Please help solve this HW question!

vu u . v w u u 3. A static IAM with utility damages Consider the following static IAM model: the representative consumer has preferences u(c) = log cyS, the production of the consumption good occurs according to c = DkI/anyagw, (coal) energy is produced according to E = Xnea there is a constraint 716 + 1% = 1 for the labor input, the carbon cycle satises 3 = LpE, and TFP does not involve any damages (climate damages only appear in utility). Finally, rms maximize prots and do not take the utility damage into account in their decisions. Temperature is determined by a standard, logarithmic forcing equation a la Arrhenius. (a (b Derive an equation determining market coal use (in the absence of any taxes). Derive the rst-order condition for a social planner maximizing consumer welfare. rx 0 Find an expression for the optimal tax on carbon in this economy. VVVV A Q. Given any outcome for coal production, E , What is the outcome for temperature (relative to its preindustrial level)? (e) If one were to use this model to compare quotas to carbon taxes, how would the two policy instruments compare in terms of consumer welfare