Fixed price purchasing

Firstly, consider a Metcard.  Let’s think about a zone 1, ten trip, two hour ticket.  In 2008, such a Metcard would cost $28.00.  In 2009, the price increased to $29.40.  This represented a 1.05% price increase – lower than CPI.  But Metcard tickets, once bought, entitle the buyer to their trip – in this case, ten zone 1 trips.  The value of your purchase is not diminished over time.  A Metcard does not store value – it stores journeys paid for in advance, with a set charge at the time of payment.

Diminishing value to the traveller

A Metcard holds its value fixed.  Myki does not.  Going by current prices, let’s consider a balance of $100 on a Myki in December 2008, as opposed to $100 worth of ten trip Metcards.  Myki is bright enough to give the same discount for buying ten trips at a time.  This gets you 35.7 trips on a Metcard or on a Myki.  In January 2009, the price increases.  Your Metcard still gets you or 35.7 trips.  Your Myki now only gives you 34 trips.  This represents a 1.05% decline in value for the traveller in the space of a month.  This will be endemic, even if smaller price increases are introduced more frequently, the number of trips a given value of money allows diminishes over time with Myki in a way that it does not with a Metcard.

Buy in bulk and save

What’s been done correctly is that the price for a two hour zone 1 trip with a Myki is $2.94 – the same cost as a ten trip Metcard.  On the assumption that prices standardise on the bulk purchase rate, this leaves a consumer who buys in bulk no worse off with Metcard or Myki.  While Myki has a fixed cost of $10 to buy, this cost can be split over the cost of every trip made throughout the life of that card.  If you lose cards frequently, you’ll pay for it, but if you don’t, the cost per trip of the purchase of your card rapidly approaches zero.  And travellers who frequently buy their tickets on the tram or bus, or who don’t usually buy in bulk will benefit from Myki’s charging regime[1].

An interest free loan

Using Myki, you don’t buy trips, but rather you store value.  You could think of it like a savings account that pays no interest, and the money in it can only be used for one thing.  It’s a store credit, if you will.  The key difference here is that when public transport costs increase, the value in your Myki in no way will reflect this, whereas the value of a Metcard does.  A 3% rise in fares coupled with a 3% increase in the cost of living is cancelled out with a Metcard (roughly – see the forthcoming page on indifference curves and CPI).  A 3% rise in fares with Myki represents decrease in the value of stored money (as seen above).  But that stored money also represents an opportunity cost for the Myki account holder and a bonus for the State Government[2].  Let’s consider 500,000 Myki holders (roughly an eighth of Melbourne’s population in 2010), each with a balance of $20.  This gives $1,000,0000 in credit.  Invested at 5%/annum, this returns $50,000 in profit.  So at the same time as the value stored in your Myki (as measured in trips) is declining, your money able to be used to get investment returns for someone else.  You’re caught coming and going[3].

Returning the value

The two flaws above are by design.  They’re part of the point of the system.  They tilt the field slightly against public transport travellers and in favour of the State Government.  Over the lifetime of Myki, this tilt may represent a reasonably significant amount of money.  Designing the system to accommodate this would be simple.

One way – which would not work – would be to not increase fares again.  This gets around the first problem, but not the second.  And it creates a new one.  Fare income is (I hope) put back into the system.  The real cost of no fee increases in an inflationary environment would, over time, approach zero.  A zero fare public transport system will still cost the state money, and would represent a transfer of wealth from areas without public transport to areas with it.  I’ve a feeling that areas without public transport are already generally less well off than areas with it, so a close to zero fare approach is probably regressive.

A way to ameliorate both problems above can be implemented with two steps.  Keep fare increases (only at a reasonable level), but increase the value stored on a Myki at the same time, to the same proportion as an increase.  If fares increase by a flat 2% across the board, increase my $20 balance by 2% (to $20.40).  Any money I put in after that increase in balance would not be subject to that increase[4].  This allows me to still make the same number of trips before and after a fare increase, but also helps fare income has the same real value from year to year[5].  In addition, balances should also be increased  by the rate of return the State Government gets on the money invested[6].  If the Myki Fund is returning 5% on the amount invested, balances could be increased by this amount annually (as with footnote 4, probably 5% of the average balance in a year).

Wrapping it up

I’m aiming to write short pieces on things that are happening to consider how basic economic concepts can be applied to real life in a way that helps to understand those concepts.  I’m not proposing public policy here – I’d be amazed if any government would do anything other than offset the profits from the two problems identified above against the losses from single trip tickets, not to mention the $1.35 billion (at least) that Myki has cost.  But hopefully this has you considering money and value, how they can change over time, and the effects of leaving money stored in a card that doesn’t increase with value over time, rather than leaving money in your bank account (or better, paying off any debts you may have).

FOOTNOTES
1. It’s likely that this will have a significant impact on ticket income, but there was never going to be any other way to implement it.  Given a single two hour zone 1 ticket is $3.70, imagine the outcry if each Myki trip cost you $0.76 more than the equivalent bulk Metcard rate?↑
2. I can’t find who owns the money stored in travellers’ Myki accounts.  I’m assuming the State Government does, but the argument holds irrespective of who keeps your money.  If it’s shared between the private consortia who are managing the public transport system, it represents a bonus for them.↑
3. Clearly, $50,000 is not a lot of money.  My point is not to suggest that there’s some grand plan to rake in loads of cash at the expense of travellers.  My point is to help you think about money and value over time.↑
4. And we introduce a new problem – if I then put in $100 on December 31, I get an increase in value of $2.  A better version would be to increase the value by the mean value stored on the card throughout the year, but my simpler example above serves as a theoretical explanation.  Software makes such tasks trivial.↑
5. In a period of sustained deflation, it would be impractical to reduce balances if fares were reduced.  But no government would actually reduce fares, so there’s no substantial problem here.↑
6. Again, a theoretical example – it would cost much more than $50,000 to return $50,000 to 500,000 Myki users.  I am not actually suggesting that this should be implemented (whereas the balance increase at the same time as a fare increase one probably should be).↑

The original Phillips curve

Inflation and unemployment

Starting with the basic AS curve in terms of unemployment:

P = (1+μ)P^eF(u, z)

The function F captures the effects on the wage on unemployment rates.  μ is the markup value (typically less than 1).  A specific form of F can be:

F(u, z) = 1 − αu + z, α > 0

The function α gives the strength of the relationship between unemployment and wages (higher unemployment leads to lower wages).  This leads to:

P = (1+μ)P^e(1 − αu + z)

Defining inflation π and expected inflation π^e gives:

1 + π ≡ P/P−1, 1 + π^e ≡ P^e/P−1

Therefore, after dividing both sides by P−1 leaves:

(1 + π) = (1+μ)(1 + π^e)(1 − αu + z)

Expanding the right-hand-side of the equation gives:

1 + π = 1+μ + π^e − αu + z + cross product terms (the cross product terms are 2nd order, e.g., if μ = 0.1 and π^e = 0.05, then μπ^e = 0.005).

Considering just the first order terms for the moment:

π = π^e − αu + (μ + z)

This predicts that:

• an increase in expected inflation π^e increases actual inflation π 1-for-1
• an increase in unemployment u reduces inflation π (for given π^e)
• an increase in markup μ increases inflation π (for given π^e)
• other factors z that affects wage-setting also affect inflation

Less complicatedly, an increase in expected inflation π^e leads to an increase in inflation π.  To see why, note that an increase in expected prices P^e leads to an increase in P.  If wage setters expect a higher price level, a higher nominal wage is set, which leads to an increase in the price level.  A higher price level leads to higher expected inflation.  So an increase in expected prices leads to an increase in actual prices, which also means that an increase in expected inflation leads to an increase in actual inflation. Additionally, with a given expected level of inflation π^e, an increase in the markup μ also leads to a higher rate of inflation.  Given an expected level of inflation π^e, an increase in unemployment leads to a decrease in inflation.

The Phillips curve – the early version

In a particular period t (say, one year)

π_t = π^e_t − αu_t + (μ + z)

This translates to saying that the inflation rate in a given time is equal to the expected rate of inflation for that time minus αu_t (the strength of the relationship between unemployment and wages multiplied by the actual rate of unemployment at that point in time) plus the markup level μ and z.  As a simplification, consider inflation as close to zero (which was the case in many countries, including Australia, in the 1960s).  This means that expected inflation is zero, and so the relationship is:

π_t = −αu_t + constant

This demonstrates the relationship between inflation and unemployment that Phillips (1957) found for the UK and Australia and Samuelson and Solow (1960) found for the US.  For Phillips, this was an empirical generalisation. For Samuelson and
Solow, it was considered a policy tradeoff (meaning that a country can choose its inflation rate and accept the corresponding rate of unemployment, or vice versa).

Australian unemployment and inflation data from the 1900s to the 1960s.

In Australia from 1900-1960, a low unemployment rate was typically associated with a high inflation rate, and a high unemployment rate was typically associated with a low or negative inflation rate.

This relationship began to break down after then.

1. persistent inflation incorporated into expected inflation
2. oil price shocks

Wage/price inflation spiral

• expansionary policy, kept unemployment rate low
• low unemployment ⇒ higher nominal wages in tight labor market
• prices rise as marginal costs (wages) rise
• expected inflation begins to increase
• wages build in higher inflation (indexation) etc
• self-reinforcing spiral of higher wages and prices

More is required on:

NAIRU – modern Phillips curve.  Consider expected inflation, which is lagged inflation (accelerationist Phillips curve).  If unemployment is above the natural rate, the price level is rising at a diminishing rate.  (more study needed here T

If two countries specialise in goods that they have a comparative advantage in producing, both are likely to be better off.  This is the case even where one country is better at producing both goods.  Consider a theoretical example – the two countries are Australia and Japan, and the goods are TVs and cars.  An example might help.So, if cars and TVs are the two goods we’re comparing, let’s consider the following example:

As can be seen, Australia builds a car in less time than Japan does, but takes more time to build a TV.  The opportunity cost of one car for Australia is three TVs.  Japan’s opportunity cost for one car is eight TVs.  In one period of 120 hours, each country – working by itself – could produce according to the following graph:

Production - Cars vs TVs

This gives a total of between 7 cars and 0 TVs, or 36 TVs and no cars.  Given a total economy-wide requirement for four cars, Australia might choose 2 cars and 6 TVs, and Japan might choose 2 cars and 16 TVs.  However, if both countries engaged in trade, Australia could produce all four cars required, and Japan could produce nothing but TVs.  Australia could sell two cars to Japan for 8 TVs.  This leaves Australia 2 TVs better off than they would have been otherwise, and leaves Japan one car better off than they would have been, given the 120 hour period of work.  In Australia, one car is worth 3 TVs.  In Japan, 8 TVs is worth one car.  If both countries trade, both are better off.

This holds true even if – as is more likely in this example, Japan is more productive in both cars and TVs.  The opportunity cost is still real – there are still only 120 hours of production time.  Even if Australia took 40 hours to produce a car, and Japan took 30, both countries are still better off trading.  This absolute advantage in production still means one car costs Japan 6 TVs, while one car only costs Australia four TVs.  Assuming the Australian workers can’t just pick up and move to Japan (either physically or in adopting Japanese production methods), Australia is still better off producing cars and Japan TVs.

Where this falls over

This is clearly a basic example.  The problem is that life isn’t this simple.  Firstly, no national economies survive on two goods only.  Secondly, no mention has been made of transportation costs, or social or political benefits of maintaining production locally. Ethical considerations – fair work laws and environmental regulations in particular – have been ignored.  Not everyone wins from free trade – the countries as a whole do, but countries don’t exist as separate identities from their citizens.  And comparative advantages can change over time – taken to an extreme, every national economy would only produce a small number of goods or services, and free trade would lead to oligopolies in national trade.  And we know how they work out.

Where this works

Trade does work.  Conventional thought indicates that putting up trade barriers will harm your economy.  Perhaps if every other country did not put up trade barriers, the one that did would be advantaged.  This example of the free rider problem is what international treaties seek to avoid.  One country can’t bar trade from others without them retaliating in some way.  Comparative advantages are also real.  Australia has a comparative advantage in natural resources, skilled labour, and education as compared with many other national economies.