F09H2ak - Econ 467 Maria Muniagurria Answer Key Homework 2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 467 Maria Muniagurria Answer Key Homework 2 (I) Consider two identical firms (Firm 1 and Firm 2) that produce an homogenous product. The demand for their product is : P= 200 -Q, where Q= q 1 + q 2 . Each firm has a cost function: C(q i ) = 20 q i ( i.e. the Mc i is 20 and there are no fixed costs) (1) Calculate the Stakelberg equilibrium assuming that Firm 1 is the Leader and Firm 2 the Follower (i.e. calculate the SPNE assuming that Firm 1 moves first). (a) Step 1: calculate the reaction function for firm 2. Done in another problem: (*) q 2 = (180 - q 1 ) / 2 . (b) Step 2 : calculate the profit maximizing q 1 assuming that firm 2 will behave according to its reaction function. Choose q 1 to maximize Π 1 (q 1 , q 2 ) assuming q 2 is given in equation (*): Π 1 (q 1 ) = [200 - q 1 - ( (180 - q 1 ) / 2 )] q 1 - 20 q 1 = [180- q 1 - ( (180 - q 1 ) / 2 )] q 1 . Setting the first derivative equal to zero : d Π 1 ( ) / d q 1 = (180 /2 ) - 2q 1 + q 1 = 0 then : q 1 = 90, q 2 = 45, p= 65 ,
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

F09H2ak - Econ 467 Maria Muniagurria Answer Key Homework 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online