SOLUTION: 2)Determine the equilibrium prices of the three interdependent commodity that satisfy. 𝑝1+3𝑝2+3𝑝3=32 𝑝1+4𝑝2+3𝑝3=37 �

Question 1169745: 2)Determine the equilibrium prices of the three interdependent commodity that satisfy.
𝑝1+3𝑝2+3𝑝3=32
𝑝1+4𝑝2+3𝑝3=37
𝑝1+3𝑝2+4𝑝3=35
(Express this system in matrix form and hence find the values of 𝑝1, 𝑝2 and 𝑝3)

Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.


𝑝1 + 3𝑝2 + 3𝑝3 = 32    (1)
𝑝1 + 4𝑝2 + 3𝑝3 = 37    (2)
𝑝1 + 3𝑝2 + 4𝑝3 = 35    (3)


From equation (3), subtract equation (1).  You will get

           p3 = 35 - 32 = 3.    (4)


Next, from equation (2), subtract equation (1).   You will get

     p2       = 37 - 32 = 5.


Sunbstitute the found values  p2= 5,  p3 = 3  into equation (1).  You will get

p1 + 3*5 + 3*3 = 32

which implies  

p1 = 32 - 3*5 - 3*3 = 8.


ANSWER.  p1= 8,  p2= 5,  p3= 3.

Solved.

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