Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta

How to derive a best response function? watch

Announcements
    • Thread Starter
    Offline

    16
    ReputationRep:
    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!
    Offline

    19
    ReputationRep:
    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.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (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?
    Offline

    19
    ReputationRep:
    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.
    • Community Assistant
    Offline

    19
    ReputationRep:
    Community Assistant
    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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 15, 2015
Poll
Do you like carrot cake?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.