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st: results by simulation


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
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