone who was refurbishing and repairing all the cosmetic issues, such as small chips on the leading edge of the wings and seats that really need to be reupholstered. But the airplane feels solid, there appears to be no corrosion, the avionics appears to work, and it looks like it would be a good buy.

This is for an Arrow II with relatively low hours, and more time on the engine than the previous–which to me is a good thing, because once you get to around 1000 hours on the engine, anything that was going to go wrong after a rebuild has probably already gone wrong.

The logs are complete, and it appears that aside from one relatively minor issue a couple of years ago there are no real problems. And the compressions look fantastic; all 78 or higher.

So I’ve sent the seller’s representative an offer on the airplane–which had only come on the market just a few weeks ago. We’ll see how this all works out.

I only have three issues that I’ve found with the airplane. It has speed mods but the owner hasn’t really waxed the airplane; turns out waxing your airplane can add a few knots to the cruise speed. The step into the airplane has a crack in it–but that step can be replaced fairly easily. And the door has a few bends and dings in it where it almost looks the at one point someone tried to close the door while a golf club was hanging out of the airplane.

But all of this is cosmetic, and over time I plan to address each of these issues.

The plusses: a Garmin 430 (not WAAS–but I don’t plan to shoot any low approaches using a GPS, since I see my IFR ticket as a way to safely get out of marginal VFR conditions and not a ticket to fly in bad weather), an up-to-date autopilot (bonus, since that was not listed on the info for the aircraft), and a very nice low-hour 3-blade McCauley scimitar prop.

Meanwhile I spoke (finally!) to the general manager of Landmark Aviation at RDU, and they have a hanger available. So I’m getting the paperwork on the hanger. It’s a very nice large hanger–but truth be told, well, it’s a hanger: a large metal box in which you park an airplane.

The price is $500/month, but if you pay a year in advance he’ll dock 1 month off the rent.

I’m getting the information through the mail now.

Second Thoughts

So now after a night of sleeping on it, I’m having second thoughts about the aircraft I looked at. Give that it is the first one that I physically took the time to look at I’m not sure if my second guessing is warranted–but I am having some second thoughts for the following reasons:

(1) The fuel gages are inaccurate. When containing a half-tank of fuel, the fuel readings show a quarter full. This was definitely on my list of things that I wanted to ask the seller to fix before I bought the airplane; it actually means the aircraft is not really airworthy: fuel gages is actually the first item on the GOOSE A CAT acronym. (Fuel Gages, Oil temperature, Oil Pressure, Seat Belts, Emergency Locator Transmitter, Air Speed Indicator, Compass, Altimeter, Tachometer.)

(2) The spring which helps return the flaps back to zero position is not able to move the flaps all the way back. When you set the flap control lever to the ground the flaps don’t move–until you nudge them by hand, at which point they pop back into position.

(3) The trim motor is unable to move the trim lever very well; sometimes it sticks and requires assistance to move.

Last night I didn’t really think of these things other than as squawks to be fixed prior to taking possession of the airplane; minor issues which just require adjustment or the replacement of an inexpensive part.

But today–I’m starting to think there is an underlying systemic problem.

See, an airplane operates as basically a series of pulleys and cables. Turn the yoke, and a bunch of pulleys and cables pull down the ailerons. Push the yoke forward, and pulleys and cables move the elevator surface. In an Piper Arrow, the lever that you use to put down the flaps pulls a cable that pulls down the flaps, and a spring returns them to the home position. Even in the fuel tank a float attached to a lever and a hinge which turns a potentiometer drives the fuel gauges.

And the one thing these squawks have in common is rust and contamination.

Rust on a pulley can cause the spring that returns the flaps to zero can cause the flaps to stick, and not return to zero. Rust on a pulley can make it harder for the electric trim motor to rotate a pulley. Even rust or contamination on the float lever arm hinge in the fuel tank can prevent the fuel gauges to read accurately.

And worse, because many of these cables pass through holes in the spar and other structural members inside the airplane, contamination or corrosion may be taking place inside those structural members rather than in the pulley itself.

So after seeing this I think the plan of attack has changed to me looking around at more airplanes.

Which is fine: my original schedule was sometime in the Spring.


The airplane was as represented; a bit rough around the edges and in need of a good paint job–but otherwise the engine is in excellent shape, the airplane handles extremely well (proving the control surfaces are in good shape), and the radios and GPS work just fine, as does the instrument panel.

So onto the next step: opening escrow, and setting up a time when I can get a pre-buy inspection done.

On an airplane to Boston

I’m now waiting at RDU to fly to Boston to check out the prospective airplane.

Yes, my original plan of attack was to check out the airplane, do the pre-buy inspection, then fly home in one trip. But my wife pointed out (correctly) that I may be better off making two trips, especially given how cheap flights to Boston from RDU are. So I’m going to fly up today and take a look at the airplane, and if it looks (and feels) fine, then I’ll arrange for a pre-buy, for escrow, and for a title search–and take possession sometime in the next two weeks.

Details: when you buy an airplane, you need a place to park it, and you need to pay both whatever sales or excise taxes your state requires, as well as property taxes. I’ve already contacted the North Carolina Department of Transportation, and have found out that for the purchase price we’re negotiating, my excise taxes will be around $1500, and my annual property tax for parking the airplane at RDU (which is in Wake County, North Carolina) will be approximately $360/year. (Property taxes in Wake County are relatively low.) I don’t know if there will be any additional taxes due to the city where RDU is located–some cities add onto the basic property taxes–but I cannot imagine them adding more than $1000 or so a year, and I strongly suspect (based on one conversation with the nice lady at NCDOT) that there are no additional city property tax add-ons.

If you’re in California and you just read my comments about the tax rates in disbelief–note that if I were in California these numbers would be around $4,500-$5,000 for the excise tax, and around $690-$750/year in property taxes.

As a side note, my father gave me a pointer to his broker (True Course Aviation in Camarillo, CA), and they quoted me $1,179/year, insuring the aircraft for $10k above the hull value that I negotiated with the seller. Much better than AVEMCO!

(Why $10k above hull value? Because at some point I intend to paint the airplane, and install new upgrades and the like–which means at some point the value of the airplane will go up above the purchase price we’re negotiating. That advise I got from my father.)

Also as a side note, after having a pleasant conversation with one of the FBOs here at RDU to rent a hanger–now I can’t get him to return my phone calls. There are two FBOs; I have a message in with the other one, so we’ll see who coughs up a quote first.

So after a night of walking through paperwork…

So step 1 for me was to walk through the paperwork; the detailed logs of all of the repairs done to the aircraft.

The good news: all of the logs for the airplane I’m planning to buy: a 1978 Arrow III with the larger fuel tanks (72 gallons useable, in case we decide to go for very long flights), seem complete–he even sent me the paperwork for the original airworthiness logs when the airplane rolled off the factory floor back in late 1978 and the original buyer of the airplane.

It appears during the 1980’s it was used commercially: I see a lot of “100 hours” instead of annuals. And it appears at one point in the 1980’s one of the wings was bent–probably rolling it into something on the ground. (The logs show a rib being replaced and some skin being repainted.) None of these things concern me: many older aircraft have some minor damage at some point in their history; the important point is that the plane continued to fly for years afterwards.

It also appears the current owner only flew the airplane perhaps 50 to 70 hours a year–which to me is sad: as soon as I have an airplane, a clear afternoon and can play hooky I plan to go up every chance I get. (Until I moved out to RDU and got caught up in stupid expensive rental rates and long hours on my current project, I was averaging around 120 hours/year.) Because flying is fun!

So the logs look complete. And I verified that all the ADs published on the FAA web site appeared to be handled in the logs; the current owner was pretty thorough about compliance. (Of course you cannot really know until you pop the covers off the wings and peek under the cowling of the aircraft. Not all A&P Mechanics got an A+ in school.)

Next step: going up to take a look at the airplane. JetBlue, for whatever reason, (a) flies direct to Boston, and (b) was offering me a nice deal despite the fact that I’m flying on the holidays and flying at the last minute. So a quick $330 round trip puts me in the area so I can drive down and take a look at his airplane.

And if it looks good–well, honestly, if the bones look good, since the price point is one where I don’t expect cosmetic perfection, only structural soundness–then we move onto the step where I find a mechanic to do a full pre-buy inspection.

(As a footnote I plan to own this airplane for a long time. So for me, it’s more important that I find something with good bones–and later, if I decide to paint the airplane or to upgrade the avionics or reupholster the airplane, I’ll have the budget and I can pick my own style. Otherwise I’m paying extra for someone else’s paint job and someone else’s aesthetics.)

Meanwhile I’ve contacted the same insurance broker my father uses for airplane insurance. Right now I have a rough quote from AVEMCO for around $2,400 a year, but everyone I’ve talked to suggests AVEMCO is relatively expensive. We’ll see if I can save any money by contacting the same broker my father uses. (My father claimed to have saved about $1,000/year using them, and while I don’t expect anywhere near that level of savings, since the hull value of the airplane I’m buying is about half what my father flies (a Beechcraft F33A Bonanza), even a couple of hundred dollars is worth it.)

(My father’s broker is True-Course Aviation Insurance in Camarillo, CA.)

And now, time to get someone to return my damned phone calls about actually renting a hanger at RDU. I’m so fed up with the general manager of Landmark Aviation not returning my calls that I called TAC Air. I suspect the bank of hangers they both rent are actually owned by RDU, and they basically handle the paperwork to rent them out.

Update: talking to a prospective seller

Well, just got off the phone of a prospective seller of an Arrow up in Massachusetts. Don’t want to jinx it, but the aircraft sounds perfect: low time on the engine, a 430 linked to the autopilot, and the price is spot on in my budget.

Waiting now for him to send me his logs.