Economics maths

freeze4real

hello guys I have this micro asignment which I am stuck on.

so I did some research and I found a similar tutorial that was kind of my assignment.

This deals with gametheory oligoploy and nash equilibrium, sweet topics lol.

How do you find the Cournot Equilibrium Level Output and Price in Economics?

Consider the following Duopoly

Market Demand = P = 14 – Q , where Q = (q1 + q2)

assume that MC = 0

a) Find the reaction curve for each firm
b) Find the Cournot Equilibrium level of Market Output (Q) and then find the Price (P)




so this is the reaction function

A=7-0.5B
B=7-0.5A
so using the reaction function to find equilibrium output and price the equation below was used.

A=7-0.5(7-0.5A) = 7-3.5+0.25A
0.75A=3.5
A=3.5/0.75=14/3≈4.67

the bold bit is what I dont understand.
from o.25A it went to 0.75A

I first thought it was a typing error but it's not.




can someone please explain how he got there,

Thanks

1st On

I think what you are asking is just the algebra?
A=7-0.5(7-0.5A)
ð A=7-3.5+0.25A
ð A-0.25A=7-3.5
ð 0.75A=3.5
ð A=3.5/(0.75)
ð A=14/3
ð A≈4.67
Hope this is what you were looking for...