Risk and Insurance - Online Tutor, Practice Problems & Exam Prep

Risk represents uncertainty about future financial outcomes, leading to a general aversion to potential losses. This aversion is quantified through utility, which measures satisfaction derived from consumption. The concept of marginal utility illustrates diminishing returns, where each additional unit consumed yields less satisfaction. Insurance mitigates the impact of catastrophic losses by allowing individuals to trade a small, certain cost for protection against significant, uncertain losses, thus maintaining a higher level of utility despite potential risks.

Risk and Insurance

Now let's see the relationship between risk and insurance. So let's talk about risk first. What is the idea of risk? This is being uncertain about the future, and specifically in financial terms, we're uncertain about future gains or losses. We're uncertain about things that are going to happen in the future. So risk occurs because the future is uncertain, right? That's the key thing about risk: we don't know what's going to happen in the future. We might make money, we might lose money. We're not sure. So let's go ahead and do a quick psychological pop quiz here. Which one would you choose? Would you choose that I just say, you can walk away from me right now, $0 and just walk away. Or would you take a gamble and you can receive $1000; we're going to flip a coin, and if it turns up heads, you get $1000. If it turns up tails, you got to pay me $1000. Would you take that bet? Well, most of you probably would just rather walk away and not take the bet, right? Because the idea here is that you're most likely risk-averse, which is a general dislike for risk. You don't like the idea of taking on additional risk because you don't want to lose. What we see is that people generally dislike bad things more than they like good things happening. Risk for no reason, right? Because you might have to pay $1000, you might get $1000. The idea is that the $1000 that you get probably wouldn't give you as much satisfaction. So, how do we describe this idea of being risk-averse? And I'm sure some of you like, hey, I'll take that bet. I'll take that bet. Sorry. I'm not taking that bet. It was just a situational thing.

So how do we quantify this idea? We're going to use what's called utility. Utility is one of these keywords in this class that they love to talk about, and it's basically the economist's way of quantifying happiness, say. Obviously, in the real world, it's not so easy to think of it like this, but it's like saying hey, this slice of pizza gives me 5 utility. I love this pizza. It gives me 5 utility. How much is 5 utility? Is that a lot? Is that a little? Can't really say but we can make some interesting conclusions related to satisfaction or happiness based on this. One thing we think about is Marginal Utility. So remember, marginal is one of these keywords in economics. Marginal, remember we talk about marginal, that's one more. So the additional satisfaction, the marginal utility, is going to be that additional satisfaction from consuming 1 more unit of a good. Okay? So by consuming 1 more unit, you're going to have a little more satisfaction. Now, the idea with utility that we've probably talked about in a previous video, but just to remind you is that it follows the law of diminishing returns. Think about a pizza. You're really hungry and you order a pizza and that first slice of pizza you're like, Oh this is so good, I'm getting like 100 utility, right? That's how you think about it, right? Oh, 100 utility. Then that second slice of pizza you're like oh yeah I'm still hungry, yeah. 80 utility, it's pretty good. 3rd slice, 60 utility. I guess I could keep eating. Yeah. 40 utility. Right? Each slice gives you less satisfaction than that very first bite of pizza. And that's the idea of diminishing returns, right? That the more you have of something, the less happiness it gets you. Think about if you had one car right now, right? You have 0 cars, you're a broke college student and you have no cars and all of a sudden you get one car. Whoa, that's awesome. And now someone gives you a second car. You're like, okay, I mean I have one car but I'll take 2 cars. Sure, yeah, yeah, yeah. 3 cars, I mean why not? You know, that first car brings you the most utility, right? Because you had less of it and you're getting more and more.

So this is what our utility graph looks like right here. Utility. So we'll have utility on the y-axis here and notice what happens here and this is, let's say quantity. Okay? And for our purpose since we're talking about risk here, let's say the amount of money that you have. Okay? So the amount of satisfaction you get from your first few dollars, you have no money and now you get a little bit of money, well, you can now buy food, you can buy a house, you can buy your basic needs. So you get a lot of utility out of those first dollars, right? So now let's say you're somewhere around here and you get a little more money. Let's say, for simplicity, let's go right on this line, right? So you get a little more money and it brings you there, right? What's the extra utility you get? However, what happens if you lost that amount of money? Look how much you would lose. A lot more utility, right? So, to make this a little more extreme, let's go ahead and use maybe 2 pieces of this puzzle of this graph to show you a little more extreme bit there. So, let's say that's the marginal utility of gaining a little bit of money, You'd get a little more satisfaction, right? You already cover your basic needs. Now, you're able to go on a vacation or something. So you get a little more satisfaction out of that. However, what happens if you lose that amount of money? Well, look how much you're going to lose here. You're going to go from here all the way down here, right? Look at all this lost utility. So this is the gain in utility here from a gain of 1 unit and this is all the lost utility, right? The idea here is that, this is why people are risk averse, they don't want to lose anything because they are going to lose a lot more than if they gain a little bit, they're not going to get as much out of it. That's the idea of being risk averse because losing something hurts you a lot more than gaining something, okay? And that's what insurance does. It helps us guard against these uncertain losses. So what people generally insure against is unlikely, sorry, what's behind me here? Unlikely but catastrophic losses like a fire. Let me get out of the way. Unlikely but catastrophic losses like a fire. Okay? So that's what people generally insure against. So that's the idea of this right here. So instead of risking all of this loss, let's say this is the loss from a fire, well, maybe someone would be willing to pay this much in insurance, let's say from here to here and be at this level of happiness. So give up a little bit of their satisfaction. Insurance is that we take a small risk of paying a little bit of insurance fees to get rid of the risk of a big loss, like a catastrophic loss from a fire or something like that. Cool? So that's the idea, insurance and risk are commingled here and the whole reason why the insurance market exists. Alright? Let's take a pause and move on to the next video.

Here’s what students ask on this topic:

What is the relationship between risk and insurance?

Risk represents uncertainty about future financial outcomes, leading to potential gains or losses. People are generally risk-averse, meaning they prefer to avoid potential losses even if it means forgoing potential gains. Insurance mitigates the impact of catastrophic losses by allowing individuals to trade a small, certain cost (insurance premiums) for protection against significant, uncertain losses (e.g., fire, theft). This trade-off helps maintain a higher level of utility, or satisfaction, despite potential risks. Essentially, insurance provides a safety net, reducing the financial impact of adverse events and stabilizing one's utility.

How does utility theory explain risk aversion?

Utility theory quantifies satisfaction or happiness derived from consumption. According to the concept of marginal utility, each additional unit consumed yields less satisfaction, following the law of diminishing returns. Risk aversion is explained by the fact that losing a certain amount of money results in a larger decrease in utility compared to the increase in utility from gaining the same amount. This is because the initial units of money provide more significant satisfaction by covering basic needs. Therefore, people prefer to avoid losses, as the negative impact on their utility is greater than the positive impact of equivalent gains.

What is marginal utility and how does it relate to risk and insurance?

Marginal utility refers to the additional satisfaction gained from consuming one more unit of a good or service. It follows the law of diminishing returns, meaning each additional unit provides less satisfaction than the previous one. In the context of risk and insurance, marginal utility helps explain why people are risk-averse. The initial units of money provide significant utility by meeting basic needs. As wealth increases, the additional utility from extra money decreases. Insurance allows individuals to pay a small, certain cost to avoid the large utility loss associated with catastrophic events, thus stabilizing their overall utility.

Why do people generally insure against unlikely but catastrophic losses?

People generally insure against unlikely but catastrophic losses because the potential financial impact of such events can be devastating. By paying a small, certain cost (insurance premiums), individuals can protect themselves from the significant, uncertain losses that could occur from events like fires, natural disasters, or major accidents. This trade-off helps maintain a higher level of utility, as the small, predictable expense of insurance is preferable to the large, unpredictable loss that could severely impact their financial stability and overall satisfaction.

How does the law of diminishing returns apply to utility in the context of risk?

The law of diminishing returns states that as more units of a good or service are consumed, the additional satisfaction (marginal utility) from each subsequent unit decreases. In the context of risk, this principle explains why people are risk-averse. The initial units of money provide significant utility by covering essential needs. As wealth increases, the additional utility from extra money diminishes. Therefore, the potential loss of money results in a larger decrease in utility compared to the increase in utility from gaining the same amount. This drives individuals to seek insurance to protect against significant losses, maintaining their overall utility.