Extension of the Cournot Model

Extension of the Cournot Model - => Q1 = 90(1 n By...

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

View Full Document Right Arrow Icon
Extension of the Cournot Model 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 n (which are identical to firm 1) to determine their reaction curves. Because the firms are identical and because no firm has a strategic advantage over the others (as in the Stackelberg model), we can safely assume all would output the same quantity. Set Q 1 * = Q 2 * = . .. = Q n * . Substituting, we can solve for Q 1 * . Q1* = 45 - (Q1*)*(n-1)/2 => Q1* ((2 + n - 1)/2) = 45
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: => Q1* = 90/(1+n) By symmetry, we conclude: Qi* = 90/(1+n) for all firms I In our model of perfect competition, we know that the total market output Q = 90 , the zero profit quantity. In the n firm case, Q is simply the sum of all Q i * . Because all Q i * are equal due to symmetry: Q = n * 90/(1+n) As n gets larger, Q gets closer to 90, the perfect competition output. The limit of Q as n approaches infinity is 90 as expected. Extending the Cournot model to the n firm case gives us some confidence in our model of perfect competition. As the number of firms grow, the total market quantity supplied approaches the socially optimal quantity....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online