We use r and i interchangeably for the interest rate so 1 plus i 1 plus r

# We use r and i interchangeably for the interest rate

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year. We use r and i interchangeably for the interest rate, so 1 plus i, 1 plus r dollars next year. So, basically, what does the interest rate represent? This is important. The wage rate I defined as the price of leisure. Remember what the wage rate was? It was the price of leisure, that basically by working I forgoed the ability to-- I'm sorry, by taking leisure I forgoed the ability to
earn a wage, w. So, literally, that was a price of sitting around on the couch was the wage, w, I could've earned. Likewise, the interest rate is the price of first period consumption. By consuming today, I'm forgoing the fact that I could've earned the interest on that money had I consumed it tomorrow or next year. So the interest rate is the price of first period consumption, just as the wage is the price of leisure. Yeah? AUDIENCE: You said before that r and i are used interchangeably for interest. Does that play into the cost function at all? Is the cost for capital going to be the interest rate? PROFESSOR: I'm going to come to that. That's exactly what I'll talk about next lecture. So, basically, this is the key thing, but the key thing to understand intertemporal choice-- and the other important point to understand on why it's a bit harder than labor is there's an extra-- well it's not harder. It's the same thing. Remember, we said we don't model bads in this course. We model goods. So we're modeling your choice of how hard to work. We model the trade-off between consumption and leisure. And then we said define labor as the total amount of hours available minus leisure. Same thing here. We don't model savings. That's a bad. Now you might not think [? some of these ?] things are good, but savings really by itself is not a good. Unless you're Scrooge McDuck-- does anyone know who Scrooge McDuck is? Wow, that hurts. OK, he was this old cartoon character when I was a kid who used to, like, fill a swimming pool with money and swim in it. Basically, unless you're like that, the savings itself does not give you utility. We don't have savings entering utility functions. We have consumption entering utility functions. Savings is a bad. Savings is the mean by which you translate consumption period one into consumption period two. But from the effect of today you wish you didn't have to save. You just do it because you want to make sure you eat tomorrow. So we model the good. The good is consumption in period one, and savings is the difference between income and consumption in period one. So we don't model savings. We define savings as y minus c1. We model c1, and define savings as y minus c1. You can see that there in the diagram. Now what happens when the interest rate changes? Let's go to Figure 21-3. What happens when the interest rate changes? Actually, go to 21-4. OK? Skip 21-3. Got to 21-4. What happens when the interest rate changes? So, initially, we're at a point like a and then the interest rate goes up from r to r2. The interest rate goes up.
Now what does that do? Well, graphically, it steepens the budget constraint. What that means is it's raised the opportunity cost of first period consumption. First period consumption is now

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