<p>After obtaining the loan, entrepreneur has two possible strategies to choose from :</p>

<ul>
<li>Strategy $a$ : Expected payoff from strategy $a$ is $\frac{3}{4} (12000-R)$</li>
<li>Strategy $b$ : Expected payoff from strategy $b$ is $\frac{1}{4} (16000-R)$</li>
</ul>

<p>He'll choose strategy $a$ if $\frac{3}{4} (12000-R) \geq \frac{1}{4} (16000-R)$, and strategy $b$ if $\frac{3}{4} (12000-R) &lt; \frac{1}{4} (16000-R)$. Or simply, he'll choose strategy $a$ if $R \leq 10000$, and strategy $b$ if $10000 &lt; R \leq 16000$.</p>

<p>Bank will maximize it's expected profits by choosing $R$ taking as given the entrepreneur's strategy. Therefore, Bank's expected profits equal $\frac{3}{4}R - 1000$ if it chooses $R \leq 10000$, and $\frac{1}{4}R - 1000$ if it chooses $10000 &lt; R \leq 16000$. Clearly, expected profits of the bank are maximum at $R^*=10000$. Observe that entrepreneur is willing to pay more for the loan than $R^*=10000$ since his expected payoff is $\frac{3}{4}(12000 -10000) = 1500 &gt; 0$, but the bank  will not charge more than 10000 because that would change the entrepreneur's choice of strategy to $b$ which is a more risky choice and yields lower expected returns to the bank.</p>

CC BY-SA 4.0
2018-06-12T02:36:06.590Z
Dear Amit, honestly I do not know how to thank you. Ι am so grateful that you help me. I also post this question with Bertrand subgame perfect equilibrium. If you have time and if you can, it would be helpful to have a look.Thank you thank you in advance.https://economics.stackexchange.com/questions/22415/bertrand-game-nash-equilibrium
Stefanos Makridis
CC BY-SA 4.0
2018-06-12T02:19:47.453Z
2018-06-12T02:19:47.453Z
Amit
<p><a href="https://i.sstatic.net/ZwkKO.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZwkKO.jpg" alt="Exercise"></a></p>

<p>I am so confused because I cannot set up the monopolist's profit maximization problem.What I did is the following one:</p>

<p><a href="https://i.sstatic.net/6sbLW.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6sbLW.jpg" alt="Picture 2 "></a></p>

<p>Any help will be appreciated. Thank you.</p>

<microeconomics><game-theory><self-study>
Subgame perfect equilibrium and expected profit
Stefanos Makridis
# Subgame perfect equilibrium and expected profit

(Asked by: username_0 on 2018-06-12)

[![Exercise](https://i.sstatic.net/ZwkKO.jpg)](https://i.sstatic.net/ZwkKO.jpg)

I am so confused because I cannot set up the monopolist's profit maximization problem.What I did is the following one:

[![Picture 2 ](https://i.sstatic.net/6sbLW.jpg)](https://i.sstatic.net/6sbLW.jpg)

Any help will be appreciated. Thank you.

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

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## 1 answers

### Answer by username_1 on 2018-06-12. Score: 2 | Accepted answer

After obtaining the loan, entrepreneur has two possible strategies to choose from :

* Strategy $a$ : Expected payoff from strategy $a$ is $\frac{3}{4} (12000-R)$
* Strategy $b$ : Expected payoff from strategy $b$ is $\frac{1}{4} (16000-R)$

He'll choose strategy $a$ if $\frac{3}{4} (12000-R) \geq \frac{1}{4} (16000-R)$, and strategy $b$ if $\frac{3}{4} (12000-R) < \frac{1}{4} (16000-R)$. Or simply, he'll choose strategy $a$ if $R \leq 10000$, and strategy $b$ if $10000 < R \leq 16000$.

Bank will maximize it's expected profits by choosing $R$ taking as given the entrepreneur's strategy. Therefore, Bank's expected profits equal $\frac{3}{4}R - 1000$ if it chooses $R \leq 10000$, and $\frac{1}{4}R - 1000$ if it chooses $10000 < R \leq 16000$. Clearly, expected profits of the bank are maximum at $R^\*=10000$. Observe that entrepreneur is willing to pay more for the loan than $R^\*=10000$ since his expected payoff is $\frac{3}{4}(12000 -10000) = 1500 > 0$, but the bank will not charge more than 10000 because that would change the entrepreneur's choice of strategy to $b$ which is a more risky choice and yields lower expected returns to the bank.

> **Comments:**
> **username_0**: Dear Amit, honestly I do not know how to thank you. Ι am so grateful that you help me. I also post this question with Bertrand subgame perfect equilibrium. If you have time and if you can, it would be helpful to have a look.Thank you thank you in advance.https://economics.stackexchange.com/questions/22415/bertrand-game-nash-equilibrium  

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