Mbot at 13:34, 8 November 2011

2011-11-08T13:34:12Z

← Older revision		Revision as of 08:34, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: lpcon		Problem type appears to be: lpcon
	Time for symbolic processing: 0.~~18169~~ seconds		Time for symbolic processing: 0.18361 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 22 ConJacEv 22 Iter 19 MinorIter 74		FuncEv 1 ConstrEv 22 ConJacEv 22 Iter 19 MinorIter 74
	CPU time: 0.~~015600~~ sec. Elapsed time: 0.~~025000~~ sec.		CPU time: 0.031200 sec. Elapsed time: 0.024000 sec.

	</pre>		</pre>

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} TomSym implementation of GAMS Example (PINDYCK,SEQ=28) This model finds the optimal pricing and extract..."

2011-11-02T21:02:34Z

Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} TomSym implementation of GAMS Example (PINDYCK,SEQ=28) This model finds the optimal pricing and extract..."

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{{Part Of Manual|title=the TomSym Manual|link=[[TomSym|TomSym Manual]]}}

TomSym implementation of GAMS Example (PINDYCK,SEQ=28)

This model finds the optimal pricing and extraction of oil for the OPEC cartel.

Pindyck, R S, Gains to Producers from the Cartelization of Exhaustible Resources. Review of Economics and Statistics 60 (1978), 238-251.

<source lang="matlab">
t = (1:17)';

% demand(t) equilibrium world demand for fixed prices
demand = 1+2.3*1.015.^(t-1);

% Due to a bug in the Matlab syntax, the parser cannot know if f(x) is a
% function call or the x:th element of the vector f. So it has to guess.
% The Matlab parser doesn't understand that "toms" creates variables, so it
% may get confused if one of the names is previously used by a function or
% script. By assigning something to each variable before calling toms, we
% inform the Matlab parser that it is indeed dealing with variables.

p = []; td = []; s = []; cums = []; d = []; r = []; rev = [];

% p(t): world price of oil
% td(t): total demand for oil
% s(t): supply of oil by non-opec countries
% cums(t): cumulative supply by non-opec countries
% d(t): demand for opec-oil
% r(t): opec reserves
% rev(t): revenues in each period
toms 17x1 p td s cums d r rev

% Positive variables
cbnd = {p >= 0; td >= 0; s >= 0; cums >= 0
d >= 0; r >= 0};

i = 2:17;

% Total demand equation
eq1 = td(i) == 0.87*td(i-1) - 0.13*p(i) + demand(i-1);

% Supply equation for non-opec countries
eq2 = s(i) == 0.75*s(i-1) + (1.1+0.1*p(i)).*1.02.^(-cums(i)./7);

% Accounting equation for cumulative supply
eq3 = cums(i) == cums(i-1) + s(i);

% Accounting equation for opec reserves
eq4 = r(i) == r(i-1) - d(i);

% Demand equation for opec
eq5 = d(i) == td(i) - s(i);

% Yearly objective function value
eq6 = rev(i) == d(i).*(p(i)-250./r(i));

profit = sum(rev(2:17).*1.05.^(1-(1:16)'));

% Fixed initial conditions
cbnd1 = {td(1) == 18; s(1) == 6.5; p(1) == 0
r(1) == 500; cums(1) == 0; d(1) == 11.5; rev(1) == 0};

% Starting point for optimization
x0 = {td == 18; s == [6.5;7*ones(16,1)]; cums == 7*(0:16)'
d == td-s; p == [0;14*ones(16,1)]};

r0 = [500;zeros(16,1)];
for i=2:17
r0(i) = r0(i-1)-(18-7);
end

i = 2:17;
x0 = {x0; r == r0; rev == [0;d(i).*(p(i)-250./r(i))] };

cons = {cbnd; cbnd1; eq1; eq2; eq3; eq4; eq5; eq6};
solution = ezsolve(-profit,cons,x0);
</source>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.18169 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Problem 1 f_k -1170.486285448881700000
sum(|constr|) 0.000000032087510419
f(x_k) + sum(|constr|) -1170.486285416794300000
f(x_0) -1676.426105656187900000

Solver: snopt. EXIT=0. INFORM=1.
SNOPT 7.2-5 NLP code
Optimality conditions satisfied

FuncEv 1 ConstrEv 22 ConJacEv 22 Iter 19 MinorIter 74
CPU time: 0.015600 sec. Elapsed time: 0.025000 sec.

</pre>

TomSym Optimal Pricing and Extraction for OPEC - Revision history

Mbot at 13:34, 8 November 2011

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} TomSym implementation of GAMS Example (PINDYCK,SEQ=28) This model finds the optimal pricing and extract..."