Your Econ Lesson for Today

**Ex Nine** · 12-16-2005 10:12 PM

The principal minors of dimension m in the determinant of the non-bordered Hessian matrix of second-order partial derivatives must have the sign (-1) raised to the m in order to satisfy the second-order conditions of the firm's unconstrained profit-mazimization model, part of which implies the existence of isoquants that are convex to the origin and, as per the first-order condition, move through a point of tangency with an isocost line for equilibrium values of the choice variables.

And don't you forget it.

**InTheMoment** · 12-16-2005 10:16 PM

Actually, I was wondering if you could tell me how to get....how to get to Sesame Street?

**Ex Nine** · 12-16-2005 10:18 PM

That would involve constrained optimization and thus, Hessian matrices that are bordered with partial derivatives of a Lagrange multiplier, at least if you're using the Laplace method.

**R.Carter** · 12-17-2005 12:42 AM

I..and I think it's for the best, have NO IDEA wtf you're talking about.
Intrigued though.

**Ex Nine** · 12-17-2005 12:49 AM

Whoops, sorry, Carter.

I forgot to mention that we are studying a two-input world.

**R.Carter** · 12-17-2005 03:48 AM

Originally posted by Ex Nine
Whoops, sorry, Carter.

I forgot to mention that we are studying a two-input world.

Wake me up when you get to third input.

**Ex Nine** · 12-17-2005 04:52 AM

Yeah, we could call it "imaginary capital" and exogenize it or something.

**R.Carter** · 12-17-2005 05:02 AM

There you go reading my mind again.

**Ex Nine** · 12-17-2005 05:10 AM

Well could it be a choice variable? There does not seem to be resource scarcity in the case of imaginary capital, which would make a choice due to scarcity meaningless. We could make it a fixed parameter and slap it next to Y as an output multiplier. The producers imagine they are putting in a third input in the form of imaginary capital to maximize profits.

We could call it the Carter multiplier and write it as a little c. So cY is net complex output, by virtue of it having both a real and imaginary component.

**R.Carter** · 12-17-2005 02:13 PM

Originally posted by Ex Nine
The producers imagine they are putting in a third input in the form of imaginary capital to maximize profits.

We could call it the Carter multiplier and write it as a little c. So cY is net complex output, by virtue of it having both a real and imaginary component.

Happy to contribute.
That's quite the brain you've got there, btw.