Production

Hal Varian
January 1992

Robinson Crusoe economy

Let's draw a picture of a Robinson Crusoe economy.

u[c_,L_,a_] := Evaluate[pc^a (16-L)^(1-a)]
f[L_] = Sqrt[L]
maxOutput=f[16]
indiffCurves=ContourPlot[u[c,L,0.5],{L,1,15},{c,.1,9},
ContourShading->False]
technology=Plot[f[16-L],{L,1,15}]
Show[indiffCurves,technology]

Nonsubstitution theorem

Here we'll solve for an equilibrium in a  world where the Nonsubstitution Theorem applies.

c1[w0_,w1_,w2_,a0_,a1_,a2_] :=
   Evaluate[(a0^a0)(a1^a1)(a2^a2) w0^a0 w1^a1 w2^a2]
c2[w0_,w1_,w2_,b0_,b1_,b2_] :=
   Evaluate[(b0^b0)(b1^b1)(b2^b2) w0^b0 w1^b1 w2^b2]

Mathematica can't solve these equations symbolically.  (However, it's not too hard to transform it so the system can be solved: if you take logs of each side you have  a linear system.)  On the other hand, it is not hard at all to solve it numerically.

FindRoot[{w1-c1[1,w1,w2,.2,.4,.4],
          w2-c2[1,w1,w2,.1,.5,.4]},{w1,1,2},{w2,1,2}]

THIS NEEDS FIXING!