# MIT - Principles of Microeconomics - Unit 6. Topics in Intermediate Microeconomics - Lec 20. Uncertainty

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PROFESSOR: Modeling decision under uncertainty turns out to be a critical part of what we do in economics. And I'll spend today's lecture talking about this set of issues.

And, let me just say, the uncertainty you face now is nothing compared to the uncertainty that you'll face later in life.

So you have uncertainty now about whether you should study for the final, or carry an umbrella, or go on a date with this person. I've got uncertainty about whether I should refinance my mortgage, or which college to send my kid to, or how much life insurance I should buy.

Uncertainty only get more and more important as you move on in life. This is an important issue.

Now, how do we think about uncertainty? Well, the tool that we use to think about uncertainty is, once again, to make simplifying assumptions which allow us to write down sensible models, but which capture the key elements of what we're thinking about.

And the simplifying assumption here is we move to the tools of what we call expected utility theory.

And so, basically, the way we think about expected utility theory is the following. Imagine that I offered you guys in this class a choice. And I'm just going to say right now, there's no right answer to this. But I do want you guys to answer me. There's no right answer.

Here's the question. I'm going to give you a choice. I'm going to flip a coin. I have a coin in pocket, and I'm going to flip it. And I'm going to offer you guys the ability to make a bet. If it comes up heads, you win $125.

If it comes up tails, you lose $100. Heads, you win a $125. Tails, you lose $100. There's no right answer. How many would take that bet. How many people would not take that bet? Very good. That's the typical set of responses I get to this.

Now, what's interesting is to think about the parameters of that bet. And to think about it, let's take a step back to something we've discussed already this semester, the concept of expected value. What's

the expected value of that gamble?

The expected value, if you remember, is the probability of each outcome times the value of that outcome. That is you remember expected value, which you defined before, is the probability that you lose times the value if you lose plus the probability that you win times the value if you win. That's the expected value of a gamble.

So, in this context, the expected value is there's a 50% probability that you lose, so 0.5. And if you lose, you lose minus $100 plus a 50% value that you win. It's flipping a coin after all. And if you win, you won $125. So the expected value of this gamble is $12.50. On average, if I did this enough times, you would win $12.50 per time. Statistically, if I did this enough times, you'd win $12.50 per time.

So, in other words, we say that this is more than a fair bet. A fair bet is one with an expected value of 0. A fair bet has an expected value of 0.

So a fair bet would be tails you lose $100, heads you win $100. This is a more than fair bet. There's more than 0 expected value. Yet, the majority of you would not be willing to take this bet. In fact, the majority of people would not take this bet.

Why is that? Why is it that I've dictated a bet which has a positive expected value and yet, people won't take it. Yeah.

AUDIENCE: But wouldn't that also depend on how much money you have.

PROFESSOR: It will absolutely depend on how much money you have.

AUDIENCE: Right.

And, let me just say, the uncertainty you face now is nothing compared to the uncertainty that you'll face later in life.

So you have uncertainty now about whether you should study for the final, or carry an umbrella, or go on a date with this person. I've got uncertainty about whether I should refinance my mortgage, or which college to send my kid to, or how much life insurance I should buy.

Uncertainty only get more and more important as you move on in life. This is an important issue.

Now, how do we think about uncertainty? Well, the tool that we use to think about uncertainty is, once again, to make simplifying assumptions which allow us to write down sensible models, but which capture the key elements of what we're thinking about.

And the simplifying assumption here is we move to the tools of what we call expected utility theory.

And so, basically, the way we think about expected utility theory is the following. Imagine that I offered you guys in this class a choice. And I'm just going to say right now, there's no right answer to this. But I do want you guys to answer me. There's no right answer.

Here's the question. I'm going to give you a choice. I'm going to flip a coin. I have a coin in pocket, and I'm going to flip it. And I'm going to offer you guys the ability to make a bet. If it comes up heads, you win $125.

If it comes up tails, you lose $100. Heads, you win a $125. Tails, you lose $100. There's no right answer. How many would take that bet. How many people would not take that bet? Very good. That's the typical set of responses I get to this.

Now, what's interesting is to think about the parameters of that bet. And to think about it, let's take a step back to something we've discussed already this semester, the concept of expected value. What's

the expected value of that gamble?

The expected value, if you remember, is the probability of each outcome times the value of that outcome. That is you remember expected value, which you defined before, is the probability that you lose times the value if you lose plus the probability that you win times the value if you win. That's the expected value of a gamble.

So, in this context, the expected value is there's a 50% probability that you lose, so 0.5. And if you lose, you lose minus $100 plus a 50% value that you win. It's flipping a coin after all. And if you win, you won $125. So the expected value of this gamble is $12.50. On average, if I did this enough times, you would win $12.50 per time. Statistically, if I did this enough times, you'd win $12.50 per time.

So, in other words, we say that this is more than a fair bet. A fair bet is one with an expected value of 0. A fair bet has an expected value of 0.

So a fair bet would be tails you lose $100, heads you win $100. This is a more than fair bet. There's more than 0 expected value. Yet, the majority of you would not be willing to take this bet. In fact, the majority of people would not take this bet.

Why is that? Why is it that I've dictated a bet which has a positive expected value and yet, people won't take it. Yeah.

AUDIENCE: But wouldn't that also depend on how much money you have.

PROFESSOR: It will absolutely depend on how much money you have.

AUDIENCE: Right.

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