A Quick Note on Footnotes

You may have noticed in many of my post that I put a little asterisk* or two** by certain words or sentences.

*These are little footnotes where I expand on those certain words or sentences.  They may be further (or more technical) explanation of the main text, or a little digression. While they are very pertinent and interesting, they would distract from the flow of the writing – which is why they are relegated to the bottom of the page.

** Sometimes I end up with several of these footnotes***. For the sake of appearance, I’ve decided now to hide these under the fold. That is, when you reach the end of a post with footnotes, you’ll see a Continue Reading→ after the main body of the post but before the footnotes . If you click on this, you’ll then get taken to an expanded screen where you can read all the footnotes.

(Click below to test how it works:)

Supply and Demand – Part 1

Before I move on to the next chapters of the economics textbook, I briefly want to talk about the last couple of chapters I’ve posted, which dealt with supply and demand.

These concepts are essential to all of economics, and luckily are very easy to understand.

They stem from two common-sense propositions:

1. The cheaper something is, the more you’ll buy.
2. The more expensive something is, the more you’ll try to sell.

Here the ‘something’ can be any good or service – apples or haircuts*, say. I’m sure your own experience will corroborate this – “buy cheap, sell dear” is a maxim much lived by.

Of course, with economics having aspirations to be a rigorous social science, we can’t leave it at the level of common sense. So we invent some fancy terms, and draws some schmancy graphs… but the basic intuition comes from our two propositions. Let’s be a bit more specific:

• When people buy things, we’ll call it demand, and when they produce and sell things we’ll call it supply.
• We’re not interested particularly in how many apples or haircuts one person buys or sells, but we are interested in how many apples or haircuts are bought and sold in the UK, say, each year**. That is, we want the market demand and market supply – which comes from totting up everyone in the market’s individual demand and supply for apples or haircuts.
• We’ll use a pair of axes, with price on the vertical axis and quantity on the horizontal axis.

Using our two common-sense propositions:

1. For the demand curve, when price decreases, the quantity demanded increases (a posh way of saying ‘people like to buy more when things are cheap’). On the graph, the curve will slope downwards from the top-left to the bottom-right.
2. For the supply curve, when price increases, the quantity supplied increases (posh for ‘people like to sell more when things are dear’) . On the graph, the curve will slope upwards from the bottom-left to the top-right.

Plotting both curves on our axes, we get:

This graph shows the supply and demand for a particular good or service. A couple of moments thought and you’ll understand why the graph is drawn the way it is***. As we move along the curves, we see how changes in price affect the quantities bought and sold of that good or service.

Where the demand curve and the supply curve intersect, at E, the amount that buyers of apples or cars want to buy equals the number of apples or cars that sellers want to sell. This is our equilibrium****, and we can read off from our graph what quantity of apples or cars will be bought and sold, and at what price – just read off P and Q.

I’m sorry for a very dry post, I’ll expand a bit more in a following post about how supply and demand curves can shift, due to underlying changes in the market, and how this affects the equilibrium. I will eventually move on to applying the concepts of supply and demand to help understand a contemporary political issue.

P.S. Supply and demand curves supply us with the ultimate economics chat-up line. If you find yourself fancying a female economist just ask, “Can you supply the curves I’m demanding?” (Disclaimer: The author of this post cannot vouch for the effectiveness of this chat-up line and takes no responsibility for slaps to the face or knees in the crotch.)

Rainbows

It’s funny how subjects can crop up in completely different contexts.

In a Geometry lecture, the lecturer spoke of the advances made by Isaac Newton in geometry and many other fields. One of his most famous discoveries was to split white light into its constituent colours by shining white light into a triangular prism*:

This is the scientific explanation of why we get rainbows. Water droplets in the air act as the prism, causing the light to disperse into its familiar form:

But as I said, the topic of rainbows came up in a completely different context the other day – what we might call the Biblical, rather than scientific, explanation for rainbows. It comes from Noah and the flood – a story I’m sure you know about.

God had sent a great flood to kill everything in the world, which had grown very sinful. He saved Noah and his family, and two of each and every animal, who stayed in a big Ark to prevent them from drowning. When all was over and done, and the flood had subsided, leaving Noah, family and animals to repopulate the world, God put a rainbow up in the sky as a symbol of his promise that never again would he try to destroy the whole world, no matter how sinful it was.**

So there you go, a scientific and Biblical explanation of rainbows. Do they conflict, or does one simply explain the how and the other the why?

Of course, this ignores the third explanation, which seems most convincing to me: How else would leprechauns know where they had left their pot of gold?

The Importance of Intentions

Come Sunday, I often feel a bit battered and beaten by the world – its adversities and temptations.  Luckily I often find a good sermon to challenge me and hopefully build me up. This Sunday’s sermon dealt (perhaps slightly embarrassedly) with the subject of sexual behaviour.

The passage that was preached came from Jesus’ Sermon on the Mount, where He specifically deals with adultery. It is a very challenging passage:

You have heard that it was said, ‘Do not commit adultery.’ But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart.

Matthew 5:27-28

What is so challenging about this is that sin does not spring from our actions, but originates in our hearts. That is, it is our will and intentions that matter, not necessarily our acts. We don’t have to have touched, or even approached a women – the adultery occurred in our minds.

It reinforces the preceding passage on murder:

You have heard that it was said to the people long ago, ‘Do not murder, and any one who murders will be subject to judgement.’… But anyone who says, ‘You fool!’ will be in danger of the fire of hell.

Matthew 5:21&22

The similarity is clear. It is the hateful thought that is sinful, regardless of whether it ends in a fatal blow or merely dissipates from our lips.

If we can murder and commit adultery with our minds, then I guess Pol Pot and Casanova have nothing on me. How wonderful that our salvation depends not at all on what we have done, but what God in His grace has done for us!

Snigger alert: Since we’re talking about sex and the Bible, I can’t resist this passage that we came across in my Bible reading group today. It is from Ezekiel 23:20:

There she lusted after her lovers, whose genitals were like those of donkeys and whose emission was like that of horses.

I almost thought I was reading Fifty Shades of Grey.

Plymouth Gilbert & Sullivan Fellowship’s 90th Anniversary Concert

I had a wonderful night at the Plymouth Gilbert & Sullivan Fellowship‘s 90th Anniversary Concert.

I’ve become a huge Gilbert & Sullivan fan in the last couple of years, and tonight’s concert was a fitting tribute to their shows, as well as to the talent of the company.

There are just too many great songs, but I’ll leave you with the Finale to The Mikado:

Fry-Ups and Psychology

My day started as every day should start… with a full English breakfast shared with a good friend. Our conversation eventually turned to what we did with our toast. My friend used it to dunk in the yolk of her fried eggs, while I used it to mop up my plate once I’d finished.

My friend, who also works as a note taker at Plymouth University and who attends a lot of Psychology lectures, said she thought that these little quirks of people’s eating habits would make an interesting psychological study.

I don’t know much about the psychology of people’s eating. But the conversation reminded me of some interesting experiments in the choices people make when ordering from a restaurant; experiments undertaken by Dan Ariely and recounted in his book Predictably Irrational: The Hidden Forces that Shape Our Decisions.

In a series of experiments, Dan and Jonathan Levav investigated how being in a group affects which beers, wines or meals people order in a bar/restaurant setting. Different groups ordered their choices in two ways:

1. the ‘public’ choice – they would go round in a circle and each would say aloud to the waiter what they wanted, which is how people often order.
2. the ‘private’ choice – they would write their order on a sheet of paper and hand it to the waiter.

The people were then asked how much they enjoyed their choice afterwards.

The aim was to see how being in a group affected people’s decisions.  Are we influenced by others’ decisions?

What they found was that when people ordered ‘publicly’, a greater variety of meals or drinks were chosen than when ordered ‘privately’.

The explanation is that when ordering food ‘publicly’ in a group, people don’t merely choose food which they’d most enjoy, but also to signal to others that they are ‘unique’ and ‘individual’. If someone had already chosen the item they would most enjoy, then they would deliberately choose something else, just to be different.

However, when people could order anonymously, this signalling effect wasn’t so prominent. People stuck to their preferred choices.

It was also found that the people who chose ‘publicly’ didn’t enjoy their food as much – which isn’t surprising when they didn’t go for their first choice. Apart from the person who ordered first, that is – who essentially was able to make a private decision and not worry about what others were choosing.

By the way, me and my friend both chose exactly the same meal. But then, if we’re the sort of weirdos who talk about psychological experiments over breakfast, do you expect us to behave like most people?

P.S. These experiments were conducted largely with Americans – who come from a Western, more individualistic culture. When the experiment was conducted in Hong Kong – there was also a difference between ‘public’ and ‘private’ choices. Only there was less variety in the ‘public’ choices – people chose what others were having even if it wasn’t their preference. This is probably because in Oriental cultures there is stronger pressure to conform.

The A – Z of Music: H

Yesterday’s post was a little… crude. So to make up for it, I’ve made a more high-minded choice for the music selection in my A – Z of music – something from Handel‘s Messiah.

Messiah is an opera, with all the music set to Bible verses – taken from the glorious King James version. I’d be shocked, shocked if you haven’t heard the Hallelujah Chorus. But that would be too obvious a choice.

Here’s the first sung part of the opera. It is taken from Isaiah 40:

Comfort ye, comfort ye my people, saith your God.

Speak ye comfortably to Jerusalem, and cry unto her, that her warfare is accomplished, that her iniquity is pardoned.

The voice of him that crieth in the wilderness, Prepare ye the way of the Lord, make straight in the desert a highway for our God.

It’s a wonderful message… and when I hear this song I immediately feel comforted:

Bad Branding

I was out for a walk the other week, and found this written on a wheelie-bin:

It should say P.C.C. – for Plymouth City Council – but those C’s look a bit too close to another letter. I hope the householders didn’t get confused and leave the wrong sort of ‘waste’ in the bin. It would be a nasty surprise when it’s emptied!

It reminded me of another great example of unintentionally rude branding. The Office of Government Commerce is a government agency that helps with public sector procurement. £14,000 (!) was spent to create this logo:

… which looks harmless enough. Until you turn it on its side, that is:

Now, if you were designing a logo for my love life…

The Great x=cape

As the new academic term has begun, I have recently started back at my job as a note taker at Plymouth University.

The main student that I help is taking the first-year Mathematics and Statistics course. I’ve always loved Maths, which I imagine is a minority position. So to try to convince you that Maths isn’t just about crusty old professors scribbling indecipherable squiggles on a whiteboard, but also about exciting tales of derring-do, I want to share something taught in one of the lectures.

To set the scene, think of all those World War II Prisoner of War (POW) films you’ve seen. Probably The Great Escape* comes to mind.

These escapes didn’t occur spontaneously. They were planned, with outside help from Military Intelligence**.

The communication between POWs and Military Intelligence was carried on through the letters the POWs were allowed to send home. Since all letters were censored, the messages had to be encoded.

How this was done was a mystery, until Plymouth University lecturer, David McMullan, cracked the codes hidden in POW John Pryor’s letters home to his parents in Cornwall. The video below gives some background:

I won’t go into all details, as the steps, while not overly complicated, would take ages to explain. I will explain the spelling rule, that allowed important messages to be hidden in innocuous sentences.

The first step is to add an extra letter to our alphabet, a full stop ‘.’. Now there are 27 letters in the alphabet, and 27 = 3 × 3 × 3. We can create a grid, with each box described by a 3-number combination of 1’s, 2’s, and 3’s. We then fill this grid alphabetically, starting with the ‘key’, which was ‘S’ in John Pryor’s case:

I hope that after a couple of minutes of looking at the grid, you can see the pattern in the numbers and the letters. Poor John Pryor had to keep this in his head when he was encoding his messages – you don’t want to leave any incriminating proof that you’ve been working out codes for the guards to find!

Now, we can use this grid to decipher a sentence in a letter. Let’s use as our example:

A few weeks ago we arranged a rather useful scheme, so men could get lager

I personally would never guess this contained a secret message. And it’s lucky for us (and the escapees) the German guards didn’t either.

The first step is to group the words into 3, and take the first letter of each:

Now, we convert these 3 letters to 3 numbers. Take the first row, A F W. Looking back at our grid, we notice that A is in column 1, F is in column  3, and W is in column 2. So A F W becomes 1 3 2.

If we look again at our grid, though, we see that 1 3 2 corresponds to the letter M.

We can then convert each of our 3-letter combinations into a single letter using the grid:

The code has converted “A few weeks ago we arranged a rather useful scheme, so men could get lager” into MAPS. – and no one suspected until recently.

The letters were used to pass German secrets to the British government, and to request things such as maps, passports, guns and so forth so the men could escape from the camp.

It may not be as impressive as the work of Alan Turing and Bletchley Park, but it shows what amazing things can be achieved using a little bit of Maths!

My Brush with Celebrity

I was Street Pastoring last night, with many of the usual crowd. Only, one of our team has undergone a transformation since last we met. She is no longer merely Anne Scarfe, but Anne Scarfe, winner of The Pride of Britain Local Hero Award 2013 for the West Country!

Well done Anne! From the feedback we got last night, Plymouth was very proud of you.

P.S. Lots of videos of Anne getting interviewed on TV and hobnobbing with the likes of Philip Schofield, Carol Vorderman, Peter Andre and The Wanted can be found… here!