In the context of the domestic economy, the law of one price states simply that: If two goods are identical, they must sell for the same price.
This looks a harmless, uncontroversial enough statement. It is in fact, just the kind of blindingly obvious statement that sceptics complain about in economics. However, the same sceptics would almost certainly change their tune if they were to consider the implications of the law of one price. On the contrary, they would prob- ably dismiss economics as a collection of very dubious propositions indeed!
In order to illustrate the kind of issues involved, let us take a look at a number of more or less everyday examples to which we can refer back in later sections.
2.1.1
Example 1
Imagine that Michael Jackson is giving a concert at Wembley Stadium in London, a fortnight from now. All the tickets have been sold at face value through the usual dis- tribution channels across the UK, but excess demand has created a black market, operating outside ticket agencies, in pubs, on street corners, in discos, in the classified ads columns of local newspapers and, of course, on the internet.
Now suppose that you are told that tickets for seats in a particular part of the stadium are on offer on the black market in Birmingham for £50. What would you expect an identical ticket to cost in, say, Manchester? By the law of one price, the answer has to be £50 and, in practice, under these circumstances, you probably would find tickets of the same category on sale at more or less the same price in dif- ferent towns.
Why would this tend to be the case? To see why, ask yourself what would be likely to happen if the law did not hold in this example. Suppose, for argument’s sake, that the price of a ticket were £5 lower in Manchester than in Birmingham. Then anyone in Birmingham who wanted to go to the concert would buy the ticket in Manchester, while no one in Manchester would buy in Birmingham. So, sellers in Birmingham would be unable to sell any tickets as long as there were any on sale cheaper in Manchester.
You may object that in reality ordinary Michael Jackson fans in Birmingham would be unlikely ever to find out that tickets were on offer at a lower price on a street corner in Manchester, in the small ads pages of Manchester newspapers or on some obscure website somewhere in cyberspace.
That is almost certainly true. At the very least, it might take some days or even weeks before word reached Birmingham, by which time it would be too late – the big day would have come and gone!
Do we then conclude that the law of one price might well break down in this, the first case we have examined?
We might do so, were it not for the well-known fact that there are people who make a living out of exploiting just such situations. What they do is to watch out for
2.1 The law of one price in the domestic economy 45
price divergences like these. In the present case, they would simply buy up as many tickets as they could in the cheap location (Manchester) and sell them immediately in the dear location (Birmingham). In the process, they would be doing three things: making a tidy profit for themselves, driving up the price of tickets in Manchester from £45 and driving down the price in Birmingham from £50. On each ticket they trade a profit is made that is equal to the price differential. The larger the price differential, the greater the profit and hence the greater the incentive to trade. As they bid up the price in Manchester and push down the price in Birmingham, the gap narrows and their profit falls from £5 per ticket to virtually nothing, so that the incentive to trade is progressively reduced. Obviously, the process tails off and stops altogether when prices in the two cities are brought into equality at some price between £45 and £50, say £47. At this point, profit opportunities have been exhausted.
People who make a living by trading rock concert (or football match) tickets on the black market are usually called ‘touts’ or ‘scalpers’, although touts also operate in the black market in another way. More generally, and more relevant to the sub- ject matter of this book, the process of moving goods from one market to another so as to take advantage of a price differential is referred to as arbitrage and those who make a living in this way are called arbitrageurs. As we shall see, they have a number of important roles to play in the currency markets and, in fact, throughout the financial sector of the economy, so the following definition is given here for future reference:
Arbitrage is the process of buying or selling something in order to exploit a price differential so as to make a riskless profit.
The word ‘something’ is intentionally vague. For the present, we are concerned with arbitrage in goods and services, but in Chapter 3 we shall be concerned with arbitrage in securities. The expression is a completely general concept and is also fre- quently encountered in markets for equities, commodities and currencies themselves. Now let us return to our example. Consider the following question: given the existence of arbitrageurs, albeit in the somewhat unsavoury form of ticket touts, are there any factors that could prevent the law of one price prevailing?
Lack of information has been ruled out as unlikely, simply because the touts will make it their business to know about any price differentials that exist and, in any case, nowadays the internet serves to spread the word extremely rapidly. Their liveli- hood depends on their keeping their ears to the ground. They specialize in gathering this type of information.
Similarly, they are unlikely to be hampered very seriously by the actual cost of trading. The costs might involve a few trips between the two cities carrying their precious cargo, possibly the price of a small advertisement or two, no doubt some long-distance phone calls, some postage, a few drinks to close valuable deals and oil the wheels and so on.1However, these costs are likely to be small, probably neglig-
ible, relative to the value of the transactions involved.
As we shall see in subsequent examples, the costs of actually transacting will not always be so insignificant. For now, it will be useful to have a definition to hand:
46 Chapter 2 · Prices in the open economy: purchasing power parity
Transaction costs are all the costs associated with a transaction, over and above the cost of the item that actually changes hands.
As a specialist trader in large blocks, the scalper’s transaction costs are minimal. A scalper who knows that a consignment of, say, 100 tickets can be bought and sold with transaction costs of only £10 will still be able to exploit the £5 per ticket price differential between Manchester and Birmingham. The profit from the purchase and sale of 100 tickets is shown in the calculation in Table 2.1.
Obviously, profit is reduced by the amount of the transaction cost (£490 instead of £500), but the deal is nonetheless well worthwhile. Notice that the profit per ticket sold has fallen from £5 to £4.90. Why? This is because while the selling price of each ticket has remained the same, the all inclusive cost of the average ticket has risen by the amount of the transaction cost per ticket, that is, £0.10 (= £10/100).2
As arbitrage proceeds, however, we have seen that the price differential is progressively reduced. At what point will arbitrage no longer be profitable? In the absence of transaction costs, the answer was: when the price differential was com- pletely eliminated. Will this still be true, now that we are allowing for the fact that simply buying and selling involves a cost?
Looking at the calculations in Table 2.1, it is plain that our previous conclusion has to be modified to read: arbitrage will cease to be profitable when the price dif- ferential is no greater than the transaction cost per item. Instead of ending up with a situation where a price of £47 reigns in both towns, the arbitrage process will come to a halt when the price differential has narrowed to £0.10. You can see this for your- self if you repeat the calculation with a price of £47.10 in Birmingham and £47 in Manchester. You will find that at these prices arbitrage profits are zero.
For future reference, we will describe this equilibrium in symbols as follows:
PB= PM+ C (2.1)
where PBis the price of a ticket in Birmingham, PMis the price in Manchester and C is the transaction cost.3
Before going on to look at a very different example, there are one or two more points worth noting. Notice that our conclusions relate to the price of tickets outside London, where the concert is to be held. Since London fans have so much shorter a
Table 2.1 The ticket tout’s profit Costs
Buy 100 tickets in Manchester @ £45 each = total outlay of £4500
Transaction costs (buying + selling) £10
Total cost £4510
Revenue
Sell 100 tickets in Birmingham @ £50 each = revenue of £5000
Profit
2.1 The law of one price in the domestic economy 47
distance to travel, it could reasonably be expected that the demand for tickets will be greater at any price level there than in the provinces. Does this mean the price in London will be higher than elsewhere in the UK?
A moment’s consideration will show that, under our assumptions, we can rewrite Equation 2.1 with PLon the left-hand side (that is, the price in London). In general,
throughout the country, arbitrage will have ‘smoothed out’ the price variations that might otherwise exist due to localized excess demand (or supply) situations.
To see what loose ends remain in our analysis of this example, let us briefly recap. It was concluded that it would be unrealistic to expect price equality to prevail, because of the existence of transaction costs. Taking them into account, however, led us to the conclusion that the modified version of the law of one price in Equation 2.1 could be expected to assert itself, thanks mainly to the activities of ticket touts spe- cializing in arbitrage operations.
Now, are there any other factors we have neglected that may prevent even our modified law of one price from asserting itself ? One obvious fly in the ointment is the unfortunate fact that ticket touting, whatever its economic benefits, is more or less illegal. In fact, legal barriers to arbitrage are not uncommon, even in much less racy sectors of the economy, particularly those sectors involving international trade and investment. Their effectiveness in preventing arbitrageurs from trading varies enormously, depending on the nature of the commodity, the type of market, the seriousness with which law breaking is treated and so on. In the present case, it seems the legal barriers would probably have very little effect – the law of one price would almost certainly prove stronger than the law of the land.4
As a matter of fact, we can claim to have taken at least some account of the legal barrier to trade in our Equation 2.1. Our transaction cost, C, will be substantially affected by the fact that the business deals involved may amount to a crime. Perhaps, for example, the choice of relatively expensive marketing channels (selling in pubs, small ads and so on and in small batches of ones and twos) is dictated by the need to evade the long arm of the law. Perhaps the £0.10 per ticket also includes an element of reward for the risks of arrest and subsequent fine by the courts or it may even incorporate an allowance for legal costs.
One important point to note is that risk of arrest is the only risk involved. In a pure arbitrage transaction, there are no trading risks in the normal sense. The arbit- rageur takes the opportunity of a near riskless profit. Arbitrageurs can be regarded as selling their tickets in Birmingham almost at the same time that they buy in Manchester, so that their actual trading risk is zero. The absence of risk is a dis- tinguishing feature of arbitrage.
Because arbitrage involves no trading risk it might seem that there is always likely to be a ready supply both of arbitrageurs and of funds to finance their operations. As the present example illustrates, however, this will not always be the case. Reputable financial institutions will not be willing to make loans to ticket touts, even though they stand to make a riskless ‘killing’. This is not simply because the funds are required for an illegal activity. Even if they can invent a respectable reason for want- ing an advance, ticket touts will probably not be in good enough standing with their bankers to be able to raise very large loans. The possibility arises, then, that the law of one price could be frustrated simply by the fact that the supply of arbitrage funds is too small to eliminate the price differential.
48 Chapter 2 · Prices in the open economy: purchasing power parity
Mention of borrowing and lending raises the question of interest rates. Ought there to be an interest charge included in our transaction cost term, C ? The answer has nothing whatever to do with the question of whether a ticket tout borrows or uses his own funds as working capital. (Why not?)
In principle, there is no interest cost to pure arbitrage for the same reason there is no risk: if buying and selling are instantaneous, the working capital needed is nil. In practice, there may be a cost of financing stocks of tickets for, say, one day prior to sale, but we shall regard this as negligible.
Finally, it will be helpful if we use this example to compare and contrast the two classes of market agent who have already been mentioned with a third type of agent. Recall that we introduced the arbitrageur into the story only after concluding that the price in different towns was unlikely to be equated simply by the interaction of bona fide Michael Jackson fans who are buying tickets with the concert organizers who are selling them. Does this mean their activities are completely irrelevant to the determination of market prices?
Certainly not. The interaction of what we could call normal traders – fans want- ing to attend the concert and the organizers supplying the seats – these are the ultimate determinants of the equilibrium, ‘central’ (say, London) price. We can then think of the operations of arbitrageurs fixing the Manchester and Birmingham prices in the way we have analysed in this example.
In cases like this, however, the equilibrium price may also be affected in the short run by the activity of a different species of ticket scalper – one who holds on to tickets in expectation of higher prices later. From now on, we shall use the following name for this form of enterprise:
Speculation is the activity of holding a good or security in the hope of profiting from a future rise in its price.
Notice that, unlike arbitrage, speculation is inherently risky, since the price rise may fail to materialize. The speculator–tout buys tickets and holds on to them so as to sell them when the time is right – typically, outside the stadium immediately before the concert starts. He backs his judgement. If, however, he miscalculates, and there turns out to be an excess supply on the day of the concert, he loses money.
To summarize, in any market, we may potentially have three different kinds of agent at work:
(1) traders (in our example, the fans, whose tastes condition their demand, and the organizers, whose costs determine the supply)
(2) arbitrageurs (touts who exploit local price variations)
(3) speculators (scalpers who hold on to tickets in the hope of making a ‘killing’). Although we shall deliberately ignore the moral and legal distinctions between the activities of these three classes of market agent, we shall often have cause to treat them separately in our analysis of other markets in Chapters 3, 6 and 7. The theoret- ical distinctions are clear. However, we must not forget, particularly when thinking about policy measures, that in practice it is often virtually impossible to separate the different classes of transactors. In our example, there may be no feasible way to tell the tout from the genuine rock music fan, let alone the arbitrageur–tout from the
2.1 The law of one price in the domestic economy 49
speculator–tout. Certainly, a legally convincing distinction may be elusive, which is precisely the problem faced by law enforcement agencies.
This case has been analysed in some depth because it illustrates many of the issues surrounding the functioning, or non-functioning, of the law of one price, as well as providing a first encounter with some of the concepts that are central to the material in the rest of the book. The remaining examples will be dealt with more briefly.
2.1.2
Example 2
The down-to-earth subject of this example is the price of potatoes. Could the price in Manchester ever deviate from the price in London? Plainly, this is a straightforward application of the modified law of one price, as in Equation 2.1. The transaction cost, C, may be quite substantial in this case, simply because potatoes are costly to move from one end of a country to the other. Provided that we allow for this fact and make sure we are looking at the same quality of potato in each case, we are likely to find that prices in the two cities are very close to each other.
Notice that the question of where the potatoes have been grown is irrelevant. Note also that we need not rely on the existence of arbitrageurs. (Anyway, whoever heard of potato arbitrageurs?!) As long as retailers are competitive, they are likely to keep price deviations within the margins set by the costs of transporting potatoes. Or, to put the point another way, genuinely competitive distributors (wholesalers or retailers) will themselves act as arbitrageurs.
2.1.3
Example 3
Take a typical manufactured good, for example, a folding umbrella made in China. Can we be sure that its price will be uniform across the UK?
At first glance, you might think the answer was no – the price even varies from shop to shop in the same town. That’s why we shop around, isn’t it?
Not really. We shop around for two reasons mainly. First, because we like to com- pare different makes of goods and, second, to compare different models produced by the same manufacturer. However, the law of one price only relates to identical goods. Where manufactures are concerned, products made by different firms are rarely, if