SOLUTION: a)The following are the demand and supply functions for three competing mobile phone models of different manufacturers. q_d1=92-20p_1+4p_2+4p_3 q_s1=24p_1-32 q_d2=60+4p_1-12p_

Algebra ->  Matrices-and-determiminant -> SOLUTION: a)The following are the demand and supply functions for three competing mobile phone models of different manufacturers. q_d1=92-20p_1+4p_2+4p_3 q_s1=24p_1-32 q_d2=60+4p_1-12p_      Log On


   

Question 1173662: a)The following are the demand and supply functions for three competing mobile phone models of different manufacturers.
q_d1=92-20p_1+4p_2+4p_3
q_s1=24p_1-32
q_d2=60+4p_1-12p_2+8p_3
q_s2=12p_2-44
q_d3=76+4p_1+8p_2-16p_3
q_s3=12p_3-20
Using Inverse Matrix Method determine whether there are prices which would bring the supply and demand levels into equilibrium for each of the three mobile phone models. If so, what are the equilibrium demand and supply quantities?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Hey, I am not an expert in Finance, no one minute.
But I have a common sense inside my head. 


My common sense says me: go to GOOGLE and look for the definition of the equilibrium of demand and supply.

GOOGLE responses to me


        Demand and Supply are said to be in equilibrium when demand equals supply. 
        The corresponding values of p and q are called the equilibrium price and equilibrium demand.


Very good.  It means that in each of the three pairs of the given equations, you should equate


        q_d1 = q_s1

        q_d2 = q_s2

        q_d3 = q_s3


It will give you three equations.


    92 - 20p_1 + 4p_2 + 4p_3 = 24p_1 - 32   is one of them.



And the remaining two equations you will create  ON YOUR OWN,  doing accordingly.


It will give you a system of three equations in three unknowns p_1, p_2 and p_3.


Write this system in its STANDARD FORM.


Then find in the Internet free of charge ONLINE solver to solve this 3x3 system of linear equations by the Inverse Matrix Method.


To find such a solver, go to GOOGLE with keywords "Inverse Matrix Method online solver".


GOOGLE will give you several web-sites on your choice.


By my experience,  web-site 

https://matrix.reshish.com/inverse.php

is very robust and comfortable.


Input/inject your matrix into the solver and get the answer in seconds with detailed explanations and steps.

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It is how a student should solve such problems in 20-es of the XXI century.

Happy solving (!)

Do not forget to post your "THANKS" to me for my teaching and pointing the way to you (!)