<p><a href="https://i.sstatic.net/CfQhz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CfQhz.png" alt="enter image description here" /></a></p>
<p>My Solution is this</p>
<p>Separating equilibrium</p>
<p>High type worker chooses <span class="math-container">$e_H = e^* &gt;0$</span></p>
<p>Low type worker chooses <span class="math-container">$e_L =0$</span></p>
<p>Firms believes that if education is <span class="math-container">$e^* &gt;0$</span> then the worker is high type and offer wage <span class="math-container">$= \alpha_H$</span>. If education is zero, then the worker is seen as a low type and offered wage <span class="math-container">$= \alpha_L$</span>.</p>
<p>For high type worker, utility is <span class="math-container">$U_H(e) = \alpha_H - \frac{e^*}{2\alpha_H}$</span>.</p>
<p>In order not to deviate H-type to L-type,</p>
<p><span class="math-container">$$\alpha_H- \frac{e^*}{2\alpha_H} &gt; \alpha_L - \frac{0}{2\alpha_H} $$</span></p>
<p><span class="math-container">$$\alpha_H- \frac{e^*}{2\alpha_H} &gt; \alpha_L$$</span></p>
<p>then <span class="math-container">$e^* &lt; 16$</span></p>
<p>Similarly, for low type, utility is <span class="math-container">$U_L(e) = \alpha_L - \frac{0}{2\alpha_L} = \alpha_L$</span>.</p>
<p>In order not to deviate L-type to H-type,</p>
<p><span class="math-container">$$\alpha_L &gt; \alpha_H -  \frac{e^*}{2\alpha_L}$$</span></p>
<p>Then, <span class="math-container">$e^* &gt;8$</span></p>
<p>As a result, <span class="math-container">$8 &lt; e^* &lt; 16$</span> is a separating equilibrium.</p>
<p>Pooling Equilibrium</p>
<p>Both type workers choose the same education level <span class="math-container">$e' &gt;0$</span></p>
<p>Firm believes that high type worker with probability p and low type worker with probability (1-p). Also, we see that <span class="math-container">$p=1/2$</span>.</p>
<p>So the wage is <span class="math-container">$w = 1/2 (\alpha_H + \alpha_L)$</span></p>
<p>For the high type, utility function is <span class="math-container">$U_H(e) = 1/2(\alpha_H + \alpha_L) - \frac{e'}{2\alpha_H}$</span></p>
<p>For the high type, utility function is <span class="math-container">$U_H(e) = 1/2(\alpha_H + \alpha_L) - \frac{e'}{2\alpha_L}$</span></p>
<p>In oder for high type not to deviate to <span class="math-container">$e=0$</span></p>
<p><span class="math-container">$$1/2(\alpha_H + \alpha_L) - \frac{e'}{2\alpha_H} &gt; \alpha_L - \frac{0}{\alpha_H}$$</span></p>
<p>In oder for low type not to deviate to <span class="math-container">$e=0$</span></p>
<p><span class="math-container">$$ 1/2(\alpha_H + \alpha_L) - \frac{e'}{2\alpha_L}&gt; \alpha_L - \frac{0}{\alpha_H}$$</span></p>
<p>Then, <span class="math-container">$e'&lt; 4$</span></p>
<p>My solution is this. But my solution does not match with the solution manuel. Where is my mistake? I cannot see the mistake. Or what is your solution? Thank you.</p>

CC BY-SA 4.0
2021-07-19T08:38:40.020Z
The steps you performed seem correct. However, note that the utility function has $e$ squared. Is the solution $e\in [\sqrt{8},4]$ for separating and $e\in[0,2]$ for pooling?
Bayesian
CC BY-SA 4.0
2021-07-19T08:40:46.547Z
As an aside, it is common practice here to type the question instead of just pasting a picture.
Bayesian
<microeconomics><game-theory><self-study><bayesian-game><signaling>
Job Market Signaling
studentp
# Job Market Signaling

(Asked by: username_0 on 2021-07-18)

[![enter image description here](https://i.sstatic.net/CfQhz.png)](https://i.sstatic.net/CfQhz.png)

My Solution is this

Separating equilibrium

High type worker chooses $e\_H = e^\* >0$

Low type worker chooses $e\_L =0$

Firms believes that if education is $e^\* >0$ then the worker is high type and offer wage $= \alpha\_H$. If education is zero, then the worker is seen as a low type and offered wage $= \alpha\_L$.

For high type worker, utility is $U\_H(e) = \alpha\_H - \frac{e^\*}{2\alpha\_H}$.

In order not to deviate H-type to L-type,

$$\alpha\_H- \frac{e^\*}{2\alpha\_H} > \alpha\_L - \frac{0}{2\alpha\_H} $$

$$\alpha\_H- \frac{e^\*}{2\alpha\_H} > \alpha\_L$$

then $e^\* < 16$

Similarly, for low type, utility is $U\_L(e) = \alpha\_L - \frac{0}{2\alpha\_L} = \alpha\_L$.

In order not to deviate L-type to H-type,

$$\alpha\_L > \alpha\_H - \frac{e^\*}{2\alpha\_L}$$

Then, $e^\* >8$

As a result, $8 < e^\* < 16$ is a separating equilibrium.

Pooling Equilibrium

Both type workers choose the same education level $e' >0$

Firm believes that high type worker with probability p and low type worker with probability (1-p). Also, we see that $p=1/2$.

So the wage is $w = 1/2 (\alpha\_H + \alpha\_L)$

For the high type, utility function is $U\_H(e) = 1/2(\alpha\_H + \alpha\_L) - \frac{e'}{2\alpha\_H}$

For the high type, utility function is $U\_H(e) = 1/2(\alpha\_H + \alpha\_L) - \frac{e'}{2\alpha\_L}$

In oder for high type not to deviate to $e=0$

$$1/2(\alpha\_H + \alpha\_L) - \frac{e'}{2\alpha\_H} > \alpha\_L - \frac{0}{\alpha\_H}$$

In oder for low type not to deviate to $e=0$

$$ 1/2(\alpha\_H + \alpha\_L) - \frac{e'}{2\alpha\_L}> \alpha\_L - \frac{0}{\alpha\_H}$$

Then, $e'< 4$

My solution is this. But my solution does not match with the solution manuel. Where is my mistake? I cannot see the mistake. Or what is your solution? Thank you.

**Tags:** microeconomics, game-theory, self-study, bayesian-game, signaling

> **Comments:**
> **username_1**: The steps you performed seem correct. However, note that the utility function has $e$ squared. Is the solution $e\in [\sqrt{8},4]$ for separating and $e\in[0,2]$ for pooling?  
> **username_1**: As an aside, it is common practice here to type the question instead of just pasting a picture.  

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## 0 answers

