U ( R ) ≡ U ( B ) ≡ U ( N ), trying to find unique values that result in indifference.The correct answers are ( 2 11 , 1 11 ) in ( p , q )I have managed to compute the following utility functions (they are correct) U ( R ) = p − 3 q − 1 U ( B ) = 1 − 11 p − q U ( N ) = − 4 p − 4 qHowever, If I apply p = 2 11 and q = 1 11 to the system of equations, the result is U ( R ) ≡ U ( B ) ≡ U ( N )

Question

U  (  R  )  ≡  U  (  B  )  ≡  U  (  N  ), trying to find unique values that result in indifference.The correct answers are       (          2      11        ,          1      11        )   in   (  p  ,  q  )I have managed to compute the following utility functions (they are correct)  U  (  R  )  =  p  −  3  q  −  1  U  (  B  )  =  1  −  11  p  −  q  U  (  N  )  =  −  4  p  −  4  qHowever, If I apply   p  =      2    11   and   q  =      1    11   to the system of equations, the result is   U  (  R  )  ≡  U  (  B  )  ≡  U  (  N  )

zupa1z · Accepted Answer

p  −  3  q  −  1  =  1  −  11  p  −  q  =  −  4  p  −  4  q  12  p  −  1  =  2  q  p  =            1      +      q        6    1  −  11      (                  1        +        q            6        )    −  q  =  −  4      (                  1        +        q            6        )    −  4  q      1    6    =      11    6    q  (  p  ,  q  )  =      (          2      11        ,          1      11        )

Izabelle Lowery · Accepted Answer

The systems of equations that you have are U(R)-U(B)=0, U(B)-U(N)=0, and U(R)-U(N)=0. This is a linear system in [p q].

U(R)≡U(B)≡U(N), trying to find unique values that result in indifference.

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