exam 5 sol

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EXAM N2 $title DICE economy $onmulti $setenv gdxcompress 1 $onrecurse $eolcom # $onText Simple one sector nonlinear optimal growth model. $offText Set t 'extended horizon' / 1*40 / tb(t) '?' tt(t) '?'; tb(t) = yes$(ord(t) = 1); tt(t) = yes$(ord(t) = card(t)); display tb, tt; Set emi /ap, co2/; Scalar dk 'rate of depreciation' / .1 / el 'exponent on capital' / .3 / r 'labor force growth rate' / .015 / eta 'elasticity' / 1.45 / z 'technical progress' / .01 / rho 'welfare discount' / .015 / k0 'initial capital' / 1.3 / pop0 'initial population' / 0.1 / tfp0 'total factor productivity' / 2 / tstep 'years in a period' / 5 / damcost 'damages from cc' / 1e-6 / abcost 'damages from cc' / 0.05 /; Parameter rr(t) 'discount function' pop(t) 'population' tfp(t) 'total factor productivity' sigma(t) 'carbon intensity of GDP'; rr(t) = 1/(1 + rho)**( tstep * ( t.val-1) ); pop(t) = min(pop0 * (1 + r) **( (ord(t) - 1) * tstep), pop0*2) ; tfp(t) = min(tfp0 * (1 + z * (ord(t) - 1) * tstep),tfp0*2.5) ; sigma(t) = max(1 - 0.005 * (ord(t) - 1) * tstep,0); Parameter ap0(emi); Parameter ap1(emi); Parameter red_pop(emi); Parameter abcost(emi); abcost(‘co2’) = 0.05; abcost(‘ap’) = ?; $if set nodam damfrac=0; Variable S(t) 'saving rates' YG(t) 'income, pre-damages' Y(t) 'income' K(t) 'capital stock' E(t,emi) 'emissions' CUMEMI(t) 'cumulative emissions' MIU(t,emi) 'fraction of emissions abated' U 'utility'; Positive variables S,Y,K,E,CUMEMI,MIU; Potitive variable E0(t,emi) initial emissions; S.up(t) = 1; MIU.up(t,emi) = 1; MIU.up(t,’ap’) = 0.75; Y.lo(t) = 1e-5; K.fx(tb) = k0; S.lo(t)$(ord(t) ge card(t) - 10) = 0.2; CUMEMI.fx(tb) = 0; S.l(t) = 0.25; Equation eq_yg eq_y 'income definition' eq_k 'capital stock balance' eq_e 'emissions' eq_emicum 'cumulative emissions' eq_util 'welfare function';…