otpop.gms : OPEC Trade and Production

**Description**

This model was used in 1974 by the World Bank for a background study for the energy task force. It was used to analyze output policies for OPEC. At the time the study was carried out no full optimization was attempted.

**Reference**

- Blitzer, C, Meeraus, A, and Stoutjesdijk, A J, A Dynamic model of OPEC Trade and Production. Journal of Development Economics 2, 4 (1975), 319-335.

**Small Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** otpop.gms

$Title A Dynamic model of OPEC Trade and Production (OTPOP,SEQ=47) $Ontext This model was used in 1974 by the World Bank for a background study for the energy task force. It was used to analyze output policies for OPEC. At the time the study was carried out no full optimization was attempted. Blitzer, C, Meeraus, A, and Stoutjesdijk, A, A Dynamic model of OPEC Trade and Production. Journal of Development Economics, 2 (1975), 318-335. $Offtext Sets tt total time horizon / 1965*1990 / th(tt) historical years / 1965*1974 / t(tt) model horizon / 1974*1990 / tp(tt) projection years / 1975*1990 / n memory (years) / 1*3 / Parameters db(t) demand scaling constant xb(t) opec production capacity rd(t) absorptive capacity del(t) foreign assets accumulation alpha(n) weights for ph / 1 .5, 2 .3, 3 .2 / phis(tt) historical prices ($ bbl) / 1965*1971 3.5, 1972 4.0, 1973 7.0, 1974 10.0 / y(tt) value of year xtr(t) x target ptr(t) p target Scalars a price elasticity of demand / 0 / b non-opec price elasticity / .2 / g long-run demand growth / .04 / r real rate of return / .03 / gr growth of absorptive capacity / .07 / c production and delivery cost / .25 / l investment lag / 4 / v terminal discounting / .25 / ph alternative investment trigger ($ per bbl) / 3.0 / pb all new energy from alternatives ($ per bbl) / 9.0 / xb74 opec production capacity (mill bpd) / 32.25 / x74 opec production (mill bpd) / 29.4 / d74 world energy demand (mill bpd) / 88.2 / db74 demand scaling constant rd74 absorptive capacity in year 1974 / 20 / con shift parameter constant; db74 = d74*phis("1974")**a; db(t) = db74*(1+g)**(ord(t)-1); con = g/pb**b/(pb-ph); rd(t) = rd74*(1+gr)**(ord(t)-1); del(t) = (1+r)**(card(t)-ord(t)); y(tt) = 1964 + ord(tt); xb(t) = xb74 + 3.0*min(y(t)-1974,6) + .9*max(y(t)-1980,0); xtr(t) = min(xb(t),x74*1.02**(ord(t)-1)); ptr(t) = 10*1.02**(ord(t)-1); Display db74, db, rd, del, con, y, xb, xtr, ptr; $Stitle mdel definition Variables x(tt) sales of opec oil (mill bpd) d(tt) demand for energy (mill bpd) as(tt) shift parameter p(tt) price of energy ($ per bbl) pd(tt) expected price of energy ($ per bbl) k final foreign assets (bill $) z value of oil in ground (bill $) xdev output deviation pdev price deviation pi criterion Positive Variable x; Equations dem(t) energy demand (mill bpd) sup(t) opec supply (mill bpd) adef(tt) shift parameter definition pdef(tt) expected price definition ($ per bbl) kdef foreign assets (bill $) zdef nonproduced reserves (bill $) xtrack x tracking error definition ptrack p tracking error definition obj criterion definition objx alternate criterion definition; dem(t).. d(t) =e= db(t)*p(t)**(-a); sup(t).. x(t) =e= d(t) - as(t)*p(t)**b; adef(tt)$tp(tt).. as(tt) =e= as(tt-1) + con*d(tt-1)*(pd(tt-l)-ph); pdef(tt).. pd(tt) =e= sum(n, alpha(n)*p(tt-(ord(n)-1))); kdef.. k =e= sum(t, del(t)*(.365*(1-c)*p(t)*x(t)-rd(t))); zdef.. z =e= v*sum(t, .365*(xb(t)-x(t))*p(t+(card(t)-ord(t)))); xtrack.. xdev =e= sum(t, sqr(xtr(t)-x(t))); ptrack.. pdev =e= sum(t, sqr(ptr(t)-p(t))); obj.. pi =e= k + z; objx.. pi =e= sum(t, del(t)*(.365*(1-c)*p(t)*x(t)-rd(t))) + v*sum(t, .365*(xb(t)-x(t))*p(t+(card(t)-ord(t)))); Model otpop1 / dem, sup, adef, pdef, kdef, zdef, obj / otpop2 / dem, sup, adef, pdef, ptrack / otpop3 / dem, sup, adef, pdef, objx / ; x.up(t) = xb(t); p.lo(tt) = 1; p.fx(th) = phis(th); x.fx(th) = x74; Solve otpop2 minimizing pdev using nlp; Solve otpop3 maximizing pi using nlp; kdef.m = 1; zdef.m = 1; Solve otpop1 maximizing pi using nlp;