Total Posts:3|Showing Posts:1-3
Jump to topic:

Cournot competition help

kali122
Posts: 1
Add as Friend
Challenge to a Debate
Send a Message
6/7/2016 9:49:11 AM
Posted: 6 months ago
Here is the question: The inverse demand function can be written as p = 100-Q. There are two companies competing in the market. Competition type is Cournot competition. Both companies have constant marginal costs equal 10. Find the Cournot equilibrium ( price and quantity produced in each of the companies ).

Someone who can help me how to start?
ResponsiblyIrresponsible
Posts: 12,398
Add as Friend
Challenge to a Debate
Send a Message
6/7/2016 8:39:55 PM
Posted: 6 months ago
At 6/7/2016 9:49:11 AM, kali122 wrote:
Here is the question: The inverse demand function can be written as p = 100-Q. There are two companies competing in the market. Competition type is Cournot competition. Both companies have constant marginal costs equal 10. Find the Cournot equilibrium ( price and quantity produced in each of the companies ).

Someone who can help me how to start?

I've done this a few times. I think the Cournot model is usually used for two firms, in which case you're computing Q1 separately from Q2 (via a whole bunch of partial derivatives), but that likely isn't the case here since you only have a single market demand curve.

Basically, you produce where MR = MC, and you assume MR = P. Therefore, MR = MC = P = 10. So you plug this into the equation above for the price:

P = 100 - Q
10 = 100 - Q
Q = 90

Then plug Q into the original equation:

P = 100 - 90 = 10

Q = 90, P = 10.

I'm not 100% sure on this, and I recall the computations being far, far more intense than this, but this sounds about right based on some old notes I found. I wouldn't necessarily hang my hat on this answer, but hopefully the logic (MR = MC = P) can at least get you started.
~ResponsiblyIrresponsible

DDO's Economics Messiah
ResponsiblyIrresponsible
Posts: 12,398
Add as Friend
Challenge to a Debate
Send a Message
6/7/2016 8:42:28 PM
Posted: 6 months ago
Yeah, the "Cournot" equilibrium is the market equilibrium, so that is probably right. I had to compute the equilibrium for both companies, lol...

This is why macro > micro, folks.
~ResponsiblyIrresponsible

DDO's Economics Messiah