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From | Tomáš Houška <xbender@gmail.com> |
To | statalist@hsphsun2.harvard.edu |
Subject | st: results by simulation |
Date | Fri, 1 Mar 2013 18:57:31 +0100 |
Dear Statalist, I am facing a problem with finding a solution for set of simultaneous equations. I will try to illustrate the situation on a simple example: mc1= f (p1,p2,s1,s2) mc2= f (p1,p2,s1,s2) s1=f(p1,p2) s2=f(p1,p2) where mc1 and mc2 are marginal costs for product 1 and 2, p1 and p2 are their respective prices and s1 and s2 are their market shares. s1 and s2 are non-linear functions and the algebra of implementing them into mc1 and mc2 equations to get smth neat did not produce any helpful results. The level of marginal costs for mc1 and mc2 is known, prices are unknown (and to be determined) and market shares are endogenous variables. In the end, I have two equations (mc1 and mc2) that I want to use to find two unknowns (p1 and p2); i.e. such that values of p1 and p2 that will correspond to the known values of mc1 and mc2. In other words, I know the values for the left hand side of the equations for mc1 and mc2, I know the functions that lead to the values and I need to solve the system for p1 and p2. I reality I have 16 products, so 16 equations for marginal costs, market shares and 16 prices to determine. I am also able to guess some intervals in which the prices should be. I would greatly appreciate any help on how to tackle the problem in Stata. Tomas PhD student * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/