Help with a simple problem.
- To: mathgroup at smc.vnet.net
- Subject: [mg28526] Help with a simple problem.
- From: Eric <hearts121 at deleteme.hotmail.com>
- Date: Wed, 25 Apr 2001 01:30:30 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi everyone,
I have a simple econ problem that I want to solve in Mathematica, but I
don't know how to input the problem correctly in Mathematica. The
following is the problem and what I tried to do in Mathematica. Any help
is greatly appreciated.
Eric
***********************************************************************
First, let Ex and Ey be some constant and Ex > Ey > 0.
Then
Xa + Xb = Ex and
Ya + Yb = Ey
Second, let functions
Ua(Xa , Ya) = V(Xa) + V(Ya)
Ub(Xb , Yb) = V(Xb) + V(Yb)
where V(.) is any strictly concave, increasing and differentiable function.
If we know that the following condition with the partial derivatives are
true:
D[Ua , Xa] D[Ub , Xb]
---------- == ----------
D[Ua , Ya] D[Ub , Yb]
prove that we must have Xa >= Ya and Xb >=Yb.
What I tried to do was solve for Xa in terms of Ya and Ex so I can
compare Xa and Ya.
*********************************************************************
Here is what I tried to do in Mathematica. But I get an error message.
Ex = Xa + Xb
Ey = Ya + Yb
U[x_, y_] := V[x] + V[y]
Solve[(D[U[Xa, Ya], Xa]/D[U[Xa, Ya], Ya]) == (D[U[Xb, Yb], Xb]/D[U[Xb,
Yb], Yb]) , {Xa, Ya, Xb, Yb}]