The Brander-Krugman model, also known as the reciprocal dumping model, talks about the likelihood of international trade in a homogenous good. In doing this, it raises an interesting issue: is this apparently pointless trade socially beneficial? In the mean time, Corden developed a more realistic traditions union (CU) theory compared to orthodox theory by soothing the assumption of constant marginal costs (MC). As the framework of these two models are similar, their conclusions are incredibly different, the reason why that are discussed further below.
Both models are set in a incomplete equilibrium framework; the costs of most substitutes and complements of the nice involved are assumed to be constant, as are the income levels of consumers, allowing for an easier evaluation of welfare benefits from the formation of the traditions union (CU).
Within this framework, there is a single company in each of the CU countries that produces a homogenous good. The other similarity between your two models is that the tariffs placed and confronted by both countries (Home (H) and Spouse (P)) before CU creation are similar. Thus, when the union is created a Common External Tariff (CET) already is present. Corden evolves his model in further periods to add made-to-measure tariffs so that the CET needs to be set upon CU formation. The assumption is that this will be place lower than the initial tariffs that were imposed.
The countries forming a CU in Corden's model are small relative to all of those other world (R), implying that its formation will haven't any influence on world prices. In the Brander-Krugman model, all three countries (R is displayed as one country) are equivalent in size.
Symmetry is assumed between the businesses in the Brander-Krugman model therefore the firms in each of the countries face the same constant marginal cost and home demand functions, contrary to Corden.
Corden relaxes the assumption of frequent marginal costs (MC) that is presented in orthodox customs union theory, and assumes instead that the companies benefit from internal economies of scale and therefore face declining marginal and average cost (AC) curves. Number 1 demonstrates the least point of the organizations' AC curves is above the purchase price paid for imports (pm). Hence a tariff is essential to protect local production, which is set at T- pm and prevents R from importing to H and P. The home price being equal to the firms' AC, they operate at a normal profit. The price received for exports (px) is assumed to be less than pm as H and P also face tariffs. Therefore, their AC is higher than px and so they cannot export their goods either. Thus, unlike in the Brander-Krugman model, there is absolutely no international trade prior to CU creation.
The main attribute of the Brander-Krugman model is usually that the firms display Cournot behavior - the firms make decisions about their own result levels to increase their profits assuming that the output degrees of the other providers will not change. This isn't necessarily the situation in Corden's model.
The presence of interior economies of level in Corden means that efficiency and welfare increases could be increased if an individual firm raises its output and catches both markets following CU creation. This, combined with the assumption that the organizations face different cost functions, contributes to the final outcome that the organization with the bigger AC will leave the market and import the nice from the company that can produce it at a lower cost (this article will assume that the partner firm exits the market). The assumption that the partner firm run at a standard profit pre-CU reveals that there will be no loss of producer surplus no welfare reduction in P as it exits the market.
Conversely, the symmetry between your organizations in Cournot means that neither firm in the CU has a cost advantage on the other. Thus, both the home and spouse countries reap the benefits of CU creation by increasing trade with each other, resulting in an increase in outcome for both companies (Appendix, equation (1)). Although H and P have increased their overall productivity, the quantity they supply in each of their domestic markets lessens (equation 2).
Although there is an overall gain in welfare in both models as a result of CU creation, the source of the gains differ. Both the home and spouse countries experience a welfare gain from CU creation in Cournot given the symmetry, whereas only the house country benefits in Corden as the partner firm exits the marketplace.
In Cournot, the price falls in the marketplaces (formula 3) and so the welfare gain is largely reflected by an increase in consumer surplus (formula 4) in both home and partner marketplaces. The countries also lose welfare through a show up in tariff income (formula 5) and the organizations' earnings may go up or fall depending on elasticity of the aggregate demand in the CU (formula 6). However, H's overall welfare gain is been shown to be always positive (equation 7).
In Corden, the assumption that the home and partner countries are small compared to the remaining world implies that the CU companies are not large enough to compete with the outside firm and then the CU formation will not affect world prices. This, along with the assumption that the remaining organization within the CU maximises his profit by charging right up to the 'import-preventing' price, which is the planet price plus the CET, means that the purchase price will stay unchanged. Thus, the increased welfare is due to an increase in the remaining firm's developer surplus (body 1, a+) as the show up in average cost (to J, figure 1) is not transferred onto consumers. However, if made-to-measure tariffs are assumed and the CET is lower than both initial tariffs, a price decrease will be induced in both countries and some of the welfare gain will be transferred onto consumers.
The symmetry in Cournot and differentiation in Corden also lead to different conclusions with regards to the impact on the rest of the world.
In Corden, the CU formation does not impact R's welfare under the assumption that there is no international trade pre-CU and there continues to be none of them post-CU. In Cournot, the semester in R's result (equation 8) and the price drop in H and P impact adversely on the R firm's revenue (equation 9). As consumption and imports in R continue to be unchanged, R's welfare is reduced.
The main assumptions that lead to different conclusions are those of symmetrical costs in Cournot and differentiation in Corden. This impacts how the welfare benefits are divided amidst the countries as well as that they are split between the manufacturers and consumers.
In speaking about the appropriateness of the models to the European union situation, the relevance of the assumptions and the expected results, and the way the factors behind these results equate to reality have to be considered.
There are many studies that analyse how European union integration has affected trade moves in conditions of trade creation and trade diversion. Trade creation is defined as intra-EU imports exchanging domestic creation; trade diversion as European union imports swapping imports from the rest of the world.
By 1992, bilateral trade between any two EC countries was 65% higher than if the EC had not existed, assisting both models' predictions that trade between your home and partner countries boosts.  Over the time from 1959/60 to 1977, which includes both phases of integration for the EC and EFTA countries, twelve-monthly trade creation was approximated at $20-31 billion and trade diversion at $5-8 billion.  This affirms the Cournot prediction that the spouse organization would increase its imports to the house country at the trouble of both domestic development and imports from all of those other world.
A analysis by the Sole Market Review on the impact of the Single Market Program (SMP) on trade creation and trade diversion provides detailed insight into the relevance of the Corden and Cournot models to the EU situation.  Its data and analysis focuses on companies within the developing sector, particularly the 15 industries that were apt to be particularly hypersensitive to the SMP. 
Although there are some industries near perfect competition with a attentiveness proportion of 0. 00 or 0. 01 - such as clothing and boiler making - most business within the EU are relatively oligopolistic relating with their average attentiveness ratios.
The assumption of perfect information is improbable to hold true. In lots of economic ideas where this is assumed, it is highly unrealistic, especially with regards to the reactions of a firm's opponents to the union formation.
While Cournot assumes that businesses face a regular MC, a 50% decrease in result from the least efficient range of output resulted in an increase in AC, and therefore MC, in all the business analysed, thus indicating the occurrence of economies of level.
The assumption that firms display Cournot behaviour will not always maintain in the framework of the EU. Through a assessment of the changes in the price-cost margins and in the house firm's market share in the domestic industry, it is noticeable that market sectors reacted in two completely different ways. One group, including office machines and pharmaceutical products, experienced large cuts in their price-cost margins and a relatively small change in their market share, while the contrary is the situation for the other group. It would appear that the first group decided to reduce its prices instead of losing market show, implying that some firms do not contend on outcome but on price. However, the effect of changes in competitive behaviour by businesses on market shares was extremely small for most business and countries, though it was usually more important in the smaller European union countries.  Thus, changes in firms' behavior are relatively insignificant in impacting market shares, in comparison to other factors.
The assumption of symmetrical organizations is, again, an unrealistic one. Given that the united states sizes within the EU are incredibly different, it is highly likely that companies across the EU confronted different market sizes and domestic demand functions before integration, and as a result, they are improbable to be the same size or have the same cost functions.
In conditions of the impact of the CU creation on the market sectors, the majority of the results expected in Cournot carry true from 1900-94, the period reviewed in this SMR statement.
The price-cost margins in the 15 'hypersensitive' industries fell by an average of 3. 9%, while they fell by 3. 6% in the processing sector all together. The extent of this drop in each industry depends on the behavior of the businesses.
The impact of the SMP on the particular market stocks in the developing sector as a whole is negative for the house business, and positive for both EU and all of those other world's market shares in the home country. Cournot's model properly predicted that the house organization would sell more while the partner organization would sell less in the house market. However, it predicts that the rest of the world's share of the house market would fall. The SMR completed two ex-post simulations; one with no direct external trade effects and one with. All of Cournot's predictions regarding changes on the market shares maintain true for the previous simulation. However, the second option simulation is more exact in reflecting the genuine changes in market stocks which were experienced over this integration period. Therefore that the Cournot model will not look at the increasing liberalisation of external trade over this period that also resulted in a reduction in extra-EU trade costs, either therefore of the CU creation or scheduled to increasing globalisation.
In conditions of welfare, the changes support Cournot's prediction that welfare increased in both H and P. The change in welfare assessed as a percentage of GDP was higher than the percentage change in GDP in each one of the EU countries analysed.
The definitive goal of creating the solitary market in the European union was to increase its competitiveness regarding large economies such as the USA through economies of scale. This implies that Corden's model should give a more accurate picture of the European union. However, certain assumptions do not indicate the EU's characteristics.
The assumption that the CU-forming countries are small may carry true for a few of the European union countries; however, the implication of this that the customs union will be unable to impact world prices might not hold. Given how big is the European union, it is large enough to compete with the top economies like the USA and Japan.
Corden's predictions regarding changes in cost and market shares aren't appropriate to the EU situation, because of the strong assumptions that there was no international trade prior to the formation and therefore no trade with all of those other world after. Also, with the partner firm exiting the marketplace, it is assumed that there is no upsurge in competition pursuing CU development, thus no change in the prices.
However, there is evidence supporting the key conclusion of the model that the welfare gain is because restructuring, which leads to increasingly concentrated market sectors as companies can benefit from economies of level as the size of the market that they have access to rises. Between 1987 and 1993, the four-firm concentration percentage increased by 2. 3% across 71 companies in the EU.  This was partly credited to increased restructuring; between 1987 and 1990, the ratio of M&As involving countries from two different member states jumped from 9. 6% to 21. 5% in anticipation of the Solo Market. This replaced M&As within country borders which dropped from 71. 6% to 60. 7% within the same period. 
While it is true that EU industry awareness has increased, this is can't be attributed solely to a expansion on the market size. Many companies already run internationally in the 1980s and therefore, market size expansion would not experienced as big a direct effect on the focus level. The solo market also resulted in a decrease in non-tariff barriers (especially barriers to admittance) between European union member says, through general public procurement liberalisation, increased simple cross-border knowledge transfer and the free movements of capital. Corden's comparative static model does not look at the dynamic ramifications of European union integration.
The aim of the SMP was much more ambitious than a mere reduction of the tariff obstacles and thus both ideas, which focus on the effects of a CU, are too simplistic to be wholly appropriate. Certain aspects of both models are comparable to the European union situation. However, Corden's model seems to be more suitable; while Cournot's results regarding changes in the costs and respected market show were more appropriate, Corden's underlying characteristics are much more appropriate to the current European union situation.
- Friedman, Wayne (1983), 'Oligopoly Theory', Cambridge College or university Press
- Frankel (1997) (Ali El-Agraa P175)
- Kreinin (1979b) (Ali El-Agraa P175
- European Commission/CEPR (1997) Trade Creation and Trade Diversion, Subseries IV/ size 3 from the Solo Market Review
- Buigues, Ilzkovitz and Lebrun (1990)
- EC/CEPR, 1997, Trade creation and trade diversion
- Subseries V, Quantity 4, Economies of Scale
- AMDATA in Western Economy (1999)