Solving these for y implicitly defines a best response function for each firm; formula_8 and formula_9. These are illustrated in the figure below, with the domestic firm's output on the x axis and foreign firm's output on the y axis. 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. A subsidy however has the effect of shifting the domestic firm's best response function to the right. Because its output is subsidized, the domestic firm increases production. This in turn means that the foreign firm's best response is to cut output, although not proportionally (hence, the market price falls). In the new equilibrium domestic firm produces more and foreign firm produces less. In the model, domestic social welfare can be defined as the home firm's profit net of the subsidy (the model can be extended so that social welfare includes the firm's monopoly profit as well as the wages paid to the firm's workers; the results are qualitatively the same). It can be shown that the profit function evaluated at equilibrium quantity levels is concave in s and eventually negatively sloped. As a result, there is an "optimal subsidy" which maximizes the domestic firm's profits and hence domestic social welfare. 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 that case one of the firms (in this case the domestic firm) has the ability to choose its output first. This creates the ability to credibly commit to a particular action, resulting in "first mover advantage". In the Brender–Spencer model, the government's subsidy creates this credible commitment even when the private firm does not have that ability. In standard models of international trade a fall in the price of a country's export good – a deterioration in its terms of trade – generally decreases the home country's welfare. In the Brander–Spencer model however the opposite is true. This is because in this model the markets are not perfectly competitive and the revenue from the expanded quantity sold compensates the firm for the revenue lost from the lower export price. If the good produced by the firm is also consumed domestically however the result is a bit more complicated. 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.