<p>Let <span class="math-container">$\pi$</span> be the fine that needs to be paid besides the parking fee (say, <span class="math-container">$\phi$</span>) if he gets caught. Further, he may or may not get caught for not paying. So let <span class="math-container">$p$</span> be the probability perceived by John about whether he will be caught. Let <span class="math-container">$u(x)$</span> be utility function of paying for amount <span class="math-container">$x$</span>, with <span class="math-container">$u(0)=0$</span>, <span class="math-container">$u'(x)&lt;0$</span>.</p>
<p>If he pays the parking fee <span class="math-container">$\phi$</span> he has the assured utility of <span class="math-container">$u(\phi)$</span>. However, if does not pay for parking, his <em>expected</em> utility is <span class="math-container">$p \cdot u(\phi+\pi)$</span></p>
<p>Now risk premium is defined as the minimum amount by which the return on risky choice must exceed the risk free choice to make the individual indifferent between the two choices. Let <span class="math-container">$\pi_m$</span> be such that: <span class="math-container">$$u(\phi) = p\cdot u(\phi+\pi_m)$$</span></p>
<p>So, for John, <span class="math-container">$\pi_m$</span> becomes the risk premium for this game. If <span class="math-container">$\pi&gt;\pi_m$</span> then <span class="math-container">$u(\phi) = u(\phi+\pi_m)&gt;u(\phi+\pi)$</span> and it would be irrational for him to not pay for parking and risk getting caught. If opposite, he takes decides to not pay for parking and risk getting caught.</p>

CC BY-SA 4.0
2021-01-05T09:09:31.957Z
Well, I know how to calculete the risk premium, but I am not able to say it in general words, without maths for somebody who does not study maths. Let us say that I will use the formula and after calculating I get the result that the risk premium is number x. How can I interpret this result? What does it mean ?
Laura
CC BY-SA 4.0
2021-01-05T09:23:10.293Z
@Laura: It means that $x$ the minimum amount of fine that should be imposed by authorities to induce him to pay for parking. If the fine is negligible (very small x) then no-one would be willing to pay for parking. If the individual is extremely risk averse even small $x$ is enough to induce him to pay for parking
Dayne
CC BY-SA 4.0
2021-01-05T08:57:04.517Z
2021-01-05T08:57:04.517Z
Dayne
<p>I do not understand the notion risk premium. Let us suppose that John goes to the city by car, but he is thinking about not paying for the parking. If he is caught in the act he must pay the fine. How to interpret the risk premium for this game (not paying the parking)?</p>

<macroeconomics><microeconomics><finance><financial-economics><risk>
How to interpret risk premium
Laura
# How to interpret risk premium

(Asked by: username_0 on 2021-01-05)

I do not understand the notion risk premium. Let us suppose that John goes to the city by car, but he is thinking about not paying for the parking. If he is caught in the act he must pay the fine. How to interpret the risk premium for this game (not paying the parking)?

**Tags:** macroeconomics, microeconomics, finance, financial-economics, risk


---

## 1 answers

### Answer by username_1 on 2021-01-05. Score: 2

Let $\pi$ be the fine that needs to be paid besides the parking fee (say, $\phi$) if he gets caught. Further, he may or may not get caught for not paying. So let $p$ be the probability perceived by John about whether he will be caught. Let $u(x)$ be utility function of paying for amount $x$, with $u(0)=0$, $u'(x)<0$.

If he pays the parking fee $\phi$ he has the assured utility of $u(\phi)$. However, if does not pay for parking, his *expected* utility is $p \cdot u(\phi+\pi)$

Now risk premium is defined as the minimum amount by which the return on risky choice must exceed the risk free choice to make the individual indifferent between the two choices. Let $\pi\_m$ be such that: $$u(\phi) = p\cdot u(\phi+\pi\_m)$$

So, for John, $\pi\_m$ becomes the risk premium for this game. If $\pi>\pi\_m$ then $u(\phi) = u(\phi+\pi\_m)>u(\phi+\pi)$ and it would be irrational for him to not pay for parking and risk getting caught. If opposite, he takes decides to not pay for parking and risk getting caught.

> **Comments:**
> **username_0**: Well, I know how to calculete the risk premium, but I am not able to say it in general words, without maths for somebody who does not study maths. Let us say that I will use the formula and after calculating I get the result that the risk premium is number x. How can I interpret this result? What does it mean ?  
> **username_1**: @username_0: It means that $x$ the minimum amount of fine that should be imposed by authorities to induce him to pay for parking. If the fine is negligible (very small x) then no-one would be willing to pay for parking. If the individual is extremely risk averse even small $x$ is enough to induce him to pay for parking  

---

