My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

LinkBack Thread Tools Display Modes
November 30th, 2016, 03:51 PM   #1
Joined: Sep 2013

Posts: 83
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 side-payment 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 first-order 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 03:53 PM.
Ku5htr1m is offline  
November 30th, 2016, 03:56 PM   #2
Joined: Sep 2013

Posts: 83
Thanks: 0

This is from F.A.Cowell - Microeconomics - Principles and Analysis p.444-445
Ku5htr1m is offline  

  My Math Forum > Science Forums > Economics

conditions, externalities, internalisation, order, pseudomarke

Thread Tools
Display Modes

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

Copyright © 2019 My Math Forum. All rights reserved.