<ul>
<li><p>Assume that the forecaster tells Maria it is going to rain. Then she will go for project <span class="math-container">$A$</span> (rather than <span class="math-container">$B$</span>) giving her a gain of 400.</p>
</li>
<li><p>If the forecaster tells her it is going to snow, then again it will be best to go for project <span class="math-container">$A$</span> (rather than <span class="math-container">$B$</span>) giving her a gain of 600.</p>
</li>
<li><p>If the forecaster tells Maria it is going to hail, she will go for option <span class="math-container">$B$</span> (rather than <span class="math-container">$A$</span>) giving her a gain of 300.</p>
</li>
<li><p>Finally if the forecaster tells Maria it is going to be sunny, she will opt for project <span class="math-container">$B$</span> (rather than <span class="math-container">$A$</span>) giving her a gain of 400.</p>
</li>
</ul>
<p>Before she hears the announcement of the forecaster, her expected profit will therefore be equal to:
<span class="math-container">$$
0.1 \times 400 + 0.3 \times 600 + 0.2 \times 300 + 0.4 \times 400.
$$</span>
This needs to be compared to the expected gain she obtains without the information of the forecaster.</p>
<p>Here information is valuable because the choice of <span class="math-container">$A$</span> versus <span class="math-container">$B$</span> can be made after the announcement of the forecaster. This means that she can condition her choice on the additional information.</p>

CC BY-SA 4.0
2024-04-27T09:31:15.293Z
2024-04-27T09:31:15.293Z
tdm
<p>Maria is a risk neutral agent who can invest in one of the two projects: Project A where she must pay 200 upfront and gain 600 if it rains, 800 if it snows, 400 if it hails and $0 if it is sunny. The other project is B where she must pay 300 upfront and gain 200 if it rains, 0 if it snows, 600 if it hails and 700 if it is sunny.</p>
<p>The probabilities of raining, snowing, hailing and being sunny respectively are 0.1, 0.3, 0.2 and 0.4. The first part of the question asks us to find the net expected payoff for each case, and we infer that Maria chooses A because the expected payoff (180) is greater than that in B.</p>
<p>The next part of the question asks the how much would Maria be willing to pay if she finds a meteorologist who can forecast the weather with perfect accuracy. I am not sure how to proceed here, because if Maria is risk neutral, then would it mean that she has no use for any information? Or not?</p>

<microeconomics><uncertainty>
Value of information for risk neutral agent?
Mayu
# Value of information for risk neutral agent?

(Asked by: username_0 on 2024-04-25)

Maria is a risk neutral agent who can invest in one of the two projects: Project A where she must pay 200 upfront and gain 600 if it rains, 800 if it snows, 400 if it hails and $0 if it is sunny. The other project is B where she must pay 300 upfront and gain 200 if it rains, 0 if it snows, 600 if it hails and 700 if it is sunny.

The probabilities of raining, snowing, hailing and being sunny respectively are 0.1, 0.3, 0.2 and 0.4. The first part of the question asks us to find the net expected payoff for each case, and we infer that Maria chooses A because the expected payoff (180) is greater than that in B.

The next part of the question asks the how much would Maria be willing to pay if she finds a meteorologist who can forecast the weather with perfect accuracy. I am not sure how to proceed here, because if Maria is risk neutral, then would it mean that she has no use for any information? Or not?

**Tags:** microeconomics, uncertainty

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## 1 answers

### Answer by username_1 on 2024-04-27. Score: 1

* Assume that the forecaster tells Maria it is going to rain. Then she will go for project $A$ (rather than $B$) giving her a gain of 400.
* If the forecaster tells her it is going to snow, then again it will be best to go for project $A$ (rather than $B$) giving her a gain of 600.
* If the forecaster tells Maria it is going to hail, she will go for option $B$ (rather than $A$) giving her a gain of 300.
* Finally if the forecaster tells Maria it is going to be sunny, she will opt for project $B$ (rather than $A$) giving her a gain of 400.

Before she hears the announcement of the forecaster, her expected profit will therefore be equal to:
$$
0.1 \times 400 + 0.3 \times 600 + 0.2 \times 300 + 0.4 \times 400.
$$
This needs to be compared to the expected gain she obtains without the information of the forecaster.

Here information is valuable because the choice of $A$ versus $B$ can be made after the announcement of the forecaster. This means that she can condition her choice on the additional information.


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