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Lecture 14

Economics 2151B - Lecture 14.docx

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Western University
Economics 2150A/B
Kristin Denniston

Economics 2151B Monday March 3 Lecture 14 Chapter 13 (con’t…) Homework 3 • Chapter 13 • Due Wednesday March 5 at midnight • The error on #9 has been corrected as of March 2 (MC = 20) • Save your answers as you work through the homework (it will time out after 6 hours) o You have 20 submissions you can do Stackleberg Model (con’t from last time) • Unique because it is a sequential model (there is a leader and a follower – the follower chooses quantity based on what the leader chooses to do) o The leader chooses quantity knowing that the follower will behave as a Cournot duopolist • This is a quantity setting model • We assume that the products are homogeneous (no product differentiation between the two firms) • Stylized assumptions: 1. Market D P = a-bQ where Q = Q + Q1 2 2. Firms have identical cost structures 3. MC = 0 • 1) We start with the leader o Residual Demand: Treats the output (Q ) of the other firm as a constant 2 o Demand for firm 1 (P 1 = a-b(Q 1 Q )2= (a-bQ )2– bQ 1 o *Substitute firm 2’s reaction function into the leader’s residual demand curve immediately before you work the problem a−bQ 1  Q2= 2b a−bQ 1  P1= a-b[ ] –bQ 1 2b a−bQ 1 a b  P1= 2b = 2 – ( 2 ) Q1 a o MR 1 - bQ 1 2 o The leader maximizes profit by setting MR1 = MC a  2 – bQ 1 0 a  Q1* = 2b • 2) The follower takes Q1* as a given and chooses Q *2like a Cournot duopolist. a−bQ 1 o Q 2 = 2b a a−b( ) o Q 2 = b 2b a o Q 2 = 4b • As more and more firms enter the market, it becomes more competitive and the Cournot model breaks down until we have a perfect competition result. The Stackleberg model falls between the Cournot duopoly and perfect competition. a a 3a • Total industry quantity = Q1+ Q 2 2b + 4b = 4b o We substitute this market quantity into the demand curve: 3a a  P = a-b( ) = 4b 4 Model Industry Market Industry π Firm Q i Firm π i Quantity Shared a a a2 a a2 Monopoly 2b 2 4b 4b 8b Cournot Duopoly Stackleberg 3a a 3 a a 2 4b 4 4 πm L = 2b , L = , F
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