Our model of consumer decision-making revolves around utility maximization, a concept fundamental to this course. This model consists of two key components: consumer preferences (what people desire) and budget constraints (what they can afford). By combining these elements, we aim to maximize individuals' happiness or satisfaction within the constraints they face. This exercise, through the magic of economics, will yield the demand curve—a sensible representation that you'll intuitively grasp.
So, we'll tackle this in three steps over the next couple of lectures. First, we'll discuss preferences—how we model people's tastes. Next, we'll delve into translating these preferences into utility functions, representing them mathematically. Finally, we'll examine the budget constraints consumers encounter. Today, we'll focus on unconstrained choice. We'll ignore affordability and costs—imagine you've won the lottery, and money is no object. Next time, we'll introduce budget constraints, acknowledging that nobody actually wins the lottery—it's a terrible deal. But for now, let's talk about what you want.
To begin, we'll introduce three preference assumptions. Firstly, completeness: individuals have preferences over any set of goods they might choose from. Secondly, transitivity: if you prefer A to B and B to C, you prefer A to C. And thirdly, the economic assumption of nonsatiation: more is always better than less. We'll assume that individuals always prefer more of a good to less, although not necessarily in equal increments of happiness.
With these assumptions in mind, let's visually represent preferences using indifference curves—graphical maps of preferences. Consider a scenario where you've received money from your parents and can spend it on pizza or cookies. While in reality, you have countless options, we'll focus on these two choices to build intuition. Let's compare three scenarios: two pizzas and one cookie (choice A), one pizza and two cookies (choice B), and two pizzas and two cookies (choice C). I'll assume you're indifferent between choices A and B but prefer choice C due to the principle of more is better.
Now, let's graph your preferences using indifference curves, representing all combinations of consumption between which you're indifferent. These curves exhibit several properties, including the preference for higher curves and the downward sloping nature due to the nonsatiation assumption.
Exactly. So basically, you're indifferent-- on this curve, you're indifferent with one of each and two of each. You can't be indifferent. Two of each has got to be better than one of each. So an upward sloping indifference curve would violate nonsatiation. So that's the second property of indifference curve.
The third property of indifference curve is that indifference curves never cross, okay? We could see that in figure 2-3, okay? Someone else tell me why this violates the properties I wrote up there, indifference curves crossing. Yeah.
AUDIENCE: Because B and C are strictly better.
JONATHAN GRUBER: What's that?
AUDIENCE: Because B and C, B is strictly better.
JONATHAN GRUBER: Because B and C, B is strictly better. That's right.
AUDIENCE: [INAUDIBLE]
JONATHAN GRUBER: But they're also both on the same curve as A. So you're saying they're both-- you're indifferent with A for both B and C, but you can't be, because B is strictly better than C.
So it violates transitivity, okay? So the problem with crossing indifference curves is they violate transitivity. And then finally, the fourth is sort of a cute extra assumption, but I think it's important to clarify, which is that there is only one indifference curve through every possible consumption bundle, only one IC through every bundle.
Okay, you can't have two indifference curves going through the same bundle, okay? And that's because of completeness. If you have two indifference curves going through the same bundle, you wouldn't know how you felt, okay? So there can only be one going through every bundle because you know how you feel.
You may feel indifferent, but you know how you feel. You can't say I don't know, okay? So that's sort of an extra assumption that sort of completes the link to the properties, okay? So that's basically how indifference curves work. Now, I find-- when I took this course, before you were-- god, maybe before your parents were born, I don't know, certainly before you guys were born-- when I took this course, I found this course full of a lot of light bulb moments, that is, stuff was just sort of confusing, and then boom, an example really made it work for me. And the example that made indifference curves work for me was actually doing my first UROP. When my UROP was with a grad student, and that grad student had to decide whether he was going to accept a job. He had a series of job offers, so he had to decide.
And basically, he said, "Here's the way I'm thinking about it. I am indifferent-- I have an indifference map and I care about two things. I care about school location and I care about economics department quality. I care about the quality of my colleagues, and the research it's done there, and the location.
" And basically, he had two offers. One was from Princeton, which he put up here. No offense to New Jerseyans, but Princeton as a young single person sucks. Okay, fine when you're married and have kids, but deadly as a young single person. And the other-- so that's Princeton. Down here was Santa Cruz. Okay, awesome.
[INAUDIBLE] is the most beautiful university in America, okay? But not as good an economics department. And he decided he was roughly indifferent between the two. But he had a third offer from the IMF, which is a research institution in DC, which has-- he had a lot of good colleagues, and DC is way better than Princeton, New Jersey, even though it's not as good as Santa Cruz.
So he decided he would take the offer at the IMF, okay? Even though the IMF had worse colleagues than Princeton and worse location than Santa Cruz, it was still better in combination of the two of them, given his preferences. And that's how he used indifference curves to make his decision, okay? So that's sort of an example of applying it.
Once again, no offense to the New Jerseyans in the room, of which I am one, but believe me, you'd rather be in Santa Cruz. Okay, so now, let's go from preferences to utility functions. Okay, so now, we're going to move from preferences, which we've represented graphically, to utility functions, which we're going to represent mathematically.
Remember, I want you understand, everything this course at three levels, graphically, mathematically, and most importantly of all, intuitively, okay? So graphic is indifference curves. Now we come to the mathematical representation, which is utility function, okay? And the idea is that every individual, all of you in this room, have a stable, well behaved, underlying mathematical representation of your preferences, which we call utility function.
Now, once again, that's going to be very complicated, your preference over lots of different things. We're going to make things simple by writing out a two dimensional representation for now of your indifference curve. We're going to say, how do we act mathematically represent your feelings about pizza versus cookies? Okay? Imagine that's all you care about in the world, is pizza and cookies.
How do we mathematically represent that? So for example, we could write down that your utility function is equal to the square root of the number of slices of pizza times the number of cookies. We could write that down. I'm not saying that's right. I'm not saying it works for anyone in this room or even everyone this room, but that is a possible way to represent utility, okay? What this would say-- this is convenient.
We will use-- we'll end up using square root form a lot for utility functions and a lot of convenient mathematical properties. And it happens to jive with our example, right? Because in this example, you're indifferent between two pizza and one cookie or one pizza and two cookie. They're both square root of 2.
And you prefer two pizza and two cookies. That's two, okay? So this gives you a high utility for two pizza and two cookies, okay, than one pizza and two cookie, or two pizza and one cookie. So now, the question is, what does this mean? What is utility? Well, utility doesn't actually mean anything. There's not really a thing out there called utiles okay?
In other words, utility is not a cardinal concept. It is only an ordinal concept. You cannot say your utility, you are-- you cannot literally say, "My utility is x% higher than your utility," but you can rank them. So we're going to assume that utility can be ranked to allow you to rank choices. Even if generally, we might slip some and sort of pretend utility is cardinal for some cute examples, but by and large, we're going to think of utility as purely ordinal.
It's just a way to rank your choices. It's just when you have a set of choices out there over many dimensions-- like if your choice in life was always over one dimension and more was better, it would always be easy to rank it, right? You'd never have a problem. Once your choice is over more than one dimension, now if you want to rank them, you need some way to combine Properties of Indifference Curves: Indifference curves represent sets of consumption bundles that yield the same level of utility. They exhibit three key properties: They slope downwards (reflecting diminishing marginal utility). They never intersect (violating transitivity if they did). Only one indifference curve passes through each bundle (related to completeness). Example Application: Gruber shared an anecdote about a grad student deciding between job offers, using an indifference map based on preferences for school location and department quality to make his decision. Transition to Utility Functions: Utility functions provide a mathematical representation of consumer preferences. Each individual has a unique utility function reflecting their preferences over different goods. Utility functions allow for ranking choices, emphasizing the concept of "more is better." Utility is an ordinal concept, representing relative preferences rather than absolute satisfaction. Marginal Utility: Marginal utility measures the additional satisfaction gained from consuming one more unit of a good. It diminishes as more of the good is consumed due to diminishing marginal utility. Gruber illustrated this concept with graphical representations of utility and marginal utility. Marginal Rate of Substitution (MRS): MRS indicates the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility. It equals the negative ratio of marginal utilities of the two goods. As consumers move along an indifference curve, MRS decreases due to diminishing marginal utility. Convexity of Indifference Curves: Indifference curves are typically convex to the origin. This convexity reflects the decreasing marginal rate of substitution as consumers move to higher levels of consumption for both goods. Concave indifference curves would imply increasing MRS, contradicting the principle of diminishing marginal utility. Gruber's explanation provides a foundational understanding of consumer choice theory, illustrating how individuals make decisions based on their preferences and the marginal benefits derived from consuming different goods.
Jonathan Gruber discussed several key concepts related to consumer behavior and market dynamics:
Diminishing Marginal Utility: As individuals consume more of a good, the additional satisfaction derived from each additional unit decreases. This principle explains why larger sizes of goods, like sodas at fast food restaurants, are priced at a lower marginal cost per ounce compared to smaller sizes.
Market Pricing and Marginal Utility: Prices reflect the market's understanding of diminishing marginal utility. For example, the price difference between a small and a large soda accounts for the fact that consumers value the first few ounces of soda more than subsequent ounces.
Bulk Purchases and Packaging: Bulk purchases may offer cost savings due to packaging efficiencies, but the extent of these savings varies depending on the product. Non-perishable items may offer larger discounts for bulk purchases compared to perishable items.
Time Frame and Utility: Utility may vary depending on factors such as time of day and frequency of consumption. For example, the utility of a soda may reset later in the day if a person becomes thirsty again, but this reset is limited by factors like the perishability of the product and the policies of the seller.
Overall, Gruber's discussion highlights how economic principles such as diminishing marginal utility influence consumer choices and market dynamics, impacting pricing strategies and purchasing behavior.
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