exam 4 sol

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EXAM N1 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; 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 / cume0 'initial cumulative emissions' / 700/ 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' A sigma(t) 'carbon intensity of GDP'; Parameter beta, rho, dkn; beta = 0.02; rho = 0.5; dkn = 0.1; damnatcap(t); rr(t) = 1/(1 + rho)**( tstep * ( t.val-1) ); pop(t) = min(pop0 * (1 + r) **( (ord(t) - 1) * tstep), pop0*2) ; L tfp(t) = min(tfp0 * (1 + z * (ord(t) - 1) * tstep), tfp0*2.5) ; sigma(t) = max(1 - 0.005 * (ord(t) - 1) * tstep,0); $if set nodam damfrac=0; Variable S(t) 'saving rates' YG(t) 'income, pre-damages' Y(t) 'income' K(t) 'capital stock' E(t) 'emissions' CUMEMI(t) 'cumulative emissions' MIU(t) 'fraction of emissions abated' U 'utility'; KL(t); K_NAT(t); S_NAT(t); DAM(t); $batinclude bounds_and_init.gms Equation eq_yg eq_y 'income definition' eq_k 'capital stock balance' eq_e 'emissions' eq_emicum 'cumulative emissions' eq_util 'welfare function'; eq_yg_new; eq_kl); eq_kn; damage; eq_yg(t).. YG(t) =e= tfp(t) * K(t)**el * ( pop(t) ) **(1-el); eq_yg_new(t).. YG =e= beta*KL(t)**rho + (1-beta)*K_NAT(t)**rho; eq_y(t).. Y(t) =e= YG(t) - damcost * CUMEMI(t) ** 2 - abcost * sigma(t) * YG(t) * MIU(t) ** 3 / 3; eq_e(t).. E(t) =e= sigma(t) * YG(t) * ( 1 - MIU (t) ); eq_emicum(t+1).. CUMEMI(t+1) =e=…