14_01_lec23

# 14_01_lec23 - 1 Multi-Plant Firm 1 14.01 Principles of...

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Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Multi-Plant Firm 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen November 9, 2007 Lecture 23 Monopoly and Monopsony Outline 1. Chap 10: Multi-Plant Firm 2. Chap 10: Social Cost of Monopoly Power 3. Chap 10: Price Regulation 4. Chap 10: Monopsony 1 Multi-Plant Firm How does a monopolist allocate production between plants? Suppose the ±rm produces quantity Q 1 with cost C 1 ( Q 1 ) for plant 1, and quan- tity Q 2 with cost C 2 ( Q 2 ) for plant 2. The total quantity is Q T = Q 1 + Q 2 . And the pro±t is π = Q T P ( Q T ) C 1 ( Q 1 ) C 2 ( Q 2 ) = ( Q 1 + Q 2 ) P ( Q 1 + Q 2 ) C 1 ( Q 1 ) C 2 ( Q 2 ) . To solve, use the ±rst order constraint: dP ( Q 1 + Q 2 ) dC 1 = P ( Q 1 + Q 2 ) + ( Q 1 + Q 2 ) = 0 , dQ 1 dQ 1 dQ 1 Since dP ( Q T ) dP ( Q T ) P ( Q T ) + Q T = P ( Q T ) + Q T = MR ( Q T ) , dQ 1 dQ T MR ( Q T ) = MC 1 ( Q 1 ) . Similarly, MR ( Q T ) = MC 2 ( Q 2 ) . Thus, MR ( Q T ) = MC 1 ( Q 1 ) = MC 2 ( Q 2 ) .

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Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2
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## This note was uploaded on 05/05/2010 for the course PHY 8.02 taught by Professor D during the Spring '07 term at MIT.

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14_01_lec23 - 1 Multi-Plant Firm 1 14.01 Principles of...

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