Two linear equations and two unknowns

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tomyy20212

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Anyone can help out with that equation please?

MR1=100-Q1
MR2=220-2Q2
equating the marginal revenue functions give us one equation in two unknowns Q1 and Q2?

100-Q1=220-2Q2 ???????

Thank you
 
tomyy20212 said:
Anyone can help out with that equation please?

MR1=100-Q1 ................................................ (1)
MR2=220-2Q2................................................(2)
equating the marginal revenue functions give us one equation in two unknowns Q1 and Q2?

100-Q1=220-2Q2 ???????

Thank you
Click to expand...
What is "given" in those equations?

What do you need to "find"?

Please post the original question, as it was given to you.
 
tomyy20212 said:
Q1 and Q2
Click to expand...
What are those?

I had asked two questions (and one request to post the original problem).

Please answer those questions in "full sentences" and please post the original question, as it was given to you.
 
They are Marginal Revenue functions in each market segment, In market segment 1 we have MR1=100-Q1, In a market segment 2 we have MR2=220-2Q2, Equating the marginal revenue functions gives us one equation in two unknowns, Q1 and Q2

100-Q1=220-2Q2

We have a system of two linear equations on two unknowns. I already know the answer as the equation is pretty simple. Q1=40 and Q2=80 but how to use straightforward algebra to solve the equation?
 
HOW do you "already know the answer as the equation is pretty simple. Q1=40 and Q2=80"? That cannot be derived from the information given.

In fact, there are many values of Q1 and Q2 that satisfy 100- Q1= 220- 2Q2.
Any values that satisfy that equation must also satisfy 2Q2- Q1= 220- 100= 120 so whatever Q1 is 2Q2= Q1+ 120 or Q2= Q1/2+ 60.

Yes 2(80)- 40= 160- 40= 120.

But it is also true that Q1= 50, Q2= 25+ 60= 85 satisfy 2(85)- 50= 170- 50= 120.
Or that Q1= 200, Q2= 100+ 60= 160 satisfy 2(160)- 200= 320- 200= 120.

A single equation in two unknowns may have infinitely many solutions.
 
We still have not been given the complete problem. For example, we have not been given any economic rationale for equating the two marginal revenue functions. Despite repeated requests, we have not been given the complete and exact statement of the problem.
 
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