<p>Adding to HREcon's answer (can not comment yet)</p>

<p>Firm 1:
$x_1= 2 + (1/3) x_2$</p>

<p>Firm 2:
$x_2= 7 + (1/8) x_1$</p>

<p>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:</p>

<p>$x_1= 2 + (1/3) (7 + (1/8) x_1)$
and
$x_2= 7 + (1/8)  (2 + (1/3) x_2)$</p>

<p>These equations only depend on one variable and in this case you can solve them to get exact values for x1 and x2.</p>

CC BY-SA 3.0
2015-10-28T11:52:05.790Z
2015-10-28T11:52:05.790Z
Wolhandkrab
<p>The reaction function tells you how a player in a game reacts to the strategy of another player.</p>

<p>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:</p>

<p>Firm 1:
$x_1= 2 + (1/3) x_2$</p>

<p>Firm 2:
$x_2= 7 + (1/8) x_1$</p>

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

CC BY-SA 3.0
2015-10-28T03:21:12.283Z
2015-10-28T03:21:12.283Z
HRSE
<p>This is the question. I cant seem to reach a concrete solution because of the scarce information.</p>

<p>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.</p>

<p>I want to know the exact procedure on such problems.</p>

CC BY-SA 3.0
2015-10-27T17:08:55.127Z
What do you mean by reaction function? The only thing I can think about with the data you provided is to solve explicitly for that system of 2 equations with 2 unknown, is that what you want? You should make you question clearer.
Louis. B
CC BY-SA 3.0
2015-10-27T17:13:26.447Z
@Louis.B The question is clear, this is a verbal description of the reaction functions.
Giskard
CC BY-SA 3.0
2015-10-27T17:14:23.657Z
Shivendra Sharma what exactly is causing you problems? Do you know what a reaction function is?
Giskard
CC BY-SA 3.0
2015-10-27T17:26:55.307Z
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.
CC BY-SA 3.0
2015-10-27T18:28:09.983Z
@HerrK. Thanks for the hint. I did that since i already have the two functions but I'm not able to teach to the demand function that has to be common for the two firms.
Shiv_90
CC BY-SA 3.0
2015-10-27T18:32:19.947Z
@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.
CC BY-SA 3.0
2015-10-27T18:42:36.950Z
@HerrK. Ok. So s1 = 2,000,000 +0.333s2 and s2=7,000,000+0.125s1 are the actual reaction functions. Fine. I thought there are things missing here since deriving reaction functions is usually not a short process and I've done some long derivations for these. Anyway, thanks for the clarification :)
Shiv_90
CC BY-SA 3.0
2015-10-27T18:56:00.410Z
@ShivendraSharma: Looks about right.
Herr K.
CC BY-SA 3.0
2015-10-28T06:52:52.297Z
Having read the comments I no longer understand this question.
Giskard
<microeconomics>
How to derive the reaction function from these provided variables?
Shiv_90
# How to derive the reaction function from these provided variables?

(Asked by: username_0 on 2015-10-27)

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.

**Tags:** microeconomics

> **Comments:**
> **username_1**: What do you mean by reaction function? The only thing I can think about with the data you provided is to solve explicitly for that system of 2 equations with 2 unknown, is that what you want? You should make you question clearer.  
> **username_2**: @Louis.B The question is clear, this is a verbal description of the reaction functions.  
> **username_2**: Shivendra Sharma what exactly is causing you problems? Do you know what a reaction function is?  
> **username_3**: 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.  
> **username_0**: @HerrK. Thanks for the hint. I did that since i already have the two functions but I'm not able to teach to the demand function that has to be common for the two firms.  
> **username_3**: @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).  
> **username_0**: @HerrK. Ok. So s1 = 2,000,000 +0.333s2 and s2=7,000,000+0.125s1 are the actual reaction functions. Fine. I thought there are things missing here since deriving reaction functions is usually not a short process and I've done some long derivations for these. Anyway, thanks for the clarification :)  
> **username_3**: @ShivendraSharma: Looks about right.  
> **username_2**: Having read the comments I no longer understand this question.  

---

## 2 answers

### Answer by username_4 on 2015-10-28. Score: 1 | Accepted answer

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.


---

### Answer by username_5 on 2015-10-28. Score: 2

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.


---

