Source: Image of Indifference Curve Graph created by Kate Eskra, Image of Preference Mapping created by Kate Eskra
Hi, welcome to economics. This is Kate. This tutorial is called Utility Theory. As always my examples will be in green, and my key terms will be in red.
So in this tutorial we'll be talking about what a utility function measures. And you'll be able to recognize that it's different for everyone. You'll be able to read and interpret what's called a preference map, which is made up of different indifference curves. You will understand that indifference curves get their shape because of what we call the law of diminishing marginal returns. And then I'll define for you what the marginal rate of substitution is.
OK. So we all know that we have to make choices every day. We also are very aware of our constraints, and most of us are constrained mainly by our time and our income. The key to all of this is, how do we make choices that maximize our utility?
You're going to see the word "utility" a lot in this tutorial. Just keep in mind, again, that utility is satisfaction. It's what we get out of something. So obviously we would want to maximize that.
OK. So the general form of a utility function is like any function. Utility is some function of variables x, y, and z. So it just means, again, that our utility, or our satisfaction that we get out of something, is dependent on various factors.
And it's going to be different for everyone. We are not all the same. We don't all enjoy the same thing. So we won't get the same amount of satisfaction out of everything.
And so as your key term, here it is defined, the utility function is a formula that's used to represent consumer preferences. The utility function itself is going to end up resulting in us mapping out indifference curves. And each of those indifference curves corresponds to a higher level of utility.
OK. So let's simplify a model, and talk about a two-good economy. So my example is, let's say you have to choose for dinner between chicken and beef every night of the week. Those are your only two choices. We're just looking, again, at a simplified model.
So how much of each one are you going to consume each week? Is this the same for everyone? Obviously not. Not everyone likes chicken and beef the same. So, obviously, they're going to choose different bundles.
OK. So how we're going to be looking at utility is on something called a preference map. And that preference map is going to include every single different possible combination of, in this example, chicken and beef. And each combination will give us some amount of satisfaction or utility.
Really, yes, it's measured by a number, the utility itself, but the numbers are different for everybody. And the scale itself really doesn't matter. So it doesn't matter if the numbers we're talking about are 1 through 10, or 100 to 500. Those numbers really don't matter. The idea is that we're looking at each combination giving us some amount of utility, and it increasing as we draw more and more indifference curves mapped out away from the origin. And I'll show you that in a couple sides.
So our individual preferences are going to affect, obviously, how much chicken versus beef I choose. And then also, it's going to affect my choice if either my income changes or the price of either chicken or beef changes.
And again, the key idea here is that we each have our own utility functions, which show our preference behaviors. They're unique to an individual. So to go over some assumptions that we make about our preference behavior, first, we assume completeness.
So if I were to get all different combinations of chicken and beef, I would have to be able to rank them. I would have to be able to say, I prefer this bundle right here to that bundle. Or, you know what? I'm indifferent to those two combinations. But I have to be able to do that for every combination.
Second, is transitivity. So we assume that we are consistent and that we're rational. So if I say, I like chicken more than beef. And I like beef more than shrimp. I must like chicken more than shrimp. OK. So we have to be consistent. We can't jump all over the place and be inconsistent in what we're saying we prefer.
Finally, is the assumption of non-satiation. And that says, more is better. Our utility is going to increase as we consume more. So if there is a bundle that's exactly the same, but it just has more chicken than the one before it, we take more chicken. We can always throw it out if we don't actually want to consume it. So that's that assumption there.
All right, so let's get into these indifference curves. Indifference curves, as your key term here, are defined as a graphical depiction of the utility function. Utility increases as these mapped indifference curves move away from the origin.
OK. So let's just look at one indifference curve first. So if I have chicken on my y-axis and beef on my x, again, we're just in a two-good economy here, these points A, B, and C are all points that this consumer is indifferent to. She does not prefer one over the other. She likes them all the same. They yield the same utility. That's why it's called an indifference curve when we connect them. So 8 chicken, 1 beef. 4 chicken, 3 beef. It looks like 2 chicken and 7 beef. All the same utility.
OK. Well now, if we take indifference-- say this was that first indifference curve. Well, if she can get more and more and more, each of these indifference curves represent combinations that yield more of both, if that becomes possible. So as we have indifference curves moving away from the origin, which is here, our utility is increasing.
So we'd have higher utility on Curve 2 than 1. The highest in this picture would be on Curve 3. There is an indifference curve for every level of utility.
OK. So now let's talk about why they have this shape. Why am I drawing them like this? This is an important concept. So if we look at-- I'm looking at four points here A, B, C, and D. And I have what each of those bundles include in terms of chicken and beef.
So here, notice that each time she is gaining 2 more beef. So here at A she has almost no beef and all chicken. OK? To move to point B, to pick up 2 beef, she's giving up 5 chicken. She's moving from 9, down to 4 chicken. But then to pick up 2 more beef, from B to C, she's not willing to give up as much chicken. And to move from C to D, again, to take up 2 additional beef, she's really not willing to give up much chicken at all. Why is that? OK. So why is she giving up less and less and less chicken each time to get the same amount of beef?
It's because of the law of diminishing marginal return. And this makes a lot of sense, if you think about it. It's defined here as, at some point in either production or consumption, that's where we're focusing today, the economic agent will experience a decrease in the level of production or utility associated with an increase in the production or consumption of an additional unit. And again, the key word here is "additional unit" because additional is what marginal means.
So if we look back at this, when we go from point A to B, she had almost no beef at all here. So she's willing to give up quite a bit of chicken to have a variety. But then, as she has some beef, I already have some beef. I'm not willing to give up quite as much chicken as before. And then here, she's almost at all beef and no chicken. So why would she give up much chicken at all to get even more beef? OK?
So basically, here's what I want you to think about when you hear about diminishing marginal utility, or diminishing marginal return. The more we have of something, we are gaining less additional utility from consuming more of it. At some point our additional or marginal utility diminishes.
Think about eating a Thanksgiving meal, you're going to keep eating. You enjoy most of that meal. Some of us overdo it, but didn't you enjoy the first few bites the most? After you've had those first few bites, you're going to go back for a second helping. You're enjoying it. So your total utility is still increasing, but your additional, or marginal utility, is what is starting to taper or diminish.
OK. And that brings us to the marginal rate of substitution, which is actually just the slope of the indifference curve. So it's showing that here it's really steep, because we are willing to give up a whole lot to get a little bit on the x-axis. But then it begins to flatten, and so the slope is not as steep here.
And so that's what the marginal rate of substitution is. And that's why indifference curves are shaped this way and they are convex to the origin. Because of the law of diminishing marginal return.
So what did you learn in this tutorial? We talked about how a utility function measures a consumer's preferences, and obviously these are different for everyone.
When we map out the utility, it's called a preference map. And it's made up of all those different indifference curves you saw.
And indifference curves get their shape because of the law of diminishing marginal returns. And the slope of the indifference curve is what we defined as the marginal rate of substitution.
Thanks so much for listening, have a great day.
A formula used to represent consumer preferences; the utility function will result in an indifference curve mapping where each curve corresponds to a higher level of utility.
Graphical depiction of the utility function; utility increases as the mapped indifference curves move away from the origin.
Law of Diminishing Marginal Return
At some point, in either production or consumption, the economic agent will experience a decrease in the level of production or utility associated with an increase in the production or consumption of an additional unit.