<p>1.1% and 1.6% are the probabilities over the lifetime of the traffic signal.</p>
<p>the difference between 1.1% and 1.6% is (0.016-0.011 = 0.005)</p>
<p>so 0.005 lives will be saved and multiply by 10 mln of human lifetime value you get $50k</p>

CC BY-SA 4.0
2024-09-25T11:09:50.597Z
slt_omz, thank you very much for your answer. Then my answer which is $(1-1.1/1.6)\times N\times T\times 10$ million dollars is wrong? What is wrong?
佐武五郎
CC BY-SA 4.0
2024-09-25T11:15:59.293Z
If the number of people using that intersection increases tenfold, I believe the number of fatalities at that intersection would also increase nearly tenfold. Therefore, the benefits of installing traffic lights should also depend on the population around the intersection. But Mankiw's answer doesn't depend on the population around the intersection. I feel it is strange.
佐武五郎
CC BY-SA 4.0
2024-09-25T13:02:07.763Z
@佐武五郎 all of that is factored into the figures of 1.1 and 1.6%. The textbook is not trying to teach you how to measure the risk - it’s taken as a given.
Dale M
CC BY-SA 4.0
2024-09-25T15:37:48.570Z
@佐武五郎 Your math is fine once you fill in that $N \times T = 0.016$, because that is what that 1.6% represents.
Marc
CC BY-SA 4.0
2024-09-25T19:19:08.463Z
@DaleM thank you very much for your comment.
佐武五郎
CC BY-SA 4.0
2024-09-25T19:19:28.597Z
@Marc thank you very much for your answer.
佐武五郎
CC BY-SA 4.0
2024-09-25T02:44:30.677Z
2024-09-25T02:44:30.677Z
slt_omz
<p>I am reading &quot;Principles of Economics 9e&quot; by N. Gregory Mankiw.</p>
<blockquote>
<p>The engineer estimates, based on data from similar intersections, that the traffic light would reduce the risk of a fatal traffic accident over the lifetime of the traffic light from <span class="math-container">$1.6$</span> to <span class="math-container">$1.1$</span> percent.</p>
</blockquote>
<blockquote>
<p>Studies using this approach conclude that the value of a human life is about <span class="math-container">$10$</span> million dollars.</p>
<p>We can now retrun to our original example and respond to the town engineer. The traffic light reduces the risk of fatality by <span class="math-container">$0.5$</span> percentage points. Thus, the expected benefit from installing the traffic light is <span class="math-container">$0.005\times 10$</span> million dollars, or <span class="math-container">$50,000$</span> dollars.</p>
</blockquote>
<p>I thought about this as follows.</p>
<p>Let the lifespan of a traffic signal be <span class="math-container">$T$</span> years. Suppose that, when there was no traffic signal at an intersection, <span class="math-container">$N$</span> people were killed in traffic accidents per year. By installing a traffic signal, traffic accidents involving fatalities are reduced by <span class="math-container">$0.5\%$</span>, so <span class="math-container">$(1-1.1/1.6)\times N\times T$</span> lives will be saved by the time the signal reaches the end of its lifespan. Therefore, the benefit of installing the traffic signal is <span class="math-container">$(1-1.1/1.6)\times N\times T\times 10$</span> million dollars.</p>
<p>I cannot understand the Mankiw's answer which is <span class="math-container">$0.005\times 10$</span> million dollars.</p>
<p>Please explain why the Mankiw's answer is right.</p>
<p>If the number of people using that intersection increases tenfold, I believe the number of fatalities at that intersection would also increase nearly tenfold. Therefore, the benefits of installing traffic lights should also depend on the population around the intersection. But Mankiw's answer doesn't depend on the population around the intersection. I feel it is strange.</p>
<p>I think the biggest problem is that Mankiw did not define &quot;<em><strong>the risk of a fatal traffic accident over the lifetime of the traffic light</strong></em>&quot;.</p>

CC BY-SA 4.0
2024-09-26T21:16:09.900Z
The 1.6% and 1.1% seem to be the probability of any fatal accident at all during the period of time the traffic light would be there.  Perhaps it might be better to say the expected total number of fatalities in that time would reduce from 0.016 to 0.011.
Henry
CC BY-SA 4.0
2024-09-27T09:41:04.627Z
@Henry thank you very much for your comment.
佐武五郎
<public-goods>
Is Mankiw 's answer really correct? The expected benefit from installing the traffic light. ("Principles of Economics 9e" by Mankiw.)
佐武五郎
# Is Mankiw 's answer really correct? The expected benefit from installing the traffic light. ("Principles of Economics 9e" by Mankiw.)

(Asked by: username_0 on 2024-09-25)

I am reading "Principles of Economics 9e" by N. Gregory Mankiw.

> The engineer estimates, based on data from similar intersections, that the traffic light would reduce the risk of a fatal traffic accident over the lifetime of the traffic light from $1.6$ to $1.1$ percent.

> Studies using this approach conclude that the value of a human life is about $10$ million dollars.
>
> We can now retrun to our original example and respond to the town engineer. The traffic light reduces the risk of fatality by $0.5$ percentage points. Thus, the expected benefit from installing the traffic light is $0.005\times 10$ million dollars, or $50,000$ dollars.

I thought about this as follows.

Let the lifespan of a traffic signal be $T$ years. Suppose that, when there was no traffic signal at an intersection, $N$ people were killed in traffic accidents per year. By installing a traffic signal, traffic accidents involving fatalities are reduced by $0.5\%$, so $(1-1.1/1.6)\times N\times T$ lives will be saved by the time the signal reaches the end of its lifespan. Therefore, the benefit of installing the traffic signal is $(1-1.1/1.6)\times N\times T\times 10$ million dollars.

I cannot understand the Mankiw's answer which is $0.005\times 10$ million dollars.

Please explain why the Mankiw's answer is right.

If the number of people using that intersection increases tenfold, I believe the number of fatalities at that intersection would also increase nearly tenfold. Therefore, the benefits of installing traffic lights should also depend on the population around the intersection. But Mankiw's answer doesn't depend on the population around the intersection. I feel it is strange.

I think the biggest problem is that Mankiw did not define "***the risk of a fatal traffic accident over the lifetime of the traffic light***".

**Tags:** public-goods

> **Comments:**
> **username_1**: The 1.6% and 1.1% seem to be the probability of any fatal accident at all during the period of time the traffic light would be there.  Perhaps it might be better to say the expected total number of fatalities in that time would reduce from 0.016 to 0.011.  
> **username_0**: @username_1 thank you very much for your comment.  

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## 1 answers

### Answer by username_2 on 2024-09-25. Score: 9 | Accepted answer

1.1% and 1.6% are the probabilities over the lifetime of the traffic signal.

the difference between 1.1% and 1.6% is (0.016-0.011 = 0.005)

so 0.005 lives will be saved and multiply by 10 mln of human lifetime value you get $50k

> **Comments:**
> **username_0**: username_2, thank you very much for your answer. Then my answer which is $(1-1.1/1.6)\times N\times T\times 10$ million dollars is wrong? What is wrong?  
> **username_0**: If the number of people using that intersection increases tenfold, I believe the number of fatalities at that intersection would also increase nearly tenfold. Therefore, the benefits of installing traffic lights should also depend on the population around the intersection. But Mankiw's answer doesn't depend on the population around the intersection. I feel it is strange.  
> **username_3**: @username_0 all of that is factored into the figures of 1.1 and 1.6%. The textbook is not trying to teach you how to measure the risk - it’s taken as a given.  
> **username_4**: @username_0 Your math is fine once you fill in that $N \times T = 0.016$, because that is what that 1.6% represents.  
> **username_0**: @username_3 thank you very much for your comment.  
> **username_0**: @username_4 thank you very much for your answer.  

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