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  The next question is in going around the ellipse,  How does it go fast when it near the sun and slower when it further from the sun? and so on .  If we take away the other focus we have the sun, and the planet going around.  Kepler found the answer to this, too,  He found this, that if you put this position  of the planet down at two times  separated  by some definite time  let's say three weeks.  A nd then at another place  in the orbit  put the positions of  the planets  again separated by  three weeks. A nd draw lines from the sun to the planet  (technically called radius vector  but anyway lines from the sun to the planet).  Then the area that's  enclosed in the orbit  of the planet and  the two lines  that are separated  by the planets' position  three weeks apart  is the same no matter  what part of the orbit  the thing is on. So that it has to g...

  That basically, at the optimum, the ratio of Marginal Utilities equals the Ratio Prices. That is the rate at which you want to trade off pizza for cookies, is the rate at which the market will allow you to trade off pizza for cookies.  Basically, it's saying the ratio of the benefits.  Think of this as the benefits and this as the costs.  The MRS as the benefits. It's what you want. The  MRT is the costs. It's where you're constrained.  You want to set the ratio of the benefits equal to the ratio of the costs I find it actually easier to think of it this way.  If you just rearrange terms, you can write it as MUc over pc  equals MUp over p sub p.  MUc / Pc = MUp / Pp   I like this way of writing it because I call this  " The bang for the buck equation " What this is saying, your marginal happiness per dollar should be equal. This is sort of the happiness per dollar spent on cookies.  This is the happiness per dollar spent...

  So the demand curve, in this case is represented by the equation Q equals 1,800 minus 400p. Now you're immediately saying well, where's the 1,800, 400 come from?  It doesn't matter right now. That's what I'm going to teach you in the next few lectures. Right now that's an equation that represents a line. And the critical aspect of that equation is that there's a negative relationship between price and quantity. As price goes up, consumers want fewer roses. Why is that? Well, it's just because of opportunity cost. The more expensive is a rose, the more youhave to give up to buy it. So it's opportunity cost is higher, so you want it less. So the higher is the price, the fewer roses you want. So we get a downward sloping demand curve. The blue line. Now the supply curve represents the same relationship between price and quantity but from the supplier's perspective. A supply curve in this case that we've drawn here has the equation q equals 200...

  AUDIENCE: What if you have just three indifference curves so there is none that hit the tangent? Do you just go for one that's like the most tangent I guess?  JONATHAN GRUBER: We could have lines, and the lines could end up - you could end up lying along a budget constraint. Or you could even have utility functions, which just touch a budget constraint at one extreme or another. And we'll talk about those cases.   Yeah? Mahasiswa: So utility function go through lines and the budget constraint, right?  Jonathan Gruber: Yeah Mahasiswa: Isn't this just Lagrange ?? Jonathan Gruber: Well, let's come to the math then. OK, let's come to the mathematical derivation. So that's the graphic. So let's come to the math.  Now, always a bit of a tightrope act when I'm doing math up here on the board, so bear with me.  OK? But the key thing is the math of constraint optimization is all about the marginal decision. Remember, it's hard to say how many cookies y...

  Adding options to people's lives can't help but increase the expectations people have about how good those options will be. And what that's going to produce is less satisfaction with results, even when they're good results.  It all looks so great. I can't wait to be disappointed Nobody in the world of marketing knows this. Because if they did, you wouldn't all know what this was about. The truth is more like this.  Everything was better back when everything was worse The reason that everything was better back when everything was worse is that when everything was worse, it was actually possible for people  to have experiences that were a pleasant surprise.  Nowadays, the world we live in -- we affluent, industrialized citizens, with perfection the expectation -- the best you can ever hope for  is that stuff is as good as you expect it to be. You will never be pleasantly surprised, because your expectations, my expectations, have gone through the roof...

  I'm the oldest of three kids in my family. We're the first generation in our family to go to college. I did well in high school. I did things like Mock Trial. I successfully fought and overturned a book ban at my high school. Things like this made me think, "Oh, maybe law - maybe being an advocate would be fun."  I came to Grinnell; I did well here. I went to a law school; I did well there. Passed the Bar, got the type of job I wanted, and I was being an actual lawyer. But to use another metaphor, I kind of realized that morning, having that (full-blawn) panic attack, that I was sort of like Wile E. Coyote chasing the Road Runner. And I was going so fast from goal to goal and step to step. At the time, I'd started doing what I wanted to do, and it was the end goal all the time. I was a mile off the edge of the cliff and just falling all the way straight down.  Now, thankfully, that situation - I used it as a wake-up call. I started things like therapy and...

  When a man named Tycho Brahe got an idea, this idea, that to look at the thing, to record  the details and to hope  that in the information thus obtained may lie a clue to one or another of a possible theoritical interpretation.  This is the key of modern  science and is the beginning  of the true understanding of nature.  So Tycho who was a rich man, and owned,  I believe an island near copenhagen.   Outfitted his island with great  brass circle and special  observing positions   (situation chair that you could  look through a little hole)  and recorded night  after night the position of the planets.  It's only through such hard work that we can find out anything.  When all these data were collected, they came into the hands of Kepler who then tried to analyze what kinds of motions the  planets made around the sun.  And he did this by a method of trial and error. ...