Cournot Duopoly with Asymmetric Costs

[@rashmitaganti1443]

Great video! However, if I have q1 on x axis and q2 on y axis, how do I find the combined CS? I yielded the correct answer through your formula but finding it difficult to interpret the base and height for both the triangles in a graphical representation. Thanks!

[@MattBirch]

Good question. I probably would not do it with that graph. I would instead take the combined quantity and price and bring them to the original demand curve. That should be a much more straightforward exercise.

[@rashmitaganti1443]

makes sense! Thank you so much :)@@MattBirch

[@phamminhkhanh7771]

Thank you very much!, you saved my exam there :'). Also out of curiosity, may I ask how to calculate the deadweight loss here?

[@shyruti]

Thank you! How would we solve , if the two firms collude, considering they have asymetrical costs?

[@MattBirch]

It would depend on the cost functions. There would be some sort of combined marginal cost, based on each firm's MC and what proportion of production each firm produces. For example, if MC1=10, and MC2=20, and firm 2 produces 40% of cartel output while firm 1 produces 60%, the combined marginal cost for the industry would be: 0.6*10+0.4*20=14. The cartel would act as a monopolist with MC=14, choosing quantity and price, and then divide up the quantity 60-40. I don't know if that makes sense or not, but good luck!

[@shyruti]

Thank you for explaining! 😊

[@MattBirch]

My pleasure. Good luck!

[@Whoisit737]

@@MattBirch Hi Matt, are those percentages for the ratios derived from somewhere or are they arbitrary? If they are arbitrary, can they be derived?

[@Whoisit737]

additionally, does this make a difference to the sustainability of firms in collusion, when there is grim trigger strategy? Ive read in Cournot marginal costs don't matter for sustainability but I cant prove it. Thanks for your help

[@olegmorozov6882]

At 6:36 you mention, that MC=ATC, but what to do if there were any fixed costs? How to imply fixed costs into the profit model?

[@MattBirch]

Profit1=Q1(P-ATC1) Profit2=Q2(P-ATC2)

[@olegmorozov6882]

@@MattBirch Would it be correct to write down formula this way Profit= Q1(P-MC)-fixed costs, if there were fixed costs as well. I don't understand, how to calculate atc, if you know only MC and FC.

[@MattBirch]

@@olegmorozov6882 As long as the MC is constant, that would work perfectly.

[@pippophol]

Thank for you very much. How do you calculate the deadweight loss here? When the costs are assymetric.

[@Bug_Sugar]

Great video! Given a circumstance where identical firms with Asymmetric costs, and all I'm given is the marginal costs, how would i get the best response function?

[@MattBirch]

Hi Fred, You could solve it like this with different MC, and then set the MC equal to each other when you have BRFs. Or you could look at what I do in this video kzbin.info/www/bejne/ZoO2o4Wsjrtjh68 Or this kzbin.info/www/bejne/gnmWZIeCodWkna8

[@huldaadriyannah1633]

Top notch! Thank you

[@MattBirch]

Well thank you much! Glad to help. If you get to Stackelberg or Bertrand, I have more stuff that may be useful.

[@michelblanc3398]

Hi can you show the calculus for getting MR1= 100-2Q1-Q2 ? thank you

[@MattBirch]

TR1 = P1Q1 = (100-Q1-Q2)Q1 = 100Q1 -Q1^2 -Q1Q2. By the power rule: dTR1/dQ1 = 100 -2Q1 - Q2

[@TheKeirathebest]

hey! this was very helpful, thanks very much : )

[@MattBirch]

I am glad to hear it, even if this comment is super old!

[@jackwu7649]

Thank you, thank u, and thank u!

[@MattBirch]

You're welcome X3!

[@FronYxTreme]

Thank you for this video. Considering a case where you have two firms with different MC thus similar to your asymmetric MC video, what happens if you have a firm with MC1=0 and the other MC2>0? How would they collude? I am aware that they set collusive price equal to the one a monopoly would choose, but how do those MC affect the answer, rather than saying MC1, MC2>0 and MC1>MC2 let's say? Assuming infinite horizon and homogeneous Bertrand of course

[@MattBirch]

I am not entirely sure without doing some looking. I would assume you are straying into some sort of game theory or bargaining thing. Nash equilibrium, or some variant of it, probably the right concept still, but now the choice of collusion ratio needs to also fit for both firms. I don't know. I'll leave this one for you. What level of class is this for?

[@FronYxTreme]

@@MattBirch thank you for your quick reply. This is for final year Bachelor level, I would say advanced microeconomics equivalent rather than intermediate. It is a past paper question from a different university and I would have no point of contact from that university

[@MattBirch]

@@FronYxTreme I am afraid I just have to wish you luck on this. I am swamped for the near future and can't really do any searching right now. Good luck though.

[@FronYxTreme]

@@MattBirch no worries, I appreciate the resources you have put up already to aid with this so many thanks in that regard

[@MattBirch]

@@FronYxTreme My pleasure!

[@jannatulferdaus9992]

What happens if the similar function is used for collusion? We know in collusion both firms tend to produce same output which is half and half of the total Q. If marginal cost is now different, how will the marginal cost calculated? And what output would they produce? Will the output still be half and half or will the split it in anothr ratio?

[@MattBirch]

As long as they both have constant marginal cost, then take the average of the marginal costs. If one firm has an MC of 10, and the other firm has an MC of 20, and they make the same amount, every 2 units costs 30 with an average MC of 15.

[@minhduong7521]

@@MattBirch Could I also ask, Does this mean that both firms will receive the same profits since they have the same MC? If so, then why would the firm with the lower cost (MC=10) choose to collude and have a MC=15?

[@MattBirch]

@@minhduong7521 If they have symmetric costs and produce the same amount, they will have the same profit. If they have different costs, they still might collude, but the low cost firm would have to be better off with collusion than without. NOTE: the low cost firm does not have a higher MC with collusion. They still have a low MC. It is just that the combined output for the two firms has a higher combined MC than the low cost firm, and a lower MC than the high cost firm. It is kind of an average of the marginal costs.

[@jackkillick4688]

Very helpful, but I have a quick question if Firm 1's marginal cost dropped even further I know they would increase quantity but would it also cause a decrease in the quantity produced by Firm 2?

[@MattBirch]

For that, I would encourage you to look at Firm 2's best response function. How does firm 1's behavior affect firm 2's response?

[@jackkillick4688]

@@MattBirch Ok thanks

[@MattBirch]

@@jackkillick4688 No problem. Good luck!

[@cbd8692]

When you calculated CS, how did you derive (100-40)? Isn't it supposed to be 1/2 (60)(100-60)?

[@MattBirch]

The CS is the area between the demand curve and the price. We solved for price=40. The demand choke price is 100, so the CS triangle ranges from 40 to 100, or is 100-40=60 dollars tall.

[@MattBirch]

This supply and demand video goes in to more detail on how to calculate CS: kzbin.info/www/bejne/ZmmrY6KfhaxpiJI

[@mpandesyambayi5898]

How didn't I see this earlier 🙆

[@MattBirch]

Better late than never!

[@MattBirch]

Love of mine

[@manuelladossouvi8549]

. Thank you so much..!!!!!!!!

[@MattBirch]

My pleasure! Plenty more of where that came from!

[@safiyahasharia]

Thanks, this was great! How do you calculate Producer Surplus after this?

[@MattBirch]

Calculate the AVC at the firm q and then PS=q(p-AVC).

[@15v1c1]

@@MattBirch is the producer surplus the profit?

[@MattBirch]

@@15v1c1 only if there are no fixed costs. PS=Q(P-AVC) and PROFIT=Q(P-ATC).

[@alessandropaul9808]

Thanks a lot!

[@MattBirch]

You're welcome!

[@kudratramazanov9036]

Fab!

[@MattBirch]

Thanks!