Transcription
[Music] In this podcast, I'm going to talk about consumer theory again. Consumer theory is really all about constrained buying. I'm going to introduce two topics: indifference curves and budget lines. An indifference curve looks something like this. We plot quantity of good Y on the Y-axis and quantity of good X on the X-axis.
A couple of things we just need to be aware of when we talk about consumer theory. One is the idea of transitive preferences, which means that if I prefer chicken to beans and I prefer beef to chicken, I prefer beef to beans. One thing in economics we have a hard time doing is actually putting numbers to things. I can say I prefer something more to another thing. I can say I prefer chicken more than beans, but it's hard to put an actual empirical number on that. We say that more is better, but there's also the law of diminishing marginal returns, which says as I consume more steak, I enjoy it less with each bite of steak I take. I enjoy the steak less and less.
We often talk about utility, and by utility, I mean happiness and satisfaction. This equation is read as: utility is equal to the function of X and Y. Utility is a function of consumption of two products, X and Y. In this case, X will be potatoes and Y will be steak. I've always had a hard time just talking about products X and Y. We want to maximize utility. So imagine you have a giant steak; a friend of yours has a giant potato. You are going to trade. How do you trade? If you have a lot of steak, then you will give up steak to get some potato. Just to be clear, this represents more; this represents less—less and more. On the Y-axis we have steak, and on the X-axis we have potato. If I have a lot of steak, then I'm willing to give up steak to get some potato. In fact, I'm willing to give up—in this scenario, I'm willing to give up a lot of steak to get a little bit of potato. So in this case, obviously, I'm giving up more steak and getting a little bit of potato. On the other hand, if I don't have very much steak and I'm down here at the lower part of the curve, then I'm willing to give up a little bit of steak, but I expect to get a lot of potato. As you move down the curve, notice that you actually conserve, or you can serve, the thing you have the least of. So again, on good Y we have steak; on X is potato. And we look at slopes of lines, and that's what measures the trade slope. We call the marginal rate of substitution. It's a change in product Y divided by the change in product X, which is the slope of the line. In this case, it's the change in quantity consumed of steak divided by the change in quantity consumed of potato. Indifference curves are negatively sloped. So your relationship, trade between two goods—in this case, X and Y, steak and potatoes.
My budget curve constrains my consumption. If I don't have a budget, I can consume as much as I want. So $5 per pound of potatoes; let's make that assumption. Let's make the assumption that it is $10 per pound for steak, and my income is $11,000. My equation looks something like this: $5 times the quantity of potatoes I consume and $10 times the quantity of steak I consume, and all that adds up to my total income of $11,000. What if I spend all my income on steak? Then I cross out that amount, and I have $10 times the amount of steak, which means I can consume 1100 lb of steak. On the other hand, what if I spend all my income on potatoes? It looks something like this, and I have 2200 lb of potatoes—a lot of potatoes. So we can plot this line. If I spend all on steak, it's 1100 steak; all on potatoes is 2200 potatoes. I can easily calculate the slope of the line, which is -1/2. The equation of my budget line looks something like this: the price of X times the quantity of X plus the price of Y times the quantity of Y. We use M instead of I, so we have income is equal to price of X times the quantity of X plus the price of Y times the quantity of Y. And now we're going to solve for Y. So we subtract the price of X times the quantity of X from both sides of the equation, which gives us income minus the price of X times the quantity of X on the left-hand side and price of Y times the quantity of Y on the right-hand side. We divide both sides by the price of Y to isolate Y, which gives us an equation like that. Eventually, we have this equation here again: again, price of X times the quantity of X plus the price of Y times quantity of Y, and all this adds up to income. Now when we plot our equation in the budget line or budget curve, this is the way our equation works. The slope of the line is the ratio of the two prices, and remember that the price of the goods we're looking at is $5 and $10, and the price—the slope should equal 1/2, which is what we calculated before. The slope of the line is the ratio of the prices. The slope changes if the price changes. So now what happens if the price of potatoes falls? What we see is it moves like that; that means you can consume more potatoes. That's it; it rotates around that axis there. You can buy more potatoes. What happens if the price of potatoes rises? You see that you can buy less potatoes, and you pivot the other way—buy less of all potatoes. What happens if the price of steak changes? What we see is as the price of steak goes down, you can actually buy more steak. That's if the price of steak goes down. On the other hand, if the price of steak goes up, you can buy less steak. Now the next question I have is what happens if income changes? In this case, if income goes up, the entire budget line shifts out—right? Buy more of everything. Income goes down; you can buy less of everything. So you see an entire shift of the line. Income changes; the entire budget line shifts. Income goes up; the budget line shifts outward. Income goes down; the budget line shifts inward. So in the end, we have constrained consumption, and we're going to draw a lot of indifference curves—that's called an indifference map—and we're going to have a budget line, and we're going to look at what happens when we combine these two together in our next class. But the key is going to be the slope of the indifference curve is going to equal the slope of the budget line; that's where you're going to maximize utility.