Brander–Spencer model
The model illustrates a situation where, under certain assumptions, a government can subsidize domestic firms to help them in their competition against foreign producers and in doing so enhances national welfare.
This conclusion stands in contrast to results from most international trade models, in which government non-interference is socially optimal.
[1] Although it is possible for the national government to increase a country's welfare in the model through export subsidies, the policy is of beggar thy neighbor type.
[2][3] This also means that if all governments simultaneously attempt to follow the policy prescription of the model, all countries would wind up worse off.
[note 1][1] The game changes however if the government credibly promises to subsidize the domestic firm if it enters the market, as illustrated in Figure 2.
The 20 million subsidy is a transfer from the government to the firm hence it has no effect on national welfare (ignoring costs of taxation; as long as these are not too large the basic insight of the model goes through).
The original Brander and Spencer paper presented the game in the framework of a Cournot competition model.
[note 2][4] With no government subsidy (s=0) the resulting equilibrium will be the standard Cournot outcome, as shown in the graph by the intersection of the best response functions.
This in turn means that the foreign firm's best response is to cut output, although not proportionally (hence, the market price falls).
It can be shown that the profit function evaluated at equilibrium quantity levels is concave in s and eventually negatively sloped.
As it turns out, if the government sets the subsidy exactly at the optimal level, the resulting equilibrium is the same as that of the "leader and follower" Stackelberg model.
In the case where the firm is able to separate the home and export market (charge different prices in each with no possibility of third party arbitrage) then the level of the optimal subsidies will depend on whether marginal costs of production are constant, increasing or decreasing.
This underscores the need on the part of the government for very precise information on industry structure and firm's cost functions.
[4] In the more general case where the firm cannot price discriminate between domestic and foreign consumers the effects of a subsidy are less clear since both an expansion of exports and deterioration of terms of trade are present.
Brander and Spencer show that in the resulting Nash equilibrium the governments choose a level of subsidy that is too high and hence they do not manage to maximize social welfare.
In fact, if the good produced is not consumed domestically, then the optimal level of subsidy is negative – an export tax.
[note 3] This is because the total quantity produced in the Cournot and the Stackelberg equilibrium is higher than the profit maximizing collusive monopoly level of output.
[4] As pointed out by Paul Krugman, the Brander–Spencer model, due to the sensitivity of the results to its assumptions, does not establish a generally applicable policy prescription in favor of government subsidies.
However, the approach is problematic, both from an analytical (it is not internally consistent) and an empirical point of view (there's no guarantee that the parameter, even if it makes conceptual sense, remains stable when a new policy – the government's subsidy – is introduced[note 4]).
[7] Marie Thursby has used an extended version of the model to examine international trade in wheat, 60% of which is produced by the United States and Canada.
Thursby includes marketing boards, possibility of a monopsony, and a variety of government policies in the analysis.
[8] In his book which presented the model to the general public, Paul Krugman used the example of the aircraft industry, with the two players being Airbus and Boeing.
[1] In fact, Krugman and Baldwin examined the industry for wide bodied aircraft in the context of the model in a 1988 paper.
The authors calibrate an extended version of the model in order to examine the effect of a subsidy to Airbus by European governments, and its presence in a market which can only support two firms at most, worldwide.
Importantly, unlike in the baseline Brander and Spencer model, Krugman and Baldwin find that the changes to consumer surplus resulting from the subsidy and entry, dominate the effect of changes in firm profits in social welfare calculations.
[9] Gernot Klepper, in an analysis similar to Krugman and Baldwin, has also used the Brander Spencer and other models to analyze the effects of entry into the transport aircraft industry.
[10] In general, like with many of the New Trade Theory models, the results of the Brander Spencer model and the policy prescriptions it generates are very sensitive to the underlying assumptions on the nature of the industry in question, the information available to the national government, its ability to credibly commit to an action and the likely response of foreign governments.
