
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
November 30th, 2016, 04:51 PM  #1 
Member Joined: Sep 2013 Posts: 68 Thanks: 0  EXTERNALITIES  First order conditions
There are just two firms: firm 1 is a polluter and firm 2 the victim. Firm 2 (the victim) makes an offer of a sidepayment or bribe to firm 1. The bribe is an amount that is made conditional upon the amount of output that firm 1 generates: the greater the pollution, the smaller is the bribe; so we model the bribe as a decreasing function $\displaystyle \beta ( \cdot )$. The optimisation problem is: $\displaystyle \mathop {\max }\limits_{\{ {q^2},\beta \} } \sum\limits_{i = 1}^n {[{p_i}q_i^2  \beta ]}  {\mu _2}{\Phi ^2}({q^2},q_1^1)$ The firstorder conditions are: $\displaystyle \eqalign{ & {p_i}  {\mu _2}\Phi _i^2({q^2},q_1^1) = 0 \cr &  1 + {\mu _2}{{d\Phi _i^2({q^2},q_1^1)} \over {dq_1^1}}{{dq_1^1} \over {d\beta }} = 0 \cr} $ How did they arrive at this expression for the FOC's? Last edited by Ku5htr1m; November 30th, 2016 at 04:53 PM. 
November 30th, 2016, 04:56 PM  #2 
Member Joined: Sep 2013 Posts: 68 Thanks: 0 
This is from F.A.Cowell  Microeconomics  Principles and Analysis p.444445


Tags 
conditions, externalities, internalisation, order, pseudomarke 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help creating pseudorandomized groups  Scott Oates  Complex Analysis  1  January 11th, 2016 03:00 PM 
Breaking news : Fermat pseudoprimes  mobel  Number Theory  38  October 15th, 2015 01:13 AM 
Pseudofinite fields  Mathworm  Abstract Algebra  1  March 5th, 2009 03:20 PM 
PseudoDistances within a depthdetermination problem  Shaitan00  Computer Science  0  November 16th, 2008 02:46 AM 
PseudoDiophantine Nuisance  reddmann  Number Theory  2  August 30th, 2007 08:03 AM 