Economics maths part 2

freeze4real

hello all i just copied this from the economics forum as i got no reply there.

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 game theory 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

Delphi91

freeze4real wrote: »

...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
....

A = 7 - 0.5(7 - 0.5A)
A = 7 - 3.5 + 0.25A [Multiply in by the 0.5 outside the brackets]
A = 3.5 + 0.25A [7 - 3.5 = 3.5]
A - 0.25A = 3.5 [group the terms involving A together]
A(1 - 0.25) = 3.5 [Factor out A from both terms]
A(0.75) = 3.5 [1 - 0.25 = 0.75]
0.75A = 3.5

which is what you have in bold above.

Hope this helps!

freeze4real

Delphi91 wrote: »

A = 7 - 0.5(7 - 0.5A)
A = 7 - 3.5 + 0.25A [Multiply in by the 0.5 outside the brackets]
A = 3.5 + 0.25A [7 - 3.5 = 3.5]
A - 0.25A = 3.5 [group the terms involving A together]
A(1 - 0.25) = 3.5 [Factor out A from both terms]
A(0.75) = 3.5 [1 - 0.25 = 0.75]
0.75A = 3.5

which is what you have in bold above.

Hope this helps!

you are legend thanks for this.