good or an intangible, invisible service. This fact should be borne in mind through- out the book.
Now, can the price of a haircut in London deviate from that in Manchester? Plainly, the answer is yes and substantially so. Even if demand is similar, the cost of the main hairdressing inputs (wages, rent and so on) is greater in London, so the supply curve is further to the left.
As before, arbitrage in the normal sense is obviously ruled out, so that the short-run price differential can be enormous. This fact has led many writers in the international economics literature to describe services such as hairdressing, motor vehicle repairing, plumbing, medical services and so on as well as some goods (such as houses), as non- traded goods. For future reference, let us introduce the following definition:
Non-traded goods (or non-tradeables) are items (usually services) for which interregional price differentials cannot be eliminated by arbitrage.
Notice that the definition does not refer to goods, if any such exist, for which price differentials can never be eliminated. All we mean is goods that, for sound practical reasons, cannot be moved from place to place so as to exploit price differences. As we saw in the previous example, and as is plainly true in the case of haircuts, there may well be other, less direct mechanisms than arbitrage that will ultimately drive London and Manchester prices into equality. For anyone who is not completely bald, haircuts figure in the cost of living in the same way as housing does and, in the long run, there may well be forces tending to eliminate price deviations over broad categories of services, as we shall see in Chapters 5 and 7. Nonetheless, since arbi- trage is impossible, haircuts and so on must be regarded as non-traded goods and the law of one price cannot be expected to apply automatically.
Put differently, we can say the transaction cost in the case of a haircut is near infinite – not in absolute terms, as was the case with houses, but because, relative to the cost of the commodity itself, the transaction cost per unit amounts to several hundred or thousand per cent (that is, the cost of travelling between Manchester and London, relative to the price of the haircut itself ). With this sort of argument in mind, we could view the vast range of goods and services produced in a modern economy as spanning the whole spectrum from most to least tradeable. At one end would be homogeneous commodities with negligible transport costs (financial assets, tickets for rock concerts and so on) and at the other end would be personal services and real estate, with all other goods and services ranged somewhere in between these two extremes.
Now that we have examined in some detail a number of examples of the working or non-working of the law of one price in a closed economy context, moving over to the open economy will turn out to be quite simple.
2.2
The law of one price in the open economy
In this section, we have the task of answering the same kind of questions as in Section 2.1, with one vital difference. What if the two cities involved are not London and
Manchester, but London and New York? What changes have to be made in our conclusions?
There turns out to be only one significant change required and it will be encountered as soon as we return to our first example.
2.2.1
Example 1
The Michael Jackson concert again. An enterprising New York travel agent is selling tickets for the concert – mainly to attract customers for his cut-price trips to London. If you make him an offer, however, he will sell the concert tickets separately. How will the price that he can get for them compare with the price of £50 which rules on the free (that is, black) market in London?
The first and most obvious point is that, in the window of the New York travel agent, the price will not be shown in pounds at all. It will be in dollars, of course. We cannot directly compare the price in London and New York in the way that we could compare the price in London and Manchester.
Let us be a little pedantic about the reason why we cannot compare prices on opposite sides of the Atlantic. Strictly speaking, it is not just because the UK and USA are two different countries. It is because they use different currencies. Quite frequently there are situations where countries, for one reason or another, share a common currency, officially or unofficially.5Where two countries do indeed share a
common currency, we can compare prices directly and, for purposes of the law of one price, we may as well be dealing with a closed economy.
Where there is no common currency, however, we have to translate dollar prices into pound prices or vice versa, so as to allow us to make a comparison. It is a prob- lem familiar to anyone who has ever been on holiday abroad. Unfortunately for our purposes, holidaymakers often buy their foreign currency, traveller’s cheques and so on before setting out on their trip, so that they do not always see the connection between the two relevant prices: the price of the goods they buy abroad and the price of the currency.
Now put yourself in the position of an enterprising London ticket tout who has just heard from some American tourists that tickets are on sale at, say, $100 each in New York. Is it worth making a transatlantic call to order tickets for resale in London? For every ticket he wants, he will have to buy $100, then send the US currency to New York. Let us ignore transaction costs for the moment. ( When all is said and done, if it doesn’t pay to do anything when we ignore transaction costs, it certainly won’t pay when we take account of them!)
The best way to look at this deal is to regard it as involving what we might call a ‘compound purchase’: first, buy the dollars, then use the dollars to buy the tickets. In the closed economy context, we exchange domestic money directly for goods. When buying from another country, we first have to exchange domestic money for foreign money, then exchange the foreign currency for the foreign goods.
In this example, the price paid by the London tout for US dollars is, of course, the sterling/dollar exchange rate. For convenience, we repeat here our definition of the exchange rate:
2.2 The law of one price in the open economy 53
The exchange rate is the price of a unit of foreign currency, measured in units of domestic currency.
Remember from Section 1.1.1 that our definition reverses the way we are used to seeing the sterling exchange rate quoted. Instead of the dollar price of pounds (for example, $1.25 = £1), we are following the practice of most countries other than UK and USA, which is units of domestic currency per unit of foreign currency ($1 = £0.80 and so on).
The advantage of doing things this way round should be clear when we work our way through the arithmetic of our imaginary international arbitrage in concert tickets. Whenever you undertake a compound purchase, buying an item for cash, then using that item to buy a second, the overall price you will have paid will be the product of the two prices. In the same way, the sterling price that the London tout will have to pay for the New York tickets will be the product of the price of each dollar and the dollar price of the tickets.
Suppose, on enquiry, that the exchange rate turns out to be $1.00 = £0.80. In other words, the price of a dollar is 80p. Obviously, it will cost 100 times 80p (£80) to buy the $100 asked for by the New York travel agent for each ticket. The £80 is the result of the following calculation:
Sterling price of a dollar × dollar price of a ticket = sterling price of a ticket If we use the letter S to denote the exchange rate (remember that this is defined as the pound price of a dollar) and PNYfor the price in dollars advertised in New York, then the overall price to a Londoner is SPNY.
We have now found out how to translate foreign prices into domestic currency prices. To put it differently, we have converted ticket prices into a common currency. Sterling was chosen because we were putting ourselves in the place of a Londoner, who was only interested in his profits measured in pounds, for the obvious reason that almost all of his spending was in pounds. As will be made clear, we would reach exactly the same conclusion if we looked at things from the American point of view. You will be glad to know that we have now finished the most important task in this section. From now on, it will be downhill all the way. All we need do is apply exactly the same logic to our translated prices as we did in Section 2.1 to our UK domestic prices.
Will it be worth paying £80 for a ticket from New York? Certainly not – they can be bought for £50 in London, remember? What is more, as soon as New Yorkers find out that they are better off waiting to buy tickets when they get off the plane in London, the demand in New York will tail off. In fact, there is every chance that an enterprising competitor of our American travel agent will steal a march, by jetting over to London and buying a consignment to take back to New York. For each ticket wanted, the competitor will need to buy £50. Each pound will cost (1/0.80) = 1/S dollars that is $1.25. The total outlay will be: $1.25 × 50 = $62.50 per ticket. It fol- lows that, if we continue to ignore transaction costs, the competitor can afford to undercut the competition by $37.50.
We can shorten the story somewhat, thanks to our analysis of the closed economy example. At some point, it is likely that the forces of normal trade and probably of
54 Chapter 2 · Prices in the open economy: purchasing power parity
arbitrage as well will eliminate profit opportunities. This will have been achieved when the price in New York stands in such a relation to the price in London that, when translated into a common currency the two prices are equal: in other words, when the price in New York has fallen to just $62.50 (assuming the New York market is, in this case, negligibly small relative to the market in the UK, where the concert is actually taking place).
To represent the equilibrium symbolically, look back at Equation 2.1. Replace PBand PMby PLand PNY, the London and New York prices. Now, on the left-hand side we have the London price (in pounds). On the right-hand side, we must have the equilibrium New York price (in dollars) times the price of a dollar which is, $62.50 × 0.80 = £50.00, or PNY× S. For good measure we will add the transaction cost, C, just to remind ourselves that in practice there will be room for some divergence from the strict law of one price, so we have:
PL= SPNY+ C (2.2)
as our open economy version of the law of one price.
All the other points made in the closed economy example follow in obvious fash- ion. There is one significant extension that needs to be made, however, and it relates to the activities of speculators in the present context. It is simply this: if there are a significant number of tickets in the hands of New Yorkers, then the London specu- lator runs an extra risk, over and above the one borne by the speculator in a closed economy context. Not only must he gamble on the underlying demand for tickets, but he must also take a chance on the exchange rate. For example, suppose in the last few days before the concert, the dollar weakens (that is, the price of a dollar falls). Since that will initially raise the equilibrium New York price, it may damp down demand by Americans and reduce the total demand for tickets even although noth- ing has happened to affect the popularity of the concert itself. We shall not follow up the implications of this fact at the moment, although we shall have cause to refer back to it in Chapters 8 and 14.
We now proceed to examine the remaining examples from the previous section.
2.2.2
Examples 2 and 3
Let us take the two cases together, potatoes and umbrellas. Can we simply apply Equation 2.2, without further ado? Obviously, transport costs are likely to be even higher in an international than in an interregional context. Is that the only difference between the open and closed economy as far as this example is concerned?
It is not, because, in addition to the difficulties involved in trading goods within a country, there will usually be man-made, or rather government-made barriers to cross-border trade.
In the first place, there will often be tariffs, which are a barrier to trade that are familiar to most tourists under the name of customs duty. A general definition would be as follows:
2.2 The law of one price in the open economy 55
Nothing has been or will be said in this book about the method used to calculate the size of the tariff payable on goods. Suffice to say, the level of tariff varies with the importing country, the broad category of goods, sometimes also with the destination of the goods, as well as a host of other factors. The calculation is sometimes so complicated as to be incomprehensible to all but dedicated industry professionals. (An example of this occurs with the imports of wines and spirits into the UK.)
The question of the impact of a tariff on the price of a good is one that would fill several chapters in a history of international trade theory. For our purposes, we need only note that it represents another factor likely to drive a wedge between foreign and domestic prices. Strictly speaking, where it is levied at a flat rate per unit, it can be regarded simply as inflating the value of our transaction portmanteau term, C. More frequently, it consists of a more or less ad valorem tax, in other words, one levied in proportion to the price per unit.
In the case of agricultural products, particularly, there may be other barriers to international trade. Some countries impose quotas that are more or less rigid limits on the quantity of a good that may be imported or, occasionally, exported.
Furthermore, this is not all. If you try carrying potatoes through UK customs, you may encounter more problems than simply a slipped disc. There are actually prohibitions on bringing into the UK a variety of agricultural products, animals, domestic pets and so on. These non-tariff barriers, as they are called, are sometimes put in place in order to protect the health of a country’s human or non-human resid- ents. There are also restrictions on the import of manufactured goods of certain types: dangerous toys, weapons and so on, as well as on the export of strategic goods, art treasures and so forth. Often the restrictions amount to little more than red tape, especially for the large firms that conduct most of the world’s international trade. On other occasions, they amount to an intentional or unintentional trade blockage, designed specifically to prevent the law of one price from asserting itself in the way described in the closed economy case.6
We can conclude, then, that the simple relationship described by Equation 2.2 is likely to hold only as an approximation. It is a reasonably accurate one for some goods but a very distant one for others. If these are our conclusions with regard to traded goods, what can we expect of non-traded goods?
2.2.3
Examples 4 and 5
In the case both of housing and of services such as haircuts, the closed economy arguments apply with somewhat greater force. As with interregional trade, it would be overstating the case to argue that the law of one price will always be completely inoperative. For example, many UK estate agents advertise homes in foreign holiday resorts such as Spain, Florida and so on alongside their domestic properties. Now obviously a holiday home on the Gulf of Mexico is hardly a substitute for the typ- ical semi-detached house in a London suburb. Nonetheless, at the margin, it may well compete directly with a holiday home in a UK resort (fortunately, not everyone likes the sun!). These kinds of consideration may place a limit on the degree to which prices can deviate internationally, even for housing.
56 Chapter 2 · Prices in the open economy: purchasing power parity
Remember also that, in the case of so-called non-tradeables, the man-made bar- riers to trade such as tariffs, quotas, red tape and so on are often fewer than for tradeables.7That being the case, the only obstacles are usually the physical ones that
apply equally in a closed economy. It follows that the price of a service like a haircut in New York may turn out to be nearly as close to the price in London as it is to the price in Los Angeles.
In the end, the question of how closely the (international) law of one price fits the facts cannot be settled by theory. Ultimately, the answer can only be found by examination of the evidence, in other words by a careful comparison of prices of individual goods and services across different countries. The evidence will be dis- cussed later in this chapter.
It is worth finishing this section, however, with a warning about a specious argu- ment often encountered in discussions of the law of one price and, indeed, in many other areas far removed from international trade issues or even from economics. In the present case, it goes something like this: ‘It is a fact that only a tiny percentage of sales of this type of good (or service) involve exports (or imports). So, with no arbi- trage between the domestic and foreign markets, there can be very little relationship between prices at home and abroad.’
To see the fallacy here, imagine that the death penalty were introduced for the crime of drunken driving (as it once was in the USSR). And suppose that it worked. Now consider the following argument: ‘There were no executions last year, so the new “get tough” policy on drinking and driving must have failed completely.’
It is obviously nonsense. In the same way that the threat of the death penalty