masAng

  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...