Cournot Duopoly vs. Collusion

[@shyruti]

What if both the firms have different cost functions? How will collision equilibrium change? I added both the cost functions and then calculated joint MC but my joint profit is coming out to be lower?

[@MattBirch]

Each firm's BRF will still start with MR=MC, but they each have their own MC. They will have different BRFs. All the steps are still the same. The low cost firm will produce a higher quantity and earn higher profits. For more detail, this might be helpful: kzbin.info/www/bejne/rYKoY2pupd93rac

[@jyotsanajoshi3704]

@@MattBirch I think he is asking about the collusion part. Can you tell how will we find collusion equilibrium in this case? 1) Equating MR= Firm with lower MC Low firm takes entire output High firm produces nothing 2) Equating MR= Sum total of both MCs

[@MattBirch]

@@jyotsanajoshi3704 think of it as more of an average of the MCs than a sum. If MC1 =10 and MC2=20, and they split production evenly, then the MC for 2 units is 30, or 15 per unit. If firm 1 produces 60 percent, then the weighted average of the MCs would be .6(10) + .4(20) = 14

[@SungilChoi-z9y]

I think that in case of collusion, MC should be Q/2. you calculated using MC=Q

[@楊佳惠-e2i]

Sorry I don't get it. Why should we double the slope?😓

[@MattBirch]

It comes from the calculus whenever you have a straight curve. TR=pq=(a-bq)q =aq-bqq. Take the derivative and the b will always have a 2 on it. Just double the slope and skip all that.

[@izazahmed6447]

Ec1a3?

[@Skey1337]

Can you please do one where you derive the discount factor and grim trigger strategy between two firms in cournot or/and bertrand in repeated setting? :-)

[@MattBirch]

Yeah. If I can finish my grading fast enough I will do it tomorrow. It might not be until next week though, just fyi.

[@MattBirch]

Here you go: kzbin.info/www/bejne/a3mpeKFre7iWmpY

[@KishoreKumar-cv4fn]

Thank you! I wanted to know that cournot equilibrium and cartel equilibrium are the same thing or not?

[@MattBirch]

They definitely aren't. Glad I could help!

[@k03dz0n3]

Hi Matt! Are you for available for a couple of hours of one-to-one tutoring? If so, I would really appreciate it! :)

[@MattBirch]

I am afraid not. At least not for any reasonable price...

[@k03dz0n3]

@@MattBirch what price do you charge? reasonableness is relative! :)

[@MattBirch]

@@k03dz0n3 haha, that is always true! My summer schedule (starting after next week) is more flexible. I would do it for $90 USD per hour (or 45 per half), due at the beginning of each session. I totally understand if that is not doable.

[@k03dz0n3]

@@MattBirch yes that is pretty heft, it just struck me though, is your approach applying algebra? because I still need to revisit algebra and may need to touch that up

[@MattBirch]

@@k03dz0n3 I have taught at all undergraduate levels, and some graduate. I personally like having the math there, as it gives me something concrete to help explain what is happening instead of memorization. But I can teach with and without it.

[@richardwebber8121]

Why did you set mc=q for the monopoly?

[@MattBirch]

It was a bit of an arbitrary choice. I just gave the monopoly the same cost as either firm. I could have added up their costs separately, in which case a 50-50 split would have MC=Q/2. Or I could have made it something else altogether.

[@richardwebber8121]

Matt Birch Ok. I am trying to figure out this problem when the two firms have asymmetric costs is why I am asking.

[@MattBirch]

@@richardwebber8121 Then you would have to do some sort of weighted cost function. If they produce the same amount, then the cost would be directly between them, etc. Hope that at least sort of helps.

[@baiqriniadekayanti3077]

how if in cartel and cournot have assumption zero cost?

[@MattBirch]

Just set marginal revenue equal to 0 (MC=0). The rest is the same.

[@baiqriniadekayanti3077]

@@MattBirch big thanks for your fast response.. It helps me alot.. I support your channel..

[@MattBirch]

@@baiqriniadekayanti3077 my pleasure. Glad to hear it helps!

[@loarmelin]

Thanks a lot!

[@MattBirch]

My pleasure!

[@requiemaeternam3658]

jesus fing christ i'm tired of you people assuming TC reamins the same for all firms

[@MattBirch]

Hey, um.... if you read through the comments or searched my profile or looked through my playlist or searched for Cournot with asymmetric costs, you might have found that we don't always assume that.: Here is an undergrad video with different costs: kzbin.info/www/bejne/rYKoY2pupd93rac Here is one with n firms that can each have a different MC: kzbin.info/www/bejne/iHzInIZ3hZZql8k Once you get to where that makes sense, I doubt you'll have to whine on KZbin about this anymore. Best of luck!

[@requiemaeternam3658]

@@MattBirch I appreciate the passive-aggressive reply, but these are videos about Cournot oligopoly with asymetric costs, not collusion. And no one seems to make that clear. What happens when 2 firms with different technologies decide to work together as a monopoly? You'll never find out, because it's not on YT!

[@MattBirch]

@@requiemaeternam3658 Yeah, it isn't in my textbook, so I didn't bother making a video on it. You need to combine the cost functions, as the monopoly will still want to do MR=MC. You need a combined MC. This is easy if they both have constant marginal costs. Not so easy otherwise. A hint: they will want to decide who makes how much of the output, first. Is it a 50-50 split? A 60-40 split? Create a weighted MC function to determine monopoly quantity. Good luck!

[@Mega-Human]

@@requiemaeternam3658 you're saying he's the passive aggressive one. Smh...