Law of One Price and Purchasing Power Parity

Introduction
The gradual emergence of globalisation in businesses has contributed towards a significant rise in international trade. Consequently, trading across countries has been prominent among businesses in order to seek higher growth opportunities available in the international markets (Michie, 2011). “Our willingness to pay a certain price for foreign money must ultimately and essentially be due to the fact that this money possesses a purchasing power as against commodities and services in that country” (Gustav Gassel, 1922). The applications and conversions of currencies have become vitally important in international businesses in order to obtain or forecast the substantial costs and revenues for the purpose of financial information. The concept of Purchasing Power Parity (PPP) enables one to forecast the exchange rate of two different countries based on the assumption of similar purchasing power under law of one price of two countries’ currencies. However, various crucial obstacles have been encountered in real life despite the concreteness of the proposed theories and one of the projected main concerns is to determine the price for a similar product across different markets and continents (Wang, 2009). According to the theory of Purchasing Power Parity (PPP), one currency should be able to buy the same amount of products which can be purchased from other currencies. This concept suggests that the currencies should be valued in a way that it allows consumers to buy similar quantity of goods irrespective of the currencies that they utilise in making purchases (Manzur, 2008). According to the Law of One Price (LOP), consumers should be able to purchase similar or same kind of goods at the same price despite the utilisation of different currencies. Nevertheless, the application of LOP is considerably difficult and would not prevail in certain predicaments across different economies and countries despite the supportive underlying theories (Mezzera, 1990).

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Conceptual Understanding of Law of One Price and Purchasing Power Parity
Law of One Price and Purchasing Power Parity play a crucial role in determining the international trade mechanism. The concept of LOP indicates that the price for homogenous goods and services should be the same despite all locations. The theory behind LOP is established through the equilibrium pricing of a product. The equilibrium market price of a product is achieved when market participants realise the different pricing for an identical product in different locations, (assuming no transaction costs and other trade restrictions) and take advantage of the arbitrage opportunities. The principle of LOP is highly justified because differences in the price of the same products in two different markets would create the perfect opportunity for arbitragers to benefit by purchasing products in a lower priced markets and selling them in markets where there are sold at a higher price. The transactions among market participants create pressure through demand and supply effect in the two locations and would substantially eliminate such opportunities and hence create an equal and transparent price. As a result, the price for the same commodity traded in two different markets should be same if they are converted into a common currency (Ignatiuk, 2009). The concept of LOP asserts that if same goods enter each country’s market basket, the PPP exchange rate should prevail between the two countries to maintain the principle of one price despite the difference in currencies (Eicher, Mutti and Turnovsky, 2009).
The Law of One Price (LOP):
Pd=S*Pf
Pd is price of the good in the domestic economy whereas Pf is the price of the good in a foreign economy and S* is the nominal exchange rate between the two economies. The concept of Purchasing Power Parity (PPP) implies that the nominal exchange rate between two currencies should be equal to the ratio of aggregate price levels between two countries. This will create the similar purchasing power of one currency as compared to that of another. Therefore, according to PPP, exchange rates need to be adjusted between countries so that the exchange can be made equivalent to each currency’s purchasing power. The question arises immediate as there are two possible ways that PPP would hold to create the perfect equilibrium. Absolute purchasing power parity relates to the circumstances when the purchasing power of a unit currency is converted into foreign currency at the exchange rate in market, it is directly equal in the domestic and foreign economy (Taylor and Taylor, 2004). However, it is relatively hard to estimate the amount of identical goods in the baskets of the two different countries. Hence, it is more occurring to test relative PPP, which implies that the percentage change in the exchange rate over a given period just offsets the difference in inflation rates in the different countries over the time horizon (Taylor and Taylor, 2004). Therefore, if absolute PPP holds, then relative PPP must also hold, but if relative PPP holds, there is a probability that relative PPP might not hold as it is possible that at different levels of purchasing power of the two currencies, there are changes in the nominal exchange rates possibly due to the transactions costs (Isard, 1977). To consider whether the theory of perfect commodity arbitrage applies in the real world to create the law of one price, consider Figure 1 and Figure 2 which illustrate the notion of absolute PPP and relative PPP. For the relative data demonstrated in both the figures, it is evidently clear that neither absolute nor relative PPP seems to hold reasonably in the short run, thus does this imply that PPP does not hold in real life? According to the perfect commodity theory, equilibrium will appear and restore the differences between the relative prices which is clearly proposed by the principle of LOP by adjusting the exchange rates for the two locations. Hence, as far as this is concerned, perfect commodity arbitrage guarantees that each good is uniformly priced even with the initial difference of transaction costs between similar products in different locations, thus within a period of time in the long run,, the prices are adjusted to establish the perfect equilibrium of LOP, ensuring the same purchasing power in terms of currencies under the influence of PPP (Isard, 1977). Nonetheless, where does all the disputation arise concerning the practicality of LOP and PPP in reality?

Analysis of the Proposition
“In the assumed absence of transport costs and trade restrictions, perfect commodity arbitrage insures that each good is uniformly priced (in common currency units) throughout the world – the “law of one price” prevails’. In reality the law of one price is fragrantly and systematically violated by empirical data” (Isard, 1977). It is undeniably true that in the presence of perfect commodity arbitrage, each good will be substantially priced accordingly to demand and supply pressure in the assumed absence of transactions costs. However, the immediate response to this is that how practical and realistic is the assumption of transactions costs applicable to the principle LOP in order to create the exchange rate in PPP?
The concept of LOP indicates that the prices for the identical products are the same across two countries, but this has not been the case in actual situation proposed by numerous scholars and researchers. The principle of LOP has been violated in actual practice and this has been supported by explanation that the transaction costs make it difficult to ensure same price for the identical products in two markets by creating a restriction in the equilibrium flow of the commodities known as the “border effect” (Rogoff, 1996). The transactions costs consist mainly of tariffs, taxes, duties and non-tariff barriers costs. For instance, the commodity that is priced lower in one market would involve transaction and transportation costs for participants to trade them in another market, and this will constitute to the additional costs of the commodity (Bumas, 1999). The volatility in the price differential would be progressively higher if the difference between the two countries is large. In addition, the transportation costs will increase due to the driving supply of arbitragers participating to transfer the commodity from one location with lower price to another with higher price, and the resulting impact would be differences in price disrupting the adjustment of arbitrage equilibrium (Clark, 2002). The study by Engel and Rogers (1996) have indicated that the price differential is greater in case of greater distance between the cities concerned, and it leads to substantial increase in the prices when they are compared in different countries proceeding to different continents.
Furthermore, single or identical consumption of goods common to everyone is highly unrealistic because different consumers from different locations will have different preferences and choices, and it is always very difficult to have the same proportion of commodity identified in the comparing countries’ consumption basket (Clark, 2002). There is no guarantee that all commodities are traded between international economies and relatively to domestic economies, there are always substitutes in products if level of competitions is high but most of the cases, more differentiated goods are available compared to the product substitutes (Kim and Ogaki, 2004). Hence, when all these circumstances applied, the proportion of consumption from different locations concerning identical commodities in aggregate price indices will vary across countries.
In sum, trading goods are more accurate drivers for the estimation of PPP compared to non-trading goods. This is because non-trading goods circulate within the domestic economy of that country and does not cross the barrier beyond international trade which involves additional transactions costs. Non-trading goods are more confined within the domestic economy compared to trading goods which are more expressed in exchange rates term when they are traded elsewhere around the world contributing towards the credibility of PPP. Hence, it is more useful to test with producer price index rather to use the consumer price index as suggested by the graphs in Figure 1 above. There is shorter deviation of PPP in producer price index compared to consumer price index in the short run from both the graphs. Hence, it often suggested that the PPP theory of exchange rates will hold at least approximately because of the possibility of international goods arbitrage. However, in real life, the practicality of PPP is disclosed to a visible amount of subjectivity and uncertainty as to which product is categorized as trading or non-trading goods, if identified, will it be the same around the world for the comparison of prices? Non-trading goods in UK might not necessarily be identical in US where that particular product might be a trading good for US instead and will this affect the producer price index, what about the LOP? To conclude the theory of PPP, there are definitely dreadful amount of assumptions underlying it to support its application and reliability. In real life, do all these assumptions prevail?
Let’s examine and explore the credibility of the assumptions mentioned above by analyzing the Big Mac Index created by The Economists in 1986. As far as we know, Big Mac is a hamburger available from Macdonald’s Restaurant, the world largest fast food chain. What happens is that the price for a Big Mac in one country is divided by the price of a Big Mac in another country (both in domestic price) to obtain the Big Mac PPP exchange rate. This value is then compared and analyzed with the actual exchange rate in the market. The aim of this discussion is to determine the practicality of Big Mac index in real world in relate to the assumptions of PPP. The limitations are closely related to the assumptions mentioned above:
•It is not possible to have the same price of a Big Mac from all around the world (results from the diagram below) due to different government tax policies, levels of competition and different transaction costs such as rental for different locations not just within particular area of a city, as well as different countries and continents. This will certainly add up to the costs of a burger and disrupt the notion of LOP.
•Being the world’s largest chain of hamburger fast food restaurants, certain products need to be imported or exported by franchises all around the world to maintain the uniformity and the quality of the world’s prominent restaurant and this will certainly contribute to the different costs of the product disrupting the free movement of goods across borders.
Source: Big Mac Index, The Economists 2013. Available at: http://www.economist.com/content/big-mac-index

Furthermore, the assumption of single consumption is not possible in many countries, for instance, eating in McDonald’s Restaurant in some countries is relatively expensive compared to others and consumers would prefer eating in local fast food restaurants instead as a close substitute at a lower price.
In addition, the demand for the consumption of Big Mac varies across different countries and this will not create an equal proportion of commodities in different countries’ basket. For example, buying Big Mac in China is not as high demand as buying Big Mac in the United States.

The assumption made by PPP is highly unrealistic due to the disruption theory of LOP as it is not possible to have one common currency price for the same product demonstrated using the study of Big Mac Index. A similar investigation has been conducted by Haskel and Wolf (2001), they explored the deviations from the LOP by making use of the retail transaction costs in IKEA, a multinational Swedish furniture company. In performing the case study, samples were gathered comprising of 100 identical goods sold by IKEA in 25 countries. The outcome of the study indicated that there are significant common currency price divergences across countries for a given product.
Conclusion
In conclusion, according to PPP theory, the exchange rates should be adjusted in a manner where equal purchasing power is established with respect to a commodity in two markets. In the real world, this is highly unachievable and it is rather unrealistic to the extent that there is always difference in prices of the same goods. However, this scenario might contradict with the results and findings from Figure 1 and figure 2 as both the figures proposed that in the short run, PPP does not hold, whereas in the long run, the law of one price will prevail and PPP is therefore determinable. In practical applications this seems rather convincing as due to the matter of time, equilibrium will kick in and adjust the prices accordingly to the LOP. Nonetheless, one question still remains unanswered, how far can the LOP brings us towards the validity of PPP and determining the exchange rate between two countries? How certain are the assumptions of PPP on the data and findings by researchers and scholars influence the outcome of the actual results obtained? As mentioned by Keynes (1923), “At first sight this theory appears to be one of great practical utility. In practical applications of the doctrine there are, however, two further difficulties, which we have allowed so far to escape our attention”. According to Keynes, the first difficulty is to make allowance for transport costs, imports and export taxes. The second difficult refers to the treatment on purchasing power of goods and services which do not enter into international level of trade. In sum, the theory of PPP derived from LOP is useful in theory for product pricing and the determination of exchange rate currencies, but as far as the limitations mentioned above is concerned, it should sensibly be considered as a guidance only rather than a direct application in real world.
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