Bertrand Oligopoly

This video shows you how to solve for the equilibrium price and quantity for both firms in a Bertrand duopoly.
Demand functions for the firms:
Qa = 100 - 2Pa + 3Pb
Qb = 120 - 2Pb + 2Pa
The marginal cost of production for both firms is $5 per unit. (Solutions below)
.
.
.
.
.
Solutions
Pa = $83
Pb = $74
Qa = 156
Pa = 138

[@Fmancillaz]

Thanks, i couldn´t find examples like this in spanish and you saved my life.

[@sebastianuyaban3939]

me too !° :D

[@priyadugar6944]

You were a great help during exams. Thank You ! for simple and easy solutions

[@HIFATS]

This is soooo helpful, thanks for this!!! actually saved my life, my lecturer on this topic in uni is pretty useless :-p

[@user-kd8oc6fe5l]

excellent my teacher

[@disintegratev6951]

I hope she finds oil in her garden fml that cleared everything up thank you so much. You saved me like 45 min of reading through lectures xD

[@femiayinuola2725]

Short of words....Thanks for the video....Really helpful

[@DD-ws6cu]

If you interpret profit as Profit = (P-MC)(Q), then you can just take the product rule and you don't have to deal with as much messy expansion. This video definitely helped me out though.

[@louisbelgrama3056]

Emma Stone's Eyes :) Thanks for the video, it helped a lot!

[@willhollon9326]

Thanks for the clear explanation I understand it now!

[@johnsimister7628]

Hello, Ashley. Thanks for making these videos; I will advise my students (at MMU, in UK) to look at them. I suggest you use a bigger whiteboard in future - your explanation of the maths is great, but many students will find it hard work.

[@adig3801]

lol

[@WeenkerIV]

Lol

[@alfredos3668]

Great video, only thing please sort all your videos in playlist that will help a lot to your followers. Great job.

[@Leslie-gj9nt]

I really like it this is like the simplest I have had but I can't seem to figure out your calculations.

[@Megan-vi5uu]

this is so clear, you saved my final!! thanks!!!

[@klimentpaskalev962]

That was simple and easy to understand. Thanks!!!

[@serinacat4781]

very clear very good, saved my life 👍👍👍👍

[@sayazdir]

firms B's best response function is (32,5 + 1/4*P), not 1/2. these videos are amazing btw. thank you so much

[@husseinnoor3430]

Pb=32.5+0.5Pa this is correct but next step of substitution Pb=32.5+0.5(27.5+0.75Pb) Pb_0.375=46.25 0.625Pb=46.25 Thus Pb=74 She is correct

[@wenyangmin6126]

OMG, you nearly saved me! Love you so much!

[@jhhxxvii]

Shouldn't the equilibrium price for each firm be equal to the marginal cost to achieve equilibrium?

[@jimmycold4408]

thank you sooo much，pf，its really easy understanding and helpful for my microe and TIO

[@AiurMedia]

wonderful video, helps me a lot! just the auto focusing of the camera is disturbing from time to time, is it possible to set it at manual focus? :)

[@muigaikamau1251]

Excellent Ashley. i now fully understand Bertrand oligopoly competition.

[@laundrettefragrance5246]

you are amazing!!! so easy to understand!

[@baraka694]

nice we enjoy it from Tanzania

[@user-kd8oc6fe5l]

baay'een irraa baradhee ebbifammii

[@nqobilelushaba4097]

thank you, you opened my eyes

[@shubhranshukumar7051]

Really helpful

[@FaraMamedoff]

Thank You ! you could also calculate for profits of both firms

[@nghianguyenhuu374]

Apparently angel doesnt need wings :D. Thank you so much for this explanation.

[@Gansosnatrip]

girl, i´, brasilian and need to say, you seved my next exam at PUC SP

[@ishratkhan542]

i am fom pakistan ilove your way of explanation. please upload videos formathematical economics

[@pawemikoajczuk9445]

Thanks a lot for your material, you are awesome. My question: How to prove by calculations that the potential merger of these two companies will be bad for the customers? All the best,

[@AshleyHodgson]

You would need a way of combining the two equations, and then solving for the monopoly price and quantity. This might require some assumptions, such as the lower of the two costs is the cost. You would also need a way of combining the demand functions. If you have identical demand and cost structures for the firms, you just solve a monopoly problem to see how much price increases and quantity decreases compared to this case.

[@pawemikoajczuk9445]

@@AshleyHodgson Thank you for answer and help ;)

[@sirajmk9967]

Good... bt one doubt for me how to find PB=74?

[@ashleycrasto9842]

When expanding the total cost in the maximization problem, why did you not multiply 5 with -2p_b for firm B and likewise 5 with -2p_a for firm A ?

[@TanvirAhmed-ye4tu]

Thank you ma for your lecture. Please help me to solve my question. My question is.. MC=$10 Qa=100-2Pa+Pb Qb=100-2Pb+Pa Now solve for Bertrand equilibrium(Pa,Pb,Qa,Qb=?).How could you explain this as a Nash equilibrium?

[@georgep262]

Can I use an Integral to find the TC (Total Cost) ? For example, TC= ∫ MC dQ = ∫ 5 dQ = 5Q + c

[@tendaimudyazhezha9762]

nice video......it waz helpful

[@SweetAlexMore]

What if the question doesn't give individual demand functions but a general demand function of Q = 1- P. And you need to find P for each firm?? So it says: Two firms A and B, produce a unit of good at a cost of a and b respectively. Q = 1-P. What prices do they choose if a=b

[@mrshaggy01]

thx a lot. this helped so much

[@TIRJOHN]

Excellent work. please carry on.

[@alejandraorjuela7058]

why is 110 and 130?

[@TIRJOHN]

for 110,100Pa-{5(-2Pa)}=110Pa. for 130 please calculate in same way

[@sbaba8241]

We could also find the best response function by setting MC=MR . But when i do , the answer is different . Can you please take a look ? TR = (100-2Pa+3Pb )*Pa , MR=100-4Pa+3Pb , MR=MC ,100-4Pa+3Pb=5 then best response function for firm 1 equals (95+3Pa)/4 .. Am i wrong ???

[@Ingrriid07]

i got the same

[@bekrookie8932]

MR is the first derivative of TR with respect to Qa, not Pa...

[@johnsolomonlegara2248]

Hi! I also thought the same thing at first, but I've realized that MR=MC's case is change in revenue with respect to quantity = change in cost with respect to quantity... for this problem, the MR is change in revenue with respect to price, so I don't think this is equal to change in cost with respect to QUANTITY. so we have to find total cost first and then find its derivative with respect to price.

[@zerrychin3562]

Really useful. Thx :)

[@TanvirAhmed-ye4tu]

Thank you mam for you solution. 😍

[@husseinnoor3430]

Excellent

[@salimelhallabi960]

thank you very much very helpful

[@saptarshimazumder5252]

Nicely explained :D

[@iMoosey49]

Amazing! thanks

[@MARYSMITH981]

What about the profit? Do you need to solve that at the end or leave it as it is?

[@Leslie-gj9nt]

How did you get 110 I can't seem to figure it out plse

[@Cinthia197704]

creo que hay un problema con la derivada de los beneficios totales en ambas empresas

[@miguelolivares3301]

Nice video

[@EconomicBearish]

what about if the MC=0 and they give you a cost=600 instead of dependant cost

[@TanvirAhmedMensWear]

i need a help, after>11o Pa-2Pa+3PbPa-500-15Pb,, How we calculate > 110-4Pa+3Pb=0,, how we can deduct 500 or where it gone,, also how we can get Pa=27.5+0.75Pb ,, pls let me know the whole derivative process.

[@chenvenice4960]

hello! why cost here is using MC*Q? Is it supposed to be average cost*Q?

[@nolantonkyn8921]

Chen Venice if mc is constant than that is the average cost

[@urabi3tube]

+Nolan Tonkyn please can you be more specific? suppose the total cost CT=5q+10 therefore MC=5 and AC= 5+10/q, so according to you if MC is a constant than that is the AC!!! will this case prove your answer is wrong, please can you be more clear to fully understand it thank you, much appreciated :)

[@johnsolomonlegara2248]

I think the correct response would be that while for a usual equilibrium MR = MC, the MR here is change in revenue with respect to PRICE, which I suppose cannot be equated to the MC which is with respect to QUANTITY. Thus, we integrate it with respect to quantity to procure a Total Cost Curve before differentiating it again with respect to PRICE. I guess the constant is assumed to be zero for simplification, but yeah, I'm still totally confused about this part.

[@serinacat4781]

mc is constant so that mc=avc, assuming no fixed cost, so that mc=ac 😊

[@blveflame]

you've saved my ass, girl

[@Mariamaria-be5jz]

why did you add 10 in 100 and 120?

[@taraxx2150]

I have no MC given, but fixed costs. So how would i solve it?

[@jhonnykokos8522]

thank you!

[@CYMRU4EVER10]

In betrand MC is always equal to P right???

[@FaraMamedoff]

in case of Bertrand Competition not Oligopoly

[@dehandede4116]

Thanks

[@ChristianTv216]

So here MR=MC doesn’t apply

[@lucavolpini2104]

Shouldn't it be P=MC for a Bertrand oligopoly? So prices are both 5??

[@patrickreilly3124]

These are differentiated products

[@kellydarco2514]

couldnt you solve for each firm's best response function by setting MR=MC?

[@pranshugarg9889]

Kelly D'Arco setting first derivative of profit equal to zero means MR-MC=0 which essentially is MC=MR... :)

[@kellydarco2514]

Oh, yeah. Thank you for responding!

[@rubaalbuni4523]

if u could answer in 2:36 why you didnt add 10pa??

[@kieranhyde8195]

because 10pa gets added to the hundred Pa on the left

[@marukiddo1416]

very helpful explanation, thank you so much. can I ask how do we figure out those parameters in the demand function? (100 ,2 , 3 for f1 and 120 , 2, 2 for f2)

[@meanmachinezzz]

Thanks dear

[@anneshirleylatorre1576]

how did you get 74?

[@matt23396]

wheres 110 come from?

[@meganlexi2623]

where does 110pa come from???

[@crupo123]

100PA +5*2PA

[@rings4433]

Is this not entirely wrong? In the Bertrand model, firms lower prices until MC, creating perfect competition.

[@FaraMamedoff]

it is an oligopoly where 2 firms control the whole demand function without supply curve, you talk about the perfect competition case where prices are equal to marginal cost

[@patrickbatman2320]

Fara he is absolutely correct,price competition doesn’t imply any profits in Bertrand Duopoly case,because firms will lower the price till reaching P=MC with the corresponding profit of 0

[@patrickbatman2320]

Fara he is absolutely correct,price competition doesn’t imply any profits in Bertrand Duopoly case,because firms will lower the price till reaching P=MC with the corresponding profit of 0

[@angelikigeorgiadou7645]

Why do we consider that dΠ/dP= 0 ??? Is it a fact ?

[@angelikigeorgiadou7645]

Ok, I found the answer to my question down ....={setting first derivative of profit equal to zero means MR-MC=0 which essentially is MC=MR... :)}

[@mustayeezalam7249]

What if when there is different marginal cost for both firm?

[@johnlihawa4145]

you will use that separately when establishing TR-TC then differentiate it with respect to price

[@joshvickery5553]

i love you

[@sananebanane7327]

nice eventually i have found someone not an indian speaking english well

[@npotufsstrugas6390]

This is hilarious.

[@alexp4385]

good stuff bad camera

[@RafaelLageDayTrader]

It's not 110 PA the correct is 100 PA

[@StephenBaBang]

no its not, she just skipped a step lmao