Quiz 27. Cournot Ans

Quiz 27. Cournot Ans - q 1 – q 2 ) q 2- 30 q 2 = 90 q 2...

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

View Full Document Right Arrow Icon
Shomu Banerjee ECON 201 COURNOT DUOPOLY ANSWERS Suppose two duopolists produce the same identical product. The market demand for their product is given by the inverse demand curve p = 120 – q 1 q 2 , where p is the price, and q 1 and q 2 the output levels of the firms. The cost of producing one unit is zero for firm 1 and 30 for firm 2. (a) How much will each firm produce in Nash equilibrium? Firm 1’s profit is: Π 1 = pq 1 = (120 – q 1 q 2 ) q 1 = 120 q 1 – ( q 1 ) 2 q 1 q 2 . Differentiate this with respect to q 1 and set equal to zero: 120 – 2 q 1 q 2 = 0. Solve for q 1 to get firm 1’s best-response: q 1 = 60 – 0.5 q 2 . Firm 2’s profit is: 2 = pq 2 = (120 –
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q 1 – q 2 ) q 2- 30 q 2 = 90 q 2 – q 1 q 2 – ( q 2 ) 2 . Differentiate this with respect to q 2 and set equal to zero: 90 – q 1 – 2 q 2 = 0. Solve for q 2 to get firm 2’s best-response: q 2 = 45 – 0.5 q 1 . Substitute for q 1 from 1’s best-response into 2’s best-response: q 2 = 45 – 0.5(60 – 0.5 q 2 ) q 2 = 45 – 30 + 0.25 q 2 0.75 q 2 = 15 q 2 *= 20. Substitute for q 2 *=20 into 1’s best-response to get q 1 *= 50. (b) Calculate the equilibrium price p * and profits for each firm. From the demand curve, p * = $50 and 1 *= $2500 and 2 * = $400....
View Full Document

This note was uploaded on 10/26/2010 for the course ECONOMICS ECON 201 taught by Professor Dr.shomubanerjee during the Summer '07 term at Emory.

Ask a homework question - tutors are online