DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES Globalisation as a ‘good times’ phenomenon: a search-based explanation

Globalisation is associated with long periods of sustained economic growth and credit expansion, whereas major recessions tend to lead to falling trade and protectionism. The sensitivity of trade to global economic conditions is not simply driven by policy: rather, in a model of costly search, rms who are engaged in a searching process are very sensitive to changing economic circumstances. In turn, this causes protectionism to be partly endogenous, since optimal noncooperative tari¤s can be high during periods when the sensitive, searching rms have exited the market. JEL classications: F15, F43.

Some of the features in Table 1 deserve special comment. In particular, the (not uncontroversial) con- clusion that more open, market-orientated economies experienced faster growth stands rather contrary to standard economic thinking. After all, standard textbooks would argue that, while trade is good for all economies taken together, in most circumstances it is in the individual interests of 'large'countries to impose a protectionist set of 'optimal'tari¤s on imports and exports, in order to improve their terms of trade 10 , so that there is a prisoner's dilemma situation, whereby the noncooperative outcome of tari¤-setting games is against the collective interest. By contrast, one might tentatively view the evidence of the last 20 years or so as suggesting that there is little evidence of a prisoner's dilemma: open trade policies, which favour a country's neighbours, also seem in many circumstances to serve its self-interest. This is a feature which I particularly wish to investigate: is there some characteristic of globalisation booms which leads to a convergence of country and global welfare-maximising policies, and, if so, does such a convergence break down during prolonged recessions or depressions?
In this paper, I link this, in particular, with point 3. -the high observed income elasticity of trade during the economic 'good times'. The starting point is that this high elasticity represents a footloose element of supply, which is explicitly linked to the dynamics of a search process, and which may be the …rst thing to be eliminated during an economic downturn. Once that footloose element is eliminated, the economics of trade protection are turned on their head -essentially, the prisoner's dilemma is returned.
I start by discussing the phenomenon of rapid trade growth in the good times -building on the ideas of existing papers by Ishii and Yi (1997), Rauch and Trindade (2003) and Rauch and Casella (2003) and Helpman (2002 and. In the rest of this paper, I start by outlining a partial equilibrium model of a single industry with two-stage production, outlining the di¤erence between growing and declining sectors and that between matched and searching …rm pairs. I then set up a three-phase time schema, whereby in phase 1 there is little trade, phase 2 sees globalisation and phase 3 sees an economic crisis. I develop an explanation of why optimal tari¤s will be low during periods of economic growth, but high during periods of economic slowdown, particularly when credit shortage is a contributory factor. Finally, the role of credit in maintaining international trust and multinational trade agreements is examined in more depth. 1 0 e.g. Gros (1987).
It has become a commonplace that costs of market entry impede global trading patterns, such that economic integration, even in the good times of the 1990s and 2000s, falls far short of what neoclassical theory would predict (Tre ‡er, 1995, Obstfeld and Rogo¤, 2000). Since this primarily re ‡ects limitations on the extensive margins of trade (in other words, the fact that most …rms do not trade most products internationally), this is widely explained in terms of a …xed cost of market entry (Tybout, 2002) -…rms need to make a particular level of pro…t in order to justify market entry, there are both selection e¤ects in favour of large and successful …rms (Bernard et al, 2007) and threshold e¤ects on entry. The latter, threshold e¤ect can also be explained simply in terms of a Ricardian model of comparative advantage (Yi, 2003): once trade costs fall su¢ ciently, the fragmentation of production becomes possible so that di¤erent stages can be carried out in di¤erent countries. Consequently, there is a rapid, nonlinear growth of market participation, particularly in terms of vertical tie-ups between …rms (Yi, 2003). In addition, where tari¤s are ad valorem, e¤ective protection against individual stages of production is magni…ed (since a tari¤ may be paid more than once, as the goods cross and re-cross borders), and the same applies to transport costs -so exaggerating the apparent price-sensitivity of intermediates trade.
Many of these arguments are often summarise as the 'new, new' trade theory -i.e. supplementing the models of Krugman, 1979 andHelpman, 1992, with the incorporation of …rm-level participation e¤ects and production fragmentation. These elements are now acknowledged to have powerful implications for growth through …rm selection, 11 distribution 12 and the observed volatility of trade. 13 By themselves, however, they o¤er only a partial explanation, containing no real evidence of the nature of the …xed costs of market participation, and under what circumstances they may become sunken rather than just …xed. To explain this, we need to turn to another branch of the literature -the evidence of informational barriers and a search process. This stems from stylised facts 5. and 6. in Table 1 : the high turnover of trading …rms (Besedes and Prusa, 2006)  (the noted example being surgical steel production in Sialkot, Pakistan). Informational barriers can generate a search process, and I argue that this process is a primary cause of threshold e¤ects, which in turn helps explain the dynamics of trade. 14 Search takes time and requires con…dence and the availability of credit. Critically, …rms need to incur a series of ongoing …xed costs during the search process, but once they eventually achieve a satisfactory match, the cost of the past search is sunken. This means that searching …rms will indeed be very sensitive to price movements, as in Ishii and Yi (1997), but that, as the search process goes on, …rms achieve matches and become more heterogeneous and less subject to threshold e¤ects.
This process indicates a sensitivity of trade during the process of globalisation to international traded prices, global aggregate demand and capital availability, 15 but the trading patterns of long-established …rms, which are likely to be much less sensitive, 16 and it is this nonlinearity -missed by the existing literature -which may underlie the danger of policy shifts during and after economic crises.
3 An illustrative model of …rm-level trade.
I set up a simple, stylised, partial equilibrium model of a monopolistically competitive industy in a twocountry world -the two countries being the North and the South, the former being characterised by higher skill endowments per head. The main market for …nal goods is in the North. Production requires two stages, which I name upstream (u) and downstream (d). Typically these are carried out by a pairing of …rms (which may or may not be vertically integrated by merger), where u sells a semi-…nished good to d, who then completes the manufacture and sells it on to …nal consumers. The two …rms are of equal size and ex ante expected e¢ ciency: however, productivity varies depending on the goodness of …t of the match, i . As in Rauch and Casella (2003) or Rauch and Trindade (2003), ; potentially follows a uniform, rectangular distribution between 0 and 1, and …rms do not know i before entering a match i, though they know its overall distribution. 17 Trade between the North and South develops over time. The historical setup takes three phases. In phase 1, trade costs are high, so that there is little trade, and most goods are produced by pairings of …rms type u and d within the North. However, the South is assumed to have a potential comparative advantage in upstream production, while the North has a comparative advantage in downstream production. We then enter phase 2: a period of growth and global integration, spurred by a technological or policy change reducing trade costs. Some Northern downstream …rms (though not all) will now search for upstream partners in the South. For example, garments might be manufactured by an upstream …rm in China, but according to designs from the downstream …rm in a Western economy, which then completes the marketing and distribution worldwide. Phase 3 represents an unanticipated crisis, where credit ceases to be available and growth stalls for a protracted period.
Concentrating on phase 2, the period of globalisation, the growth of the outsourcing trade is impeded by search friction deriving from an assumed need for at least one …rm to make a relationship-speci…c investment: in order to avoid a potential hold-up problem, 18 this generally requires a contractual relationship for at least some minimum period, which I characterise by a …xed contract period, t, during which the two …rms have an exclusive relationship.
Firms employ labour in the form of …xed and variable elements. The cost of the latter is normalised at C = C N for North-North pairings, and at C = C S (C S < C N ) for North-South pairings. The elasticity of substitution between …nal goods varieties is ", which will also closely approximate the own-price elasticity for the output sold by …rm pairings, at least as long as the number of …rms, N , is large. Sales by pairing i will equal where P is the CES aggregate price index. Pro…ts of the pairing, before subtracting …xed costs, will equal The model is driven by an assumed cost which is inversely linearly related to the quality of the match i match with the nearest. 1 8 See Hart (1995).
between …rms in pairing i. For simplicity, I concentrate on a rather stylised model where quality of match a¤ects …xed cost, rather than unit variable costs. More precisely, I assume that …xed costs are F i , so that pro…ts after subtracting …xed cost, Note I am also assuming equal Nash bargaining weights between the upstream and downstream …rms.

The matching process
We now want to look at the matching process in more detail. Appendix 1 explains the matching process in more detail. I assume …rms take a series of blind matches, where match quality, i , varies according to a uniform rectangular distribution between 0 and 1. Further, assume that …rms are stuck with an existing partner for a …xed contract period, t, during which time …rms face a discount rate r. Firm pairings are also subject to sudden, random death with a constant probability of d. For simplicity, I normalise the discount rate in terms of the contract period, de…ning the discount rate and depreciation rate per contract period, Note that the depreciation rate re ‡ects the probability of either …rm in a pairing dying during the contract period.
At the end of each contract period, the …rm may either stick with its existing partner (which it will do if match quality i exceeds a reservation match quality, R ), or else seek a new partner (which it will do if i < R ). Note that, as we have assumed a uniform, rectangular ex ante probability distribution of match quality, the probability that search will be renewed, after the initial match period will equal R : However, over time, the probability of not having found a successful match will decline geometrically. By noting that, when i = R , a pair of …rms will be indi¤erent between renewing search or staying together, we can derive the condition for equating discounted present value of searching and not searching, and so …nd a value for the reservation match quality. This can be shown to satisfy which is declining as or D increases.
From (8), we can conclude that, with zero discount rates and zero probability of …rm death (r = d = = D = 0), …rms will be in…nitely patient in their search, so that the long-run equilibrium is for all …rms to be equally and successfully matched. By contrast (and more realistically), with positive time preference, the long-run equilibrium has a uniform distribution of surviving matches, of quality ranging from R to 1, with pro…ts likewise varying. A consequence is that …rm pairings are heterogeneous in the long-run, both in terms of pro…ts and trade volumes, with heterogeneity increasing when long-run interest rates are higher or contract periods are longer.

The role of monopolistic competition
I assume there is free entry and exit into the industry. Consequently, the number of …rm pairings will vary, with competition forcing the industry aggregate price, P up or down so as to make the marginal …rm indi¤erent as to whether to enter or exit.
I focus …rst on an expanding industry. In this case, the marginal …rm is a new, searching …rm. The condition for determining the reservation match quality means that the expected present discounted pro…t of entering and engaging in a new search will equal that of a …rm in a stable match of quality R : where C m is the unit cost of the marginal pairing (so it will equal C N during the pre-globalisation phase 1, and C S during phase 2). In phase 1, all …rms have the same unit cost C m , and if we also note that the CES aggregate price where N is the number of pairings in the industry, then the initial number of pairings The basic situation is shown in Figure 1, below. Since unit variable cost with Northern pairings is 1, …rm pairs will supply at a price of Searching …rms will only engage in search if the price is at least P 1 : free entry will keep the price to this level, as long as the industry is not shrinking. Matched …rm pairings will also supply at this price, though most of these are intramarginal matches, which would continue to produce if the price were to fall (hence the upward-sloping supply curve for matched …rms). The number of …rms in the industry will satisfy (8), and also balance demand and supply at the price P 1 : I will denote this initial demand level for the industry's products as Y 1 .
If …rms were in…nitely-lived, the economy would tend towards a steady-state equilibrium where all …rms were matched ( i > R ). However, if proportion D of …rm pairings su¤er in a given contract period from one or both …rms randomly expiring, then there will be some new …rms entering and searching. In equilibrium, I denote the number of matched …rms in period 1 as N m1 and the number of searching …rms as N s1 . In the next contract period, proportion D of existing matched pairings will expire, while proportion (1 R ) of searching pairings will …nd established partners. In a static equilibrium, where N m is constant over time, If the number of …rms in the industry were growing at rate G, this would become This situation is shown in Figure 1, above. The price in equilibrium, P 1 , is given by the entry price for new, searching pairings. However, there is a kink in the supply curve, since searching pairings will all enter or leave the market at P 1 = P 1 , while matched …rms are heterogeneous in the price at which they would exit the market. The most e¢ cient …rm pairing would potentially leave the market at P 1 = P 1 , as given in equation (9). The ratio of searching to matched …rms in equilibrium is given by equation (10) or (10a).

Phase 2: The globalising economy
Now assume that trade costs fall, so that upstream production in the South becomes more competitive.
In particular, assume that unit variable costs, including trade costs, for a North-South pairing are C S , as opposed to 1 for a North-North pairing. However to enter the market, foreign …rms of type u have to engage in a costly search process, and so will only do so at a World reference price of at which a …rm in a reservation-quality pairing breaks even.
The e¤ect on existing North-North pairings is variable. The N S1 searching Northern pairings would not expect to break even at the new, lower price, and consequently will exit the market, except for a fraction who …nd their existing partners pro…table and become matched.
The N m1 existing matched North-North pairings are heterogeneous, since they vary in match quality between R and 1. The price at which a matched pairing of quality i will exit the market is given by The last …rm will exit when I assume North-South pairings are not su¢ ciently low-price to drive the price down to this level. At price P 2 ; the proportion of …rms in existing North-North pairings which will continue in the market is which is declining as C S falls. Output of these pairings will also be lower than before the start of globalisation by proportion ( ) " , since the industry aggregate price has fallen. However, total industry output will be higher, due to the fall in prices: I denote the own-price demand elasticity for the industry's output as ; so that The residual will be made up by new, North-South pairings. Initially, these will be searching, but over time, in a model with static overall demand, the proportion of these still searching will decline, as some gain matches, until eventually the ratio of searching to matched pairs among the North-South pairings will equal that in equation (10). (foreign) pairings are prepared to enter the market at price P 2 , which is lower than P 1 ; but assumed to be above P 0 1 . Consequently, all North-North (domestic) searching pairings exit the market, as do some matched North-North pairings. Once some North-South pairings …nd successful matches, the result is a supply curve with three segments (i.e. two kinks). First, between P 0 2 and P 0 1 (the left segment), only the most successful North-South pairings will be prepared to supply. Between P 0 1 and P 2 we are summing horizontally the supply curves of North-North and North-South matched pairings, so the gradient is somewhat less steep.
Finally, when the industry aggregate price, P = P 2 , there is a horizontal segment made up of searching North-South pairings.
The kinks in this supply curve are an important element in explaining the di¤erential e¤ects of economic shocks, and the potential change in policy following such shocks -as explained in the subsequent sections.   5 The impact of a negative economic shock

A demand shock
We now want to conside the e¤ect of shocks to an economy which has been undergoing the process of globalisation (in the sense of entry by searching foreign upstream …rms, and the gradual development of successful, importing partnerships). Take the situation in Figure 2, and assume that there is a sudden inward shift in the demand curve, caused by a recession. The situation is shown in Figure 4 : essentially, searching foreign …rms are footloose, and will simply exit the market at the end of their existing contracts (except for the minority who …nd pro…table contracts). This is a component of import supply which is very sensitive to demand changes. Consequently, unless the demand shock is very large, it can be accommodated simply by the exit of these …rms: the remaining foreign and domestic …rms see very little change in their demand or prices. Only larger shocks will force established …rm pairings back down their supply curves. Note that, at the point where searching North-South pairings have been eliminated, the elasticity of imports with respect to the industry aggregate price falls from in…nite to " R ; and continues to rise thereafter, as more …rms are driven out.
The situation with a larger negative demand shock is that, only after seaching …rms have been eliminated will prices be driven down. At this point, existing domestic pairings, as well as established importing pairings will be faced with falling prices, and the least e¢ cient will be eliminated (so driving the …rms down their supply curves). This is shown in Figure 5, below. Note that an implication is that the …rst …rm pairings to exit the market are searching, North-South pairings, so that trade is especially vulnerable to a medium shock. In the larger shock in Figure 4, matched North-North pairings will exit faster than matched North-South pairings in the ratio

A credit shock
A credit shock is somewhat harder to model -particularly where it results in shortages of cash, rather than a rise in headline interest rates. Nevertheless, I will assume that …rms suddenly face a rise in risk premia on their interest rates, so that the interest rate per contract period rises to 0 > : I consider the unlikely phenomenon of a pure credit shock (one which a¤ects supply, but does not result in a recession shifting the demand curve inwads). It is worth noting that this type of shock hits di¤erent …rms disproportionately. In particular, by raising the de facto interest rate facing …rms, a credit shortage will make the search process costly. As a result, the reservation match quality will fall (…rms will accept lower-quality reservation matches than previously, when they were more patient). The implication of this is that the reservation match quality falls to However, since the reservation price which overseas …rms type u will demand in order to enter into search ; this will now be higher than previously. However, while the supply price of searching …rms is raised, the supply curves of established …rms are unchanged. Figure 6,. below, shows a pure credit shock, just su¢ cient to drive searching foreign …rms out of the market, while raising prices at home (hence leading to established domestic and foreign …rms supplying marginally more than before). Note that the price does not rise as far as P , so that search is halted entirely in the short/medium run. 19 Existing …rms can supply somewhat more than previously, as the market price, P ; rises, in accordance with equation (1). However, new …rms cannot enter unless the price rises to P , so below that level supply is relatively inelastic. In reality, we should perhaps consider that, at least in their initial stages, credit shocks are usually associated with demand shocks as well. However, in both cases we should note that it is the searching importing …rms (and their domestic partners) which are the most sensitive to macroeconomic shocks: established pairings, whether domestic or international, are far more robust.
The conclusion should be that, in the event of a combined credit and demand shock hitting an economy which had been undergoing a process of steady growth and increasing trade openness, there will be a relatively large proportion of trading …rms and their partners (as implied by equation (15)) which will exit the market relatively quickly.
One should perhaps not be surprised by this …nding. Trade search can be viewed as a kind of capital formation, with …rms prepared to undergo losses in the early years of search, in order to make an expected positive return thereafter, once they are established. Like any form of capital formation, we would expect search capital formation to be sensitive, both to changes in the cost and availability of credit, and to accelerator-type changes in overall demand growth. That is what this model indicates.

Endogenous policy responses to a boom or a shock
We have so far established that, during a globalisation boom, where demand and imports are rising fast, there will be at any one time a relatively high proportion of trade which is accounted for by searching …rms, whose presence in the market is footloose, and who are vulnerable to either demand and/or credit shocks.
This, by itself, implies that the globalisation process can be suddenly halted by unexpected shocks, regardless of any policy response. Moreover, since search is necessary for the long-run growth of trade, a shock may have a prolonged negative impact upon trade.
We now want to consider how trade policy might respond to economic circumstances, given a search model, where di¤erent components of foreign supply di¤er greatly in terms of their price sensitivity. Figure 7, below, shows schematically the e¤ects of imposing a tari¤ on an economy with a large amount of initial importers who are searching (and hence price-sensitive). The elastic portion of the supply curve, accounted fo by the initial searching importers, means that a tari¤ has to be substantial before it can begin to lower the import price. Consequently, the transfer from foreign …rms to the government imposing the tari¤ (area D) is small relative to the loss of domestic surplus (A+B+D), and it is highly unlikely a non-zero tari¤ can improve national welfare. Now compare this with …gure 8, where there are no searching …rms initially. In this case, it is relatively easy to set an optimal tari¤, which improves national welfare by forcing down import prices. The implication is that there is likely to be a discontinuity in tari¤-setting: when the sector is shrinking, or growing slowly, optimal tari¤s are positive, while, when the sectoral rate of import growth exceeds a threshold rate, optimal tari¤s fall to zero.
The analysis here is somewhat simpli…ed, since in reality one needs to consider tari¤s in a dynamic setting. In due course, even with a tari¤, the natural death of existing matched …rms will lead the economy back to a position where searching …rms begin to reenter the market -under some circumstances, we would expect this to lead to a cycle of optimal tari¤s over time. Nevertheless, the situation with stalled growth indicates a signi…cant di¤erence between eras of prolonged trade growth, where protection is not favoured, and eras of stagnation, where it is.

Return of the Prisoner' s Dilemma in trade liberalisation?
The title of this section is deliberately somewhat provocative. Trade liberalisation is often portrayed as a prisoner's dilemma situation: liberalisation bene…ts countries collectively, but large countries, individually, have an incentive to cheat and impose optimal (terms-of-trade-improving) tari¤s.
The argument of this paper is that, in a rapidly changing, globalising world,. the incentives to impose protection in this way would be greatly reduced by the presence of a relatively large share of footloose trade, associated with searching …rms. In such circumstances, the incentives of individual countries are not far out of line from those of the global economy, which bene…ts from free trade.
This conclusion might raise some eyebrows: few involved in trade negotiations over recent decades would argue that they were pushing on an open door (as the failure of the Doha Round talks indicates). Nevertheless, trade liberalisation has undoubtedly made substantial strides -particularly with respect to developing countries abandoning previous autarkic developmental strategies, but also in terms of successive rounds of tari¤ reduction by the advanced countries. Perhaps most signi…cantly, where protection has been maintained, or liberalisation has been resisted, the reasons have tended to be argued in terms of distributional impact, or in terms of damage to countries within trade blocs which were dependent on trade diverted from poorer countries outside the bloc (for example, Portugal or Italy resisting EU liberalisation of textiles and footwear industries). In general, the argument that high tari¤s bene…t national income -at least, when based upon terms of trade arguments -has rarely been used. An exception may be in agricultural commodities.
Part of the reason may be a trend towards accepting that the price elasticity of demand for traded commodities is perhaps higher than we used to think -for example, Anderson and van Wincoop's (2004) survey cites elasticities of between 5 and 10 for many commodities: a far higher number than traditionally used in Armington CGE models of the 1980s and 1990s. These higher trade elasticities are seen as …tting the data because of Ricardian, …xed-factor elements in trade, 20 including …rm heterogeneity, which mean that supply elasticities are reduced. However, a search-based interpretation would say that supply elasticities di¤er considerably ex ante and ex post, and that expanding supply may be more elastic than contracting supply.
In addition, the recent wave of globalisation has essentially involved connecting a large workforce in China, India, Asia and Eastern Europe to global markets from which they were previously isolated by autarkic policies and/or by their location in pre-industrial societies. The supply of labour to the globalising cities of Asia has been elastic at a low wage, so ensuring that, once search and other capital costs are met, there is an elastic supply of unskilled labour-intensive goods, meaning that optimal tari¤s for large, advanced countries are likely to be much less than at some other stages of global development. 21 2 0 Eaton and Kortum, 2002. 2 1 The situation described here in some ways mimics Sir Arthur Lewis's model of the development of trade, whereby large A prolonged global recession -perhaps especially one where credit is short -is likely to change this situation for the worse (as memories of the 1930s indicate). In terms of the very schematic analysis of this paper, we are moving from the situation in …gure 6, where there is a substantial volume of footloose trade, to that in …gure 7, where the supply of price-elastic, searching trade is insu¢ cient to maintain the incentive to keep tari¤s low. In such a situation, the interests of individual countries (which may wish to try to manipulate their terms of trade by protection) and those of the global economy are no longer aligned, hence raising the risks of triggering a round of beggar-thy-neighbour policies. Given the recent advances in understanding the interaction between trade integration and growth, 22 there must be a danger that protection could trigger a self-perpetuating circle, whereby trade growth is reduced, increasing incentives to protect.
A secondary element, which must be of particular concern when countries are credit constrained, is the potential e¤ect on the stability of existing agreements, where these are sustained by the threat of retaliation in a trigger strategy. Such a strategy depends upon people weighing the loss of future welfare, from the collapse of trade agreements, more highly than the short-term gain from imposing a terms-of-trade-improving tari¤.
Again, if credit constraints shorten national time-horizons, the prisoner's dilemma will be restored.
In sum: the recent wave of globalisation has been sustained and strengthened by the coming-together of national and global interests, when trade is relatively footloose and credit is available. The removal of those conditions, once a shock drives out the more price-elastic elements of trade, creates a totally new set of incentives, where national interests are to protect, yet the global interest still requires a liberal trade regime.
If cooperation is allowed to fall, it may be very di¢ cult to restore global trade to its recent Golden Age.
supplies of Indian and Chinese labour in the late 19th and early 20th centuries pushed down prices of unskilled-intensive commodities. Ironically, this led Lewis towards pessimism about export-led development in developing countries, on the grounds of elasticity pessimism. 2 2 Not just the standard comparative advantage e¤ects, but the pro-competitive, choice-widening and scale-exploiting e¤ects identi…ed by the New Trade Theory (Krugman, 1979), as well as the …rm selection e¤ects of the New New Trade Theory (Melitz, 2003). The starting premises of this paper -that search costs, even in phase 2 of our time-schema, maintain trade at below the level which would be favoured in the presence of full information, rather emphasise that trade-impeding policies will push the World further from optimality.

Appendix 1: The matching setup
The paper follows Rauch and Trindade (2003) and Rauch and Casella (2003) in using a matching framework based upon Salop's circular cylinder (note that Grossman and Helpman, 2002, use a similar setup). This is shown in Figure A1, below. Position on the circle refers to some …rm-speci…c characteristics. The essence of the Salop model is that …rms are ex ante equal in e¢ ciency, but that …rm performance is determined by the degree of …t with the match partner: the aim is to match with a …rm directly opposite on the cylinder. Hence, match quality, i ; is measured by the circumference distance between the two …rms. Firms only have a single partner at any time. The key di¤erence between the match-searching model employed here and the models in the earlier papers is the ability of a …rm in an unsatisfactory match to renew search, after a given contract period. This determines the generation of a reservation match quality, R : The decision process of the …rm is shown in Figure A2 below. Any match with a circumference length greater than R will yield a pro…t great enough for the …rms to choose to continue. This gives a probability of acceptance of 1 R . However, of these pairings, proportion D will naturally expire anyway during the …rst contract period, so any surviving …rm will have to renew search. By contrast, proportion R of initial pairings will be unsatisfactory, and be dropped after one contract period.
We note that the pro…t of a reservation quality match ( i = R ) is zero. Pro…t increases linearly with respect to match quality, so that the expected pro…t of a successful match (where R < i < 1) is 1+ R 2 minus the pro…t of a reservation quality match. This yields an expected pro…t of 1 R 2 : Likewise, an unsatisfactory match qill have an expected pro…t of R 2 : Finally note that a renewed search will yield a present discounted value of zero. We wish now to solve this problem, based upon the knowledge that monopolistic competition will equate the expected return from entering a search process to zero.
Discounted pro…t with a successful match = one period expected loss with a poor match; (1 R ) 2 2 = 2 R