How to derive a best response function? Watch

Superunknown17
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#1
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Can anyone help me derive the following best response functions:

q1 = 1-4/3(p1) +2/3(p2)
q2 =4/3(a) +2/3(p1)-4/3(p2)

Thanks!
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MagicNMedicine
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No marginal costs in there?

This looks like you are doing Bertrand competition with differentiated goods right?

You need to turn these in to profit functions so you can maximise profit with respect to own price (ie for firm 1 it will be d(profit)/d(p1) and set equal to zero.

Profit = TR - TC but it seems here you don't have costs unless it says anything about costs somewhere else in the question, if there are no costs then it's just TR. TR is PxQ.

So for the first one you can start by multiplying both sides by p1. Now you will have p1q1 on the left hand side which is TR. Differentiate with respect to p1 and set equal to zero.

Do the same for firm 2, but use p2 instead of p1 these are the best response curves.
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Superunknown17
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(Original post by MagicNMedicine)
No marginal costs in there?

This looks like you are doing Bertrand competition with differentiated goods right?

You need to turn these in to profit functions so you can maximise profit with respect to own price (ie for firm 1 it will be d(profit)/d(p1) and set equal to zero.

Profit = TR - TC but it seems here you don't have costs unless it says anything about costs somewhere else in the question, if there are no costs then it's just TR. TR is PxQ.

So for the first one you can start by multiplying both sides by p1. Now you will have p1q1 on the left hand side which is TR. Differentiate with respect to p1 and set equal to zero.

Do the same for firm 2, but use p2 instead of p1 these are the best response curves.
Thanks so much. Sorry, the MC's are just c1=c2=c with c between 1 and 0.

Thanks for your help, do you have any resource that helps explain this so I can understand it for next time?
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MagicNMedicine
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OK you will have to put the MCs in that profit function then so its TR - TC (where TC will be MC x Q) and differentiate that.

If you are at uni do they have Perloff's Microeconomics book (ideally Microeconomics: Theory and Application with Calculus) as this is quite good on Cournot, Stackelberg and Bertrand models and has nice simple worked examples.
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.ACS.
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Equally, have a look at this:
http://disciplinas.stoa.usp.br/plugi...ChurchWare.pdf

It's a fantastic resource in industrial organization problems like the one you're working on.
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