Information

Hal Varian
January 1992

Hidden action

Let's generate the diagram in the text for the hidden-action problem.  Suppose that the agent's utility function is Log[s].  The inverse of this is Exp[u].  Suppose also that the two states have probability (1/3,2/3) under action b and (2/3,1/3) under action a.  Make  cb=10, ca=5 and u bar=20.  The diagram looks like this:

actionB=ContourPlot[(2/3)*u1 + (1/3)*u2 - 10,
   {u1,0,10},{u2,0,10},
   ContourShading->False
   ]
actionA=ContourPlot[(1/3)*u1 + (2/3)*u2 - 5,
   {u1,0,10},{u2,0,10},
   ContourShading->False]
principal=ContourPlot[(2/3)*(200-E^u1) + (1/3)(100-E^u2),{u1,.1,5},
   {u2,.1,5},ContourShading->False]

Show[{actionB,actionA,principal}]

Hidden information

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