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etamac.gms : ETA-MACRO Energy Model for the USA

This is an Energy Macro Economic Interaction model for the United
States developed by Prof A Manne, Stanford University.
Reference:
Small Model of Type: NLP
$Title Eta-Macro Energy Model for the USA (ETAMAC,SEQ=80) $Ontext This is an Energy Macro Economic Interaction model for the United States developed by Prof A Manne, Stanford University. Manne, A S, ETA-MACRO: A Model of Energy-Economy Interactions. In Hitch, C J, Ed, Modeling Energy-Economy Interactions, Resources for the Future. ?, Washington, DC, 1977. *------------------------------------------------------------------------ These are notes on changing the time horizon and number of years per period. You must first enter the set t which is the time periods that will be used. The number of years between entries in t must be the value nyper. you must choose the number of years per period, nyper, and this must correspond to the set t. You must change the number of years per period, nyper, in two places. nyper must be greater than or equal to 2. You must also enter the set inityrs which contains the years from the base year to the year before the first year. Units Used: Electric Energy 10**12 kwh Non-Electric Energy 10**15 btu Price of Electric Energy $/(10**3 kwh) Price of Non-Electric Energy $/(10**6 btu) GNP 10**12 $ *------------------------------------------------------------------------ $Offtext Scalars nyper number of years per period / 5 /; Sets inityrs years before first year / 1985*1989 / bsyr base year t actual time periods / 1990, 1995, 2000, 2005, 2010, 2015, 2020, 2025, 2030 / tfirst(t) first period tlast(t) last period nypset set from 1 to nyper / 1*5 /; bsyr(inityrs) = yes$(ord(inityrs) eq 1); tfirst(t) = yes$(ord(t) eq 1); tlast(t) = yes$(ord(t) eq card(t)); *------------------------------------------------------------------------ Scalars spda speed of adjustment / 0.96 / kpvs capital share parameter / 0.28 / elvs electric share parameter / 0.35 / esub elasticity between k-l and e-n / 0.45 / k0 initial capital / 10.90 / e0 initial electric energy / 2.50 / n0 initial non-electric energy / 50 / i0 initial investment / 0.7 / c0 initial consumption / 3.2 / pe0 initial price of electric energy / 50 / pn0 initial price of non-electric energy / 4.5 / pnref reference price of non-electric energy / 3.0 / y0 initial output htrt0 initial heat rate thsnd one thousand / 1000.0 / rho esub minus one divided by esub aconst constant for capital-labor index bconst constant for electric-non-electric energy index ninit number of years before the first year tol tolerance factor for lower bounds / 0.3 /; *------------------------------------------------------------------------ Parameters dfactcurr(t) current annual utility discount factor dfact(t) utility discount factor grow(t) potential annual gnp growth rate pegrow(t) current growth of electricity price pelec(t) growth of electricity price pngrow(t) current growth of non-electricity price pnelec(t) growth of non-electricity price l(t) current labor force (efficiency units) ln(t) new labor force ipm(t) investment period multiplier htrt(t) heat rate knew(t) new capital stock; *------------------------------------------------------------------------ * the following input factors refer, respectively, to utility discounting * (dfactcurr), growth of electric and nonelectric energy costs (pelec and * pnelec), and of potential gnp (grow). dfactcurr(t) = 0.96; pegrow(t) = 0.01; pngrow(t) = 0.02; grow(t) = 0.03; htrt0 = 10.809; htrt(t) = 10.809; *------------------------------------------------------------------------ ninit = card(inityrs); rho = (esub - 1)/esub; y0 = i0 + c0 + (e0*pe0 + n0*pn0)/thsnd; bconst = (pnref/thsnd)*y0**(rho - 1) / ((1 - elvs)*(e0**(rho*elvs))*(n0**(rho*(1 - elvs) - 1))); aconst = (y0**rho - bconst*(e0**(rho*elvs))*(n0**(rho*(1 - elvs)))) / (k0**(rho*kpvs)); *the following calculations allow for the growth of investment within each *period, and also for its geometric decay. knew(tfirst) = i0*(sum(inityrs, spda**(ord(inityrs) - 1)* (1 + grow(tfirst))**(ninit - ord(inityrs)))); ipm(t) = sum(nypset, spda**(ord(nypset) - 1)* (1 + grow(t))**(nyper - ord(nypset))); dfact(tfirst) = dfactcurr(tfirst)**ninit; l(tfirst) = (1 + grow(tfirst))**ninit; ln(tfirst) = l(tfirst) - (spda**ninit); pelec(tfirst) = pe0*((1 + pegrow(tfirst))**ninit); pnelec(tfirst) = pn0*((1 + pngrow(tfirst))**ninit); Loop(t, dfact(t+1) = dfact(t)*dfactcurr(t+1)**nyper ; l(t+1) = l(t)*(1 + grow(t+1))**nyper ; ln(t+1) = l(t+1) - l(t)*(spda**nyper) ; pelec(t+1) = pelec(t)*(1 + pegrow(t))**nyper ; pnelec(t+1) = pnelec(t)*(1 + pngrow(t))**nyper ); dfact(tlast) = dfact(tlast)/(1-dfactcurr(tlast)); Display ipm, kpvs, elvs, l, ln, rho, aconst, bconst, pelec, pnelec, knew; Variables k(t) capital stock kn(t) new capital stock y(t) production yn(t) new production e(t) electric energy en(t) new electric energy n(t) non-electric energy nn(t) new non-electric energy c(t) consumption i(t) investment ec(t) energy cost in trillions utility; k.l(t) = k0*l(t); y.l(t) = y0*l(t); e.l(t) = e0*l(t); n.l(t) = n0*l(t); c.l(t) = c0*l(t); i.l(t) = i0*l(t); Display k.l, y.l, e.l, n.l, c.l, i.l; Equations newcap(t) new capital newprod(t) new production fnewelec(t) new electric energy in first period newelec(t) new electric energy fnewnon(t) new non-electric energy in first period newnon(t) new non-electric energy totalcap(t) total capital stock ftotalprod(t) total production in first period totalprod(t) total production costnrg(t) cost of energy cc(t) capacity constraint tc(t) terminal condition util discounted log of consumption; newcap(t+1).. kn(t+1) =e= i(t)*ipm(t); newprod(t+1).. yn(t+1) =e= (aconst*(kn(t+1)**(rho*kpvs)) * (ln(t+1)**(rho*(1 - kpvs))) + bconst*(en(t+1)**(rho*elvs)) * (nn(t+1)**(rho*(1 - elvs)))) ** (1/rho); fnewelec(tfirst).. en(tfirst) =e= e(tfirst) - e0*(spda**nyper); newelec(t+1).. en(t+1) =e= e(t+1) - e(t)*(spda**nyper); fnewnon(tfirst).. nn(tfirst) =e= n(tfirst) - n0*(spda**nyper); newnon(t+1).. nn(t+1) =e= n(t+1) - n(t)*(spda**nyper); totalcap(t+1).. k(t+1) =e= k(t)*(spda**nyper) + kn(t+1); ftotalprod(tfirst)..y(tfirst) =e= y0*(spda**ninit) + (aconst*(knew(tfirst)**(rho*kpvs)) * (ln(tfirst)**(rho*(1-kpvs))) + bconst*(en(tfirst)**(rho*elvs)) * (nn(tfirst)**(rho*(1 - elvs)))) ** (1/rho); totalprod(t+1).. y(t+1) =e= y(t)*(spda**nyper) + yn(t+1); costnrg(t).. thsnd*ec(t) =e= pelec(t)*e(t) + pnelec(t)*n(t); cc(t).. y(t) =e= c(t) + i(t) + ec(t); tc(tlast).. k(tlast)*(grow(tlast) + (1 - spda)) =l= i(tlast); util.. utility =e= sum(t, dfact(t)*log(c(t))); Model etamac /all/; k.lo(t) = k0; kn.lo(t) = tol*i0*ipm(t); y.lo(t) = y0; yn.lo(t) = tol*y0*ln(t); e.lo(t) = e0; en.lo(t) = tol*e0*ln(t); n.lo(t) = n0; nn.lo(t) = tol*n0*ln(t); c.lo(t) = c0; i.lo(t) = i0; k.fx(tfirst) = k0*(spda**ninit) + knew(tfirst); Solve etamac maximizing utility using nlp; $Stitle report definitions Parameter valuerep report for c-i-gdp-e-en-tpe growthrep report of growth rates; valuerep("con", bsyr) = c0; valuerep("inv", bsyr) = i0; valuerep("gdp", bsyr) = c0 + i0; valuerep("elec", bsyr) = e0; valuerep("nelec", bsyr) = n0; valuerep("tpe", bsyr) = htrt0*e0 + n0; valuerep("con", t) = c.l(t); valuerep("inv", t) = i.l(t); valuerep("gdp", t) = c.l(t) + i.l(t); valuerep("elec", t) = e.l(t); valuerep("nelec", t) = n.l(t); valuerep("tpe", t) = htrt(t)*e.l(t) + n.l(t); growthrep("con", "'85-00") = 100*((c.l("2000")/c0)**(1/15) - 1); growthrep("inv", "'85-00") = 100*((i.l("2000")/i0)**(1/15) - 1); growthrep("gdp", "'85-00") = 100*(((c.l("2000") + i.l("2000"))/ (c0 + i0))**(1/15) - 1); growthrep("elec", "'85-00") = 100*((e.l("2000")/e0)**(1/15) - 1); growthrep("nelec","'85-00") = 100*((n.l("2000")/n0)**(1/15) - 1); growthrep("tpe", "'85-00") = 100*(((htrt("2000")*e.l("2000") + n.l("2000"))/ (htrt0*e0 + n0))**(1/15) - 1); growthrep("con", "'00-20") = 100*((c.l("2020")/c.l("2000"))**(1/20) - 1); growthrep("inv", "'00-20") = 100*((i.l("2020")/i.l("2000"))**(1/20) - 1); growthrep("gdp", "'00-20") = 100*(((c.l("2020") + i.l("2020"))/ (c.l("2000") + i.l("2000")))**(1/20) - 1); growthrep("elec", "'00-20") = 100*((e.l("2020")/e.l("2000"))**(1/20) - 1); growthrep("nelec","'00-20") = 100*((n.l("2020")/n.l("2000"))**(1/20) - 1); growthrep("tpe", "'00-20") = 100*(((htrt("2020")*e.l("2020") + n.l("2020"))/ (htrt("2000")*e.l("2000") + n.l("2000"))) **(1/20) - 1); Display valuerep, growthrep;