# Lecture7 - 1 Imperfect Competition Â We consider...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1/29/2009 1 Imperfect Competition Â¡ We consider competition in a market with a linear demand curve: Â¡ Inverse demand: P P D Q âˆ’ = = 302 ) ( Q P âˆ’ = 302 Â¡ First think of a monopolist with cost Â¡ Monopolist seeks to maximize profit: Q Q C 2 ) ( = 2 300 2 ) 302 ( ) ( Q Q Q Q Q Q C PQ âˆ’ = âˆ’ âˆ’ = âˆ’ = Î  500 , 22 , 152 , 150 2 300 = Î  = = â‡’ = âˆ’ = Î  M M M P Q Q dQ d Imperfect Competition: Cournot Â¡ 2 firms, 1 & 2 Â¡ Each simultaneously brings its quantity to market: Â¡ Total market quantity: 2 , 1 q q 2 1 q q Q + = Total market quantity: Â¡ Each has costs: Â¡ We seek a Nash Equilibrium q q C 2 ) ( = * 2 & * 1 q q Imperfect Competition: Cournot Â¡ We calculate Firm 1â€™s Best Response Function 1 2 1 )] 2 1 ( 302 [ ) 2 , 1 ( 1 q q q q q q âˆ’ + âˆ’ = Î  2 1 2 1 1 300 q q q q âˆ’ âˆ’ = 2 2 300 1 1 2 2 300 1 1 q q q q dq d âˆ’ = â‡’ = âˆ’ âˆ’ = Î  2 2 300 ) 2 ( 1 1 q q B q âˆ’ = = Imperfect Competition: Cournot Â¡ Similarly for Firm 2: Â¡ We seek a NE, so we want 2 1 300 ) 1 ( 2 2 q q B q âˆ’ = = * 1 300 * 2 300 q q âˆ’ âˆ’ Â¡ Solving two equations in two unknowns yields 2 1 300 * 2 , 2 2 300 * 1 q q q q âˆ’ = âˆ’ = 100 * 2 , 100 * 1 = = q q Imperfect Competition: Cournot 2 q ) 2 ( 1 q B 300 1 q ) 1 ( 2 q B 150 150 300 100 * 1 = q 100 * 2 = q Imperfect Competition: Cournot Â¡ If Â¡ Then 100 * 2 , 100 * 1 = = q q 102 = P 2 000 10 1 Î  = = Î  and- the Cournot-Nash Equilibrium Â¡ Then 102 = P 2 000 , 10 1 Î  = = Î  and 1/29/2009 2 Imperfect Competition: Cournot...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

Lecture7 - 1 Imperfect Competition Â We consider...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online