Environmental Economics: Answers to Exam December 2013

Transcription

1 Environmental Economics: Answers to Exam December 2013 Short Questions (a) In the industries with imperfect competition, if only one regulatory instrument is used such as an emission tax, it has to correct two market failures: the exercise of market power and the pollution externality. The tax is reduced compared to the Pigou rate to mitigate for the market power effect. This correction depends on price-elasticities. (b) When the penalty that the firm has to pay if it is audited and found out of compliance depends on how much it departs from the reported emissions (e.g. fine per unit of emission not reported), the firm might prefer to reduce the expected penalty by doing some abatement. In the model analyzed in class, an optimal strategy can be to invest the efficient abatement effort while wrongly reporting no emissions. (c) Too much competition is bad because it increases resource extraction and thus exacerbates over-exploitation. The more firms are in the industry, the higher is the fishing effort above the efficient level. Some competition can be good to lower fish prices and thus increase the consumers surplus. Yet, on the resource side, too much competition leads to an inefficient extraction of the resource, which is detrimental to society including fishermen. Problem 1 (a) The pollution levels in East and West are respectively p E = αe E + (1 α)e W and p W = αe W. The efficient allocation of emissions maximizes the overall welfare impact of emissions C(e E ) + D(αe E + (1 α)e W ) + C(e W ) + D(αe W ). The first-order conditions are: C (e E) = αd (αe E + (1 α)e W ) C (e W ) = αd (αe W ) + (1 α)d (αe E + (1 α)e W ) That is marginal abatement cost equals the marginal impact of pollution reduction on welfare. For East, it is the marginal impact of one tty of SO2 emitted in East on pollution damage in East, that is α times the marginal damage of SO2 pollution. For West, it also includes the marginal impact on pollution in East, that is 1 α times the marginal damage of SO2 pollution. With our function al forms, it leads to: C (e E) = α 2 e E + α(1 α)e W C (e W ) = (α 2 + (1 α) 2 )e W + (1 α)αe E See Figures 1 and 2 below. 1

2 euros α 2 e E + α(1 α)e W C (e E ) euros e E e E (α 2 + (1 α) 2 )e W + (1 α)αe E α 2 e W (1 α)αe E + (1 α)2 e W C (e W ) e W e W 2

3 (b) West sets the regulation cap e W that minimizes the welfare impact of pollution control in West that is the damage plus de cost of abating pollution within West territory C(e W ) + D(αe W ). The first order-condition yields: C (e S W ) = αd (αe S W ) The marginal abatement cost for the thermal power plant equals to the marginal damage due to one tty of SO2 in West. Similarly, given the pollution coming from West that is deposed in East (1 α)e S W, East chooses the cap that minimizes C(e E) + D(αe E + (1 α)e S W ). The first-order condition leads to: C (e S E) = αd (αe S E + (1 α)e S W ) The marginal cost of abating SO2 in East equals to the marginal impact on damage in East given the pollution coming from West. Using the functional form of the damage function, it leads to: C (e S W ) = α 2 e S W C (e S E) = α 2 e S E + α(1 α)e S W Figures 3 shows that e S W > e W and then Figure 4 shows that es E < e E. Since West does not care about the welfare impact of its emissions on West, it would over emit compared to the first-best. Therefore, more pollution coming from West ends up in Est. Since damage cost are convex, East substitute pollution by reducing its emissions compared to the first-best. There is over-emissions in West and under-emissions in East. Figures 3 and 4 below illustrate our analysis. 3

4 euros (α 2 + (1 α) 2 )e W + α(1 α)e E α 2 e W C (e W ) euros e W e S W α 2 e E + α(1 α)e S W e W α 2 e E + α(1 α)e W C (e E ) e S E e E e E 4

5 (c) Since both plants have same abatement costs, they would choose to emit the same for any permit allocation (i.e. the condition marginal abatement cost equals permit price leads to same emissions for any price) that is exactly ē. Since East has more pollution but same damage function than West, it set a more stringent cap on its emissions that West. Indeed, the local cap that East would pick minimizes C(e E ) + D(αe E + (1 α)ē) with respect to e E. Denoted e c E, it is characterized by the following first-order condition yields: C (e c E) = αd (αe c E + (1 α)ē = α 2 e c E + α(1 α)ē. It defines a local cap as a function of the global cap ē. As long as e c E < ē, the emission cap is binding. On the other hand, West would set a local cap if ē > e S W which never occurs for emission not lower than the first-best. (d) No because a permit has more impact on welfare if it is used in West rather than East. Indeed the market equilibrium would lead to equalization of abatement marginal costs, which here means same abatement levels for both plants e E + e W 2. Yet, since emissions in West has more impact on the welfare (because it pollutes more), emissions should be lower in West than in East. This is cannot driven by market forces with a single market on emissions. The permits should be defined on pollution in each state (SO2 deposit) rather than emissions like ambient pollution permits. Each plant can be assigned tradable permits on pollution, p E = αe E + (1 α)e W in East and p W = αe W in west. The plant located in East have to buy α East pollution permits to be able to emit one tty of SO2 while the plant located in West must buy 1 α pollution permits in East in addition to α pollution permits in West to be allowed to emit one tty of SO2. Problem 2 1. The first-best probability of accident p (θ) minimizes the expected damage and cost of safety pd + θ/p. The first-order condition yields: D = θ p 2 That is the marginal benefit of safety (reduction of expected damage) equals to the marginal cost. Thus (p (θ)) 2 = θ/d and p (θ) = θ/d On the other hand, the regulator does not know θ. It thus chooses the safety standard p that minimizes its expectation on damage and costs E[pD + p θ E[θ] ] = pd + p. The first-order condition is: D = E[θ] p The marginal benefit of a reduction of accidental risk equals to the average marginal cost. Thus p 2 = E[θ]/D and p = E[θ]/D. Compared to the first-best, p > p (θ) if E[θ] > θ and p < p (θ) if E[θ] < θ: the safety prescribes an under-investment in safety (higher probability) for low safety costs and over-investment for high costs. 5

6 2. Given φ, the firm minimizes the expected payment and cost pφd + θ/p. The solution yields p L (θ) = θ/φd. We have p L (θ) > p (θ) for every θ [θ, θ] because φ < 1: the firm underinvest is safety (higher probability of accident) because it is not always found liable. Therefore the expected payment in case of accident is lower than the real one. p 2 (p L (θ)) 2 (p (θ)) 2 p 2 θ θ E[θ] θ θ 3. See Figure 5 above. The safety standard is closer to the first-best when costs are high or close to the average while the probability with liability rule is closer to the first-best one for low costs. Formally, the liability rule is more efficient for θ θ while the safety regulation is better for θ θ. We can get closer to the first-best if the two regulations are combined: the liability rule drives the firm s incentives when costs are below θ while the firm matches the safety rule for higher costs. 4. The new safety standard minimizes the expected damages and cost given that it drives the incentives of firms of cost θ θ (the decision of firms of type θ θ are determined by the liability regulation) that is: θ θ p L (θ)d + θ θ p L df (θ) + pd + df (θ) (θ) θ θ p 6

7 with θ such that p L ( θ) = p = θ. Solving the program using the first-order conditions φd leads to the proposed solution: p 2 E[θ θ θ] = (1 F ( θ))d Indeed the safety standard is now define on the average of firms with costs higher than the threshold θ. That is why the probability is higher which means that the standard is less stringent: since E[θ θ θ] E[θ] (1 F ( θ))e[θ], where the last inequality holds because F ( θ) 1, p is higher than in question Under full information, the regulator would ask the firm to invest the first-best safety efforts and thus probabilities p (θ H ) = θ H /D and p (θ L ) = θ L /D. It would pay exactly the cost of this safety investment to make sure that the two types of firm adhere to the agreement: t H = θ H /p (θ H ) = Dθ H and t L = θ L /p (θ L ) = Dθ L. If θ is not observable by the firm, the low cost θ L would pretend to be high cost to invest less in safety and get higher transfer. Doing so, it obtains t H θ L /p (θ H ) = (θ H θ L )/p (θ H ) > 0 which is higher than the zero profit it gets by reporting truthfully its type. The program of the regulator under asymmetric information is: min {(ph,t H ),(p L,t L )} ν(p H D + t H ) + (1 ν)(p L D + t L ) subject to t L θ L pl 0 t H θ H ph 0 t L θ L pl t H θ L p H t H θ H ph t L θ H pl The two first constraints are the participation constraints (IR=Individual-Rationality) for both type of firms while the two second ones are the incentive-compatibility constraints that make sure that firms report truthfully their cost. 6. The program is solved by binding the participation constraint for the high cost firm and the incentive-compatibility constraint for the low cost firm. This sets transfers to t H = θ H /p H and t L = θ L /p L + (θ H θ L )/p H. Substituting in the objective function and deriving with respect to p H and p L leads to the following first-order conditions: D = θ L p 2, L D = θ H p 2 H + ν θ H θ L 1 ν p 2 H Comparing with the first-order conditions in question 1, the safety probability of the low cost firm is first-best, while the one of the high cost is distorted to minimize the information rent paid to the low cost firm which is a bonus paid to make the agreement incentive-compatible. The probability p H is higher than the efficient level which means that safety investment is lower. IR L IR H IC L IC H 7