Environmental economics – mathematical exercises for practice (solutions can be found at the end of the document) A factory producing chemical fertilisers (MNPB=4-0,5q) is polluting the nearby river, causing environmental damage: MEC=1,5q a) How much will the factory produce to maximise its profit, and how much profit will it then have? b) If the goverment decides to regulate the company using a tax, how high should the tax rate be, how much tax will the company be paying,and how much profit will it then have? A paper company (MNPB = - q) is operating next to a river, dumping harmful chemicals into it As a result, the soft drink factory operating further down the river is suffering losses (MEC = 1/3 q) because of the incerased water purification costs a)If the government now passes a law that everybody has the right for a clean environment, how much would the paper company have to pay (minimum and maximum) to the soft drink company in order to be allowed to continue operation? What will be the output of the paper company at the end of the bargaining process? Please make a drawing showing the situation! b) If the government would like to ensure the pollution reduction using a norm or a tax, which instrument should it choose and why? (Taking into account that the goverment does not know exactly the MNPB curve of the paper company) (You not need to draw or make any calculations here!) The profit curve of a steel plant is MNPB=9-q, the associated environmental pollution causes social costs in the order of MEC=1/2q The authority tries to estimate the company’s profit curve and arrives at the following result: MNPB’=6-q a) If the government decides to regulate using a norm, where will it set the norm, and what will be loss caused by the mistake? b) If the government decides to regulate using a tax, where will it set the tax, and what will be loss caused by the mistake? Two large factories are operating in the same area, causing serious SO 2-emissions (70 and 40 units) The authorities would like to reduce the emissions of SO to 60 units using a tax The total abatement cost curves of the factories are: TAC1=2q12 TAC2=3q22 (where q means the amount of removed pollution) a) How many units of pollution will each company remove and what is the tax rate necessary to achieve this? What will be the cost of this policy solution for the companies? b) What will happen if another factory starts operation in the same area? (Please describe the nature of the effect on the two existing factories, the authorities and the environment!) And what is the effect of a new entry if there is an emissions trading system instead of a tax? The marginal abatement cost curves of two companies are the folowing: MAC1 = 5q1; MAC2 = 4q2 (where q means the amount of removed emissions) The companies are regulated by a tax, and the revenue of the authorities from the two companies is 880 and 1200 The total cost of the regulation for the two companies is 1040 and 1400 What were their original emissions? Three coal power plants are operating in the same area, causing serious SO 2emissions (40, 60 and 20 units) In order to protect the health of the local population, the authority would like to bring down the total emissions of SO2 to 60 units The marginal abatement cost curves of the power plants are: MAC1=2q1 MAC2=2q2 and MAC3=5q3 (where q means the amount of pollution removed by the company) The authority is considering two instruments to achieve the desired goal: a) Setting a norm requiring equal remaining emissions b) Introducing an emissions trading system, where the SO2 permits are auctioned to the companies (they not get any for free) Questions: How many units of pollution will each company remove in the two situations? In situation a), how high does the penalty at least have to be in order to ensure that all three power plants comply with the norm? In situation b), what will be the permit price? Please compare the financial effect of the two solutions for -the authorities -the companies -the society as a whole! Two companies’ pollution abatement costs can be described by the following curves: MAC1=30q1 MAC2=20q2 Their original emissions are 54 and 40 units The authorities would like to reduce the total pollution by 30 units, and they this by issuing tradable permits, which are equally distributed between the two companies How many permits will change hands between the companies and at what price? Solutions a) It will produce units, and the profit will be 16 b) The social optimum is The necessary tax rate is 3, the tax payed by the company is 6, the remaining profit is a) At the end of the bargaining process, the output of the paper company will be 3, and it will have to pay minimum 1,5; maximum 7,5 b) The government should use a tax, because MEC is flatter than MNPB, so using a tax will lead to a smaller loss if the goverment makes a mistake when estimating the paper company’s MNPB curve a) The norm will be 4, the loss is b) The tax will be 2, the loss is 0,75 a) q1=30 q2=20, the tax rate is 120 Costs: company 1: reduction cost=1800 + tax paid=4800; total cost 6600 Company 2: reduction cost 1200 + tax paid 2400; total cost 3600 b) If another company starts operation, the first two companies will not be affected, the authorities will have more income from the taxes – but there will be more environmental damage (unless the government raises the tax rate) If there is a permit trading system instead of a tax, then the permit price will automatically go up (because the number of permits stays the same) This means higher costs for the companies and no effect on the environment Company1: removed emission:8, remaining emission 22, original emission 30 Company2: removed emission:10, remaining emission 30,original emission 40 Norm situation: equal rest emissions mean 20 for all companies, so the removed pollution is: 20; 40; The minimum penalty necessary is 80 (the 2nd company will only respect the norm if the penalty is at least this high) The costs for the companies are: 400, 1600 and (in this case the reduction cost is the only cost) Emissions trading: removed pollution is: 25, 25, 10 The permit price is 50 Financial effects: The costs for the companies are: company 1: reduction cost: 625 + buying permits: 750, total 1375 Company 2: reduction cost 625 + buying permits 1750, total 2350 Company 3: reduction costs 250 + buying permits 500, total 750 So, for each company, the total costs are lower if there is a norm For the authorities, the permit system results in an income of 3000, if there is a norm, they have no income For society, the permit system is better, because the total cost of the reduction is lower in this case (1500 vs 2000) Company will buy 10 permits from company a the price of 360/permit