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  Can anyone tell me what that means?  Your marginal rate of substitution (MRS) is 2.5.   What does that mean?   That is a meaningful concept.   Utils are not, but that is. Yeah, say it loudly so we can hear.  AUDIENCE: You're willing to trade -- you're willing to trade two pizzas for one cookie.  JONATHAN GRUBER: You're willing to trade?  Exactly, you're willing to give up 2.5 slices of pizza for one cookie. That's what that number means. And that is a meaningful number.  That's not an ordinal. That's cardinal. We can use that.  You are willing to give up 2.5 slices of pizza to get one cookie.  What is the market asking you to give up?  How much pizza do you have to give up to get one cookie? Half a slice. You are happy to give up 2 and 1/2 slices of pizza to get a cookie, but the market is saying we'll let you have a cookie for half a slice of pizza .  So what should you do?  AUDIENCE: Trade.  JO...

  And this is proportional to the mass, So that if we were to take two different objects, first swing one, and then swing another one at the same speed around the head and measure the force in the second one , that second one, the new force is bigger than the other force in the proportion that the masses are different.  This is a way of measuring the masses by how hard it is to change the speed.  Now then Newton saw from this, that for instance, to take a simple example, if a planet is going in a circle around the sun no force is needed to make it go sideways, tangentially if there were no force at all on it, it would have just keep coasting this way. But actually, the planet doesn't keep coasting this way, but finds itself later not out here, Where it would go if there were no force at all. But further down toward the sun. In other words, its velocity, its motion has been deflected toward the sun.  So what the angels have to do is to beat their wings in toward the s...

  There's got to be somepart of our mind that came out our nature. I know that because I'm in a twin, an identical twin. And so when it came to writing my PhD dissertation. I thought to myself if there's any part of human behavior that has a biological origin. It must be our patterns of love and marriage. Because as Darwin would have said, if you have four  children and I have no  children, You live on  and I die out.  The game of love matters.  And so you would think there would have been selection for all kinds of behaviors that would enable you to fall in love with somebody, form a partnership and raise your babies as a team. And so that's why I started to study love, And you know people will often think,  "Well she studied love because had a bad relationship in high school" Well, nobody gets out of love alive. We all have problems with love. But that did not stimulate me to study romantic love. It was simply because I was an identical twin. And I w...

  Basically we write down the functions are invertible. And we use them both ways, it's the bottom line. It doesn't we're really writing down equilibrium in Q and P. It doesn't really matter what X and Y is. We're really just writing down an equilibrium relationship.  It's just the convention is to put Q on the X- axis. Even though the convention will sometimes write demand curves with P on the left hand side the graphic convention will never change but  How I write the curves might change How I write the equations might change You use opportunity cost to justify why demand sloping? Great question. Okay, let's go through it. That's exactly the kind of question I want to hear this semester. Is does someone want to take a crack at it? Anyone want to explain? and speak up  If the price is higher to in order to get that rose, you had to give up more because the price represents sort of like your opportunity. Right, for the opportunity cost of any good in the...

  Drunkards the word occurs, "He will forgive even the drunkards" .  What is it about that scene?  Why does cats think that's my favorite scene? besides knowing what the original title of the book is.. What's so important about that scene?  It's kind of it's about forgiveness and that's kind of what like the strong four throughout the book is like to forgive himself or to be forgiven.   To be forgiven ? not I think not so much to forgive himself but to be... to be forgiven (..) good other things?  other thoughts about this?  Well it also kind of  contrasts with Raskolnikov because he does believe that he's worth in some way and Marmeladov is saying like that he's not worthy. And that's why he'll like get forgiveness but Raskolnikov hasn't really realize that he's not worthy. That's good because I mean somebody said right raskolnikov's theories he's still very much wetted to his theory in fact he goes to Siberia, even wet...

  So let's say this mathematically.  At a point like A you  have your marginal utility for pizza is the derivative of the utility function with respect  to the number of slices of pizza. It's the marginal utility. It's derivative of the utility function. So it's dU/dp, which is equal to 0.5 times C over square root  of P times C.  MUp = dU/dp = 0.5 x c /  And at point A we had  two cookies and five pizzas. At point A,  P was five C was two  that's true of point A.  So we can evaluate the marginal utility.  dU/dp, which equals 0.5 times C over square root of P times C.  So that's 1 over the square root of 10.  That's the marginal utility of the next slice of pizza.  The next slice of pizza makes you 1 over square root of 10 happy.  Once again, that number is meaningless.  So we only care about it in ratios. So we need the ratio. So let's do the marginal utility of cookies.  That's dU/dc, which is 0...

  So if it's not survival of the fittest individual and it's not survival of the fittest group, then what is it? The Beginning Life Well, to explain that, I want to take you on a little journey, all the way back to the beginnings of the Earth.  Where we are now, there is nothing. Well, not really nothing, but nothing interesting. There are only simple things, like these blobs. This one might be a carbon dioxide molecule, or it might be cyanide. We don't know for sure what they are, but we do know that these compounds are very simple. So for now, they'll just be blobs floating around our void. In fact, much of what we'll encounter along our journey here are just hypotheses. A lot of Earth's early history is still a mystery, so keep that in mind.  Now, every so often, our blobs get a surplus of energy, maybe from a ray of UV light or a nearby hot source. This is the first major upgrade to our void, excess energy, as it allows our blobs to interact with each other....