Command-and-control policies and market-based policies. Two coal-burning electric power plants emit sulfur dioxide

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Command-and-control policies and market-based policies. Two coal-burning electric power plants emit sulfur dioxide, which leads to acid rain. To solve the problem, EPA is considering two policies: requiring both plants to abate by the same amount, orallowingthemtotradepollutionpermits.PlantA’sabatementcostisCA(qA)=1.5(qA)^2 and plant B’s abatement cost is CB(qB) = 6(qB)^2 . EPA would like to reduce emissions from 200 to 80 (therefore total abatement qA + qB = 120 units). Each firm initially emits x∗A = x∗B = 100 units. Suppose that the profit the firms make if there is no regulation is equal to RA = 50000 and RB = 50000 respectively. a) Command-and-control: a1) If the EPA follows a command-and-control policy and tells each firm to abate by the same amount, what will be abatement costs of each firm and the total costs of abatement? b) Permits: b1) Suppose the EPA gives each plant 40 permits to pollute for free, but plants are allowed to trade them. Write down the profit function for each firm (π(q) ). What is the first order condition for each firm for the optimal level of abatement? How many permits will each firm hold in equilibrium? b2) In the permit-trading equilibrium, at what price would permits trade? b3) Calculate the abatement cost for each plant under permit trading (part b1) and compare it to part a). b4) Calculate the profit each firm makes. c) Taxes c1) What is the optimal tax that would achieve the targeted total pollution reduction from 200 to 80? c2) Write down the profit function for each firm? What is the first order condition for the optimal abatement level of each firm? c3) What are the abatement costs of each firm under the tax? Compare to a) and b) c4) Calculate the profit each firm makes. Compare to b4) and discuss. d) Incentive to innovate. Company B has discovered a new abatement technology that would lower marginal abatement cost to CB(xB) = 0.5(xB)^2 d1) How much would profit of company B under the tax regulation (c2) change (as- suming the government would leave the tax rate unchanged). d2) How much would profit of company B under the permit regulation (b3) change (assuming the government would leave the number of permits unchanged) d3) Does company A’s profit change in d1) and/or d2)?

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