Given this market demand curve and cost structur1

# Given this market demand curve and cost structur1 - Given...

This preview shows page 1. Sign up to view the full content.

Given this market demand curve and cost structure, we want to find the reaction curve for Firm 1. In the Cournot model, we assume Q i is fixed for all firms i not equal to 1. Firm 1's reaction curve will satisfy its profit maximizing condition, MR 1 = MC 1 . In order to find Firm 1's marginal revenue, we first determine its total revenue, which can be described as follows Total Revenue = P * Q1 = (100 - Q) * Q1 = (100 - (Q1 + Q2 +. ..+ Qn)) * Q1 = 100 * Q1 - Q1 ^ 2 - (Q2 +. ..+ Qn)* Q1 The marginal revenue is simply the first derivative of the total revenue with respect to Q 1 (recall that we assume Q i for i not equal to 1 is fixed). The marginal revenue for firm 1 is thus: MR1 = 100 - 2 * Q1 - (Q2 +. ..+ Qn) Imposing the profit maximizing condition of MR = MC , we conclude that Firm 1's reaction curve is: 100 - 2 * Q1* - (Q2 +. ..+ Qn) = 10 => Q1* = 45 - (Q2 +. ..+ Qn)/2 Q 1 * is Firm 1's optimal choice of output for all choices of Q 2 to Q n . We can perform analogous analysis for Firms 2 through
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/13/2011 for the course ECO 1320 taught by Professor Staff during the Fall '11 term at Texas State.

Ask a homework question - tutors are online