### Fellow Blogger

I have not been able to access Chris Silvey's blog for a while now (over a week). Is it just my computer, or is there something wrong with his blog? Did he recover fully from the appendectimy?

A blog about becoming an economist (way in the future) and beer (daily!).

Well, I got three kick ass books for Christmas this year!

1.__Five Golden Rules__, this is a math book about the most important mathematical discoveries of the 20th century. Covers the fixed-point theorem, simplex, mini-max... others. I've read the fixed-point stuff and some of the simplex so far. I'm enjoying it.

2.__America: The Book__, No math, just hilarious.

3. A new collection of Dave Eggers short stories. I loved BWSG and I find him much better in small short story sized doses.

I also posed the following puzzle to my girlfriend's little brother:

Two (non-parallel) lines intersect at a point. Three can intersect at up to three points. How many intersections are possible if you have five lines? Ten? An arbitrary number, "n"? I just came up with this little puzzle, seems kind of neat.

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3. A new collection of Dave Eggers short stories. I loved BWSG and I find him much better in small short story sized doses.

I also posed the following puzzle to my girlfriend's little brother:

Two (non-parallel) lines intersect at a point. Three can intersect at up to three points. How many intersections are possible if you have five lines? Ten? An arbitrary number, "n"? I just came up with this little puzzle, seems kind of neat.

First, Merry Christmas everybody.

Grades are in tomorrow... The only class that I'm not sure about is diff eqs, it will all come down to whether or not I got the following right:

Prove that [Phi] is a solution to dy/dx = f(x,y) with y(x0)=y0 iff [Phi] solves the equation y(x) = y0 + Integral[f(t,y)dt] from x0 to x. I think I got it right on.

I have a Booneville Winter Solstice Ale that I plan on drinking with pumpkin pie Christmas Day. Should be awesome.

Classes next semester: Calc 3, Discrete Systems, and BS classes. Next Fall things get really fun: Abstract Algebra, Real Analysis 1, Topology, and Probability. I am really starting to love math.

Also, I got a kick ass idea last night. I love when I get econ ideas inspired by Jay-Z songs.

Grades are in tomorrow... The only class that I'm not sure about is diff eqs, it will all come down to whether or not I got the following right:

Prove that [Phi] is a solution to dy/dx = f(x,y) with y(x0)=y0 iff [Phi] solves the equation y(x) = y0 + Integral[f(t,y)dt] from x0 to x. I think I got it right on.

I have a Booneville Winter Solstice Ale that I plan on drinking with pumpkin pie Christmas Day. Should be awesome.

Classes next semester: Calc 3, Discrete Systems, and BS classes. Next Fall things get really fun: Abstract Algebra, Real Analysis 1, Topology, and Probability. I am really starting to love math.

Also, I got a kick ass idea last night. I love when I get econ ideas inspired by Jay-Z songs.

Finals are over! After not going to my computer program since the midterm, I stumbled into the room at 7:30 Thursday morning and probably got a B- or so on the test... that would put my grade at around a B+ I think. Stupid programming.

Then today at 7:30 AM I had my math finance final. I am glad that class is over. Four days a week, 8AM... I missed an average of 1.3 classes a week. I think I should end up with a good grade in there.

And finally, the mother of all finals, my differential equations take home. Four problems, 100 points, and 8 hours of work. My hands are cramped from the algebra and my brain is putty from Laplace transforming a bunch of shit. Not fun, my friends, not fun.

So anyways, I hope everybody else had equally enjoyable finals.

Then today at 7:30 AM I had my math finance final. I am glad that class is over. Four days a week, 8AM... I missed an average of 1.3 classes a week. I think I should end up with a good grade in there.

And finally, the mother of all finals, my differential equations take home. Four problems, 100 points, and 8 hours of work. My hands are cramped from the algebra and my brain is putty from Laplace transforming a bunch of shit. Not fun, my friends, not fun.

So anyways, I hope everybody else had equally enjoyable finals.

I really think that Dr. Becker has some of the most interesting ideas I've ever read, about economics or otherwise. A prof at my school has recently written a comment on one of Becker's papers, 1991's A Note on Restaurant Pricing and Other Examples of Social Influences on Price. In the paper, Becker argues that demand curves could conceviably be upward sloping, given the following:

D = Sum[di(p, D)] = F(p, D), given that dF/dp <>0 (I can't make partial derivative symbols on here...)

He then takes the differential of D-F(p,D) = 0 and gets:

dD - dF/dp dp - dF/dD dD = 0, which is rearranged to yield:

dD/dp = [(dF/dp) / (1-dF/dD)] > 0 iff dF/dD > 1

He then looks at what would happen if dF/dD > 1, which yields upward sloping demand curves. Here is my problem with the argument:

If demand is equal to F(p,D), and dF/dp < 0, then how can market demand be upward sloping? In other words, if each individual demand curve is downward sloping, how can the sum of all of these curves be upward sloping? It would seem to me that we have really just found a bound for the df/dD term at 1.

My professor has a problem with looking at an increase in income's effect on demand. In this case. It leads to an odd situation: income goes up, but in order for this to reflect a higher value for a normal good we have to shift demand to the left. But this would mean that people will buy a smaller quantity at each price. How can this be?

I have begun writing about the following way of incorporating bandwagon effects:

Let y be the proportion of some population that purchases a good or service. Then dy/dp is the change in this proportion with respect to a change in the price. If we wish to allow for bandwagon effects, we can model using the Ricatti Equation:

dy/dp = (1-y)[g(p) + ky]

Here we can alter g(p) to allow for only downward sloping demand curves and still include bandwagon effects, or we can let the demand curves slope upwards over intervals... all kinds of stuff. Anyway, I'm beginning with the simpler: dy/dp = (1-y)[-rp+ky], where r and k are constants.

D = Sum[di(p, D)] = F(p, D), given that dF/dp <>0 (I can't make partial derivative symbols on here...)

He then takes the differential of D-F(p,D) = 0 and gets:

dD - dF/dp dp - dF/dD dD = 0, which is rearranged to yield:

dD/dp = [(dF/dp) / (1-dF/dD)] > 0 iff dF/dD > 1

He then looks at what would happen if dF/dD > 1, which yields upward sloping demand curves. Here is my problem with the argument:

If demand is equal to F(p,D), and dF/dp < 0, then how can market demand be upward sloping? In other words, if each individual demand curve is downward sloping, how can the sum of all of these curves be upward sloping? It would seem to me that we have really just found a bound for the df/dD term at 1.

My professor has a problem with looking at an increase in income's effect on demand. In this case. It leads to an odd situation: income goes up, but in order for this to reflect a higher value for a normal good we have to shift demand to the left. But this would mean that people will buy a smaller quantity at each price. How can this be?

I have begun writing about the following way of incorporating bandwagon effects:

Let y be the proportion of some population that purchases a good or service. Then dy/dp is the change in this proportion with respect to a change in the price. If we wish to allow for bandwagon effects, we can model using the Ricatti Equation:

dy/dp = (1-y)[g(p) + ky]

Here we can alter g(p) to allow for only downward sloping demand curves and still include bandwagon effects, or we can let the demand curves slope upwards over intervals... all kinds of stuff. Anyway, I'm beginning with the simpler: dy/dp = (1-y)[-rp+ky], where r and k are constants.