# How to derive the reaction function from these provided variables?

This is the question. I cant seem to reach a concrete solution because of the scarce information.

Firm 1 spends 2 million, plus 33.33% on advertising what firm 2 spends on and firm 2 spends $7 million plus 12.5% of what firm 1 spends. Draw the reaction functions and label them from the provided information. I want to know the exact procedure on such problems. • @Louis.B The question is clear, this is a verbal description of the reaction functions. – Giskard Oct 27 '15 at 17:13 • Shivendra Sharma what exactly is causing you problems? Do you know what a reaction function is? – Giskard Oct 27 '15 at 17:14 • Hint: Let$s_1$and$s_2$denote the total spending of firms 1 and 2, respectively. Write down two equations in terms of these two variables and go from there. – Herr K. Oct 27 '15 at 17:26 • @ShivendraSharma: I still don't understand your confusion. The two equations you write down are the reaction functions:$s_1$is a function of$s_2$and vice versa. Therefore, the two equations tells you how the spending of firm 1 reacts to the spending of firm 2 (and vice versa). – Herr K. Oct 27 '15 at 18:32 • @ShivendraSharma: Looks about right. – Herr K. Oct 27 '15 at 18:56 ## 2 Answers Adding to HREcon's answer (can not comment yet) Firm 1:$x_1= 2 + (1/3) x_2$Firm 2:$x_2= 7 + (1/8) x_1$In order to find the equilibria, you could substitute$x_2$for firm one by$7 + (1/8) x_1$, and vice versa for firm 2, you would get:$x_1= 2 + (1/3) (7 + (1/8) x_1)$and$x_2= 7 + (1/8) (2 + (1/3) x_2)$These equations only depend on one variable and in this case you can solve them to get exact values for x1 and x2. The reaction function tells you how a player in a game reacts to the strategy of another player. As noted by denesp in the commentary, the statements provided in the question are verbal descriptions of reaction functions. The mathematical description (in millions) is given as follows: Firm 1:$x_1= 2 + (1/3) x_2$Firm 2:$x_2= 7 + (1/8) x_1\$

There is not really any procedure to it, besides rewriting the verbal description into a mathematical description.

• if this answer was correct, you may want to consider accepting it. especially if the accepted answer simply references to this one – HRSE Oct 29 '15 at 5:52