7401ENV Exam – Practice Calculation Examples – 20211. The marginal social benefit from cotton production is MBsoc = 800 – 0.4Q. The marginal privatecost of cotton production (to the cotton producing industry) is MCind = 260 + 0.06Q. Cottonproduction imposes external costs on society as a consequence of pesticide runoff. This marginalexternal cost is given by MEC = 36 + 0.02Q. Here MBsoc, MCind and MEC are quoted in $/tonne ofcotton produced, and Q reports cotton production in tonnes.(a) Calculate the socially efficient level of cotton production(b) Calculate the Pigouvian tax rate ($/tonne) on cotton production which would be requiredto induce the cotton industry to produce at the socially efficient level2. The marginal social benefit from beef production is MBsoc = 7600 – 0.25Q. The marginal privatecost of beef production (to the beef producing industry) is MCind = 2605 + 0.12Q. Beef productionimposes external costs on society as a consequence of nutrient runoff from cattle lands. Thismarginal external cost is given by MEC = 0.08Q. Here MBsoc, MCind and MEC are quoted in $/tonne ofbeef produced, and Q reports beef production in tonnes.(a) Calculate the socially efficient level of beef production(b) Calculate the Pigouvian tax rate ($/tonne) on beef production which would be requiredto induce the beef industry to produce at the socially efficient level by ‘internalising theexternality’(c) Calculate the total external cost at the socially-efficient level of beef production3. Society comprises two households P and Q, both of whom benefit from the provision of publicgreen space G in their neighbourhood. Green space here is an environmental public good. Themarginal benefit which household P derives from public green space is MBp = 26 – 2G. The marginalbenefit which household Q derives from public green space is MBq = 18 – 0.9G. The local councilestimate that the marginal cost of providing public green space is MC = 4 + 1.1G. Green space G ismeasured in hectares (ha). MBp, MBq and MC are reported in $/ha of green space.(a) Sketch society’s demand for green space. Label the axes of your sketch graphappropriately, and specify the equations for the separate segments of society’s piecewiselinear demand curve for green space across the range G = 0 ha to G = 20 ha.(b) Calculate the area of public green space which the council should provide to maximisetotal social net benefit from providing public green space24. Society comprises two households J and K, both of whom benefit from the provision of improvedair quality A in their neighbourhood. Air quality here is an environmental public good. The marginalbenefit which household J derives from air quality is MBJ = 280 – 100A. The marginal benefit whichhousehold K derives from air quality is MBK = 120 – 30A. The local council estimate that the marginalcost of improving air quality (by fitting clean-burn engines to the town’s buses) is MC = 9 + 7A. AirQuality A is measured using an index which varies from 0 = very poor up to 5 = very good. MBJ, MBKand MC are reported in $/unit change in the air quality index.(a) Sketch society’s demand for air quality. Label the axes of your sketch graph appropriately,and specify the equations for the separate segments of society’s piecewise-linear demandcurve for air quality across the range A = 0 to A = 5 on the air quality index.(b) Calculate the air quality index level which the council should aim to provide to maximisethe total social net benefit from air quality improvement.5. A steel works can cut its NOx emissions from their current level of 80 tonnes a year according tothe MAC curve: MAC = 1.2 + 0.14A, where MAC = marginal cost of NOx abatement (1000$/tonne)and A = level of abatement undertaken (tonnes). A NOx emissions tax of $7500/tonne is introduced.Calculate:(a) How many tonnes of NOx abatement the steel works will undertake as a result of theemissions tax being introduced(b) The total abatement cost which the steel works will choose to incur once the emissionstax is introduced.(c) The total emissions tax bill paid by the steel works once the emissions tax is introduced6. A brick works can cut its CO2 emissions from their current level of 40 tonnes a year according tothe MAC curve MAC = 30 + 5A; where MAC = marginal cost of CO2 abatement ($/tonne) and A = levelof abatement undertaken (tonnes). A CO2 emissions tax of $ 200 per tonne is introduced.Calculate:(a) How many tonnes of CO2 abatement will the brick works undertake when the tax isintroduced ?(b) The total abatement cost ($) which the brick works will choose to incur when the $200/tonne CO2 emissions tax is introduced.(c) The total emissions tax bill which the owners of the brick works will choose to incur oncethe $ 200/tonne CO2 emissions tax is introduced.37. Firm A and Firm B both emit a uniformly mixing pollutant. The marginal costs of pollutionabatement for each firm are given by: For Firm A:For Firm B:MACa = 50 + 0.4AaMACb = 75 + 0.25Ab Where: Aa = pollution abatement by Firm A [measured in tonnes]Ab = pollution abatement by Firm B [measured in tonnes]MACa and MACb are measured in $/tonneThe regulator will introduce an emissions tax and aims to reduce pollution emissions from the twofirms by 355 tonnes in total. At what rate should the emissions tax be set to achieve the desiredlevel of pollution reduction at the first attempt ?8. Two firms S and T have the following MAC curves for abatement of a uniformly mixing pollutant:???? = 3?? and ???? = 9??where MACS and MACT are the marginal costs ($/tonne) which firms S and T, respectively, incur inabating pollutant emissions, and AS and AT are the levels of abatement (tonnes) undertaken by therespective firms. Before any regulations or taxes are introduced Firms S and T emit 70 and 60 tonnesof pollutant annually, respectively.The regulator aims to cut combined total pollution emissions from firms S and T combined by 40tonnes annually. What emissions tax rate should the regulator set to achieve the desired pollutionreduction at the first attempt ?9. Firm 1 and Firm 2 both emit a uniformly mixing pollutant. The marginal costs of pollutionabatement for each firm are given by: for Firm 1:for Firm 2:MAC1 = 418 – 3E1MAC2 = 480 – 4E2 where: E1 = emissions by Firm 1 [measured in tonnes]E2 = emissions by Firm 2 [measured in tonnes]MAC1 and MAC2 are measured in $/tonneA marketable permit scheme will be used to regulate this uniformly mixing pollutant. 180 permitswill be issued. Each permit allows the permit holder to emit 1 tonne of the pollutant.(a) Assuming the permit market is ideal, calculate how many permits each firm will holdafter permit trading is complete ?(b) What will the final (market clearing) trading price of the permits be ?410. Two firms 1 and 2 have MAC curves for SO2 emissions of:MAC1 = 60 – 2E1andMAC2 = 125 – 3E2where MAC1 and MAC2 are the marginal costs ($/tonne) which firms 1 and 2, respectively, incur inabating SO2 emissions, and E1 and E2 are their respective levels of SO2 emissions (tonnes).Before any regulations, taxes or marketable permit schemes are introduced, Firm 1 emits 25 tonnesof SO2 annually and Firm 2 emits 35 tonnes of SO2 annually. A cap and trade marketable permitscheme is introduced to regulate SO2 emissions. The regulator initially grants 20 emission permits toFirm 1 and 20 emission permits Firm 2. One emission permit entitles the holder to emit one tonne ofSO2. The two firms then trade permits voluntarily in the market. Calculate the following outcomeswhen the two firms stop trading emissions permits:(a) the number of permits held by Firm 1 and Firm 2(b) the final trading price of the permits in the permit market511. An individual-based travel cost valuation has been used to estimate the net benefit that visitorsobtain from recreational visits to a national park. Individual-specific data were collected from visitorsto the park. These data detailed individual visitors’ socio-demographics, recreational preferencesand travel costs. A count data regression was used to predict the number of visits that an individualrecreator would be expected to make to the national park over the summer season. The regressionequation used was:??(??) = ?????? + ?????? + ??????? + ????? + ?????? ∙ ?????Where: ??expected number of visits for individual i (expected visits over the summerseason)???individual i’s travel cost to the national park (reported in $)????age of individual i (in years)?????number of children in individual i’s household (number of children)???categorical variable denoting whether individual i is a mountain biker (0 = no, 1 =yes)lndenotes the natural logarithm Regression results are shown in the table below: ParameterParameter estimateStatisticallysignificant????-0.026yes??0.021no??0.234yes??1.489yes???0.341yes (a) Which of the following statements are correct ? (i)Increasing age does not affect the number of visits an individual isexpected to make to the national park(ii)Individuals would be expected to make more visits to the national parkif there are more children in their household(iii)Travel cost has a significant impact on the number of visits anindividual is expected to make to the national park(iv)Mountain bikers are expected to make less visits to the nationalpark if there are more children in their household (b) Use the regression results to calculate the access value (i.e. the net benefit in $)that the average recreator obtains from a visit to the national park.612. A hedonic price analysis has been undertaken to estimate the impact of traffic noise on the priceof urban properties. The hedonic price function estimated was:P B G D AC N=0 +1 +2 +3 +4 +5Where:P = house sale price ($1000 i.e. $350,000 is recorded as ‘350’)B = number of bedrooms (number)G = garden area (m2)D = distance from nearest school (km)DG = double-glazing installed (yes = 1, no = 0)N = traffic noise (in decibels [bigger number means LOUDER traffic noise])Regression analysis produced the following results: Driving variableParameterParameter estimateStatisticallysignificant ?constantα0220.6yesBα136.4yesGα20.76yesDα3-0.15yesDGα46.4yesNα5-0.23yesOverall regression R2 = 0.55 (a) Briefly (1 sentence each) interpret the meaning of the estimated hedonic price regressionparameters for:(i) Number of bedrooms(ii) Distance from the nearest school(iii) Double glazing(iv) Traffic noise(b) A road bypass is proposed for one of the city’s suburbs. If the bypass is constructed, traffic noisewill drop by 5 decibels at a total of 4,500 urban properties. Use the hedonic regression results toestimate the total $ benefit which the owners of these properties will obtain from local reduction intraffic noise.713. A choice experiment has been used to estimate public willingness to pay for provision ofdifferent levels of the following attributes associated with habitat restoration: AttributeLevelsBirdsCurrent population sizeCurrent population size +20%Current population size +40%InsectsCurrent species diversityCurrent species diversity +5%Current species diversity +10%Payments$0 (status quo only)$5, $10, $25, $50, $200 Each of the choice cards featured two alternative outcomes (option A and option B) from possiblehabitat management in the future, plus a status quo option. The status quo option was available at$0 cost and delivered the current population size of birds and the current level of insect diversity.Options A and B delivered different combinations of bird population sizes and insect diversities atvarious prices (higher than $0).A regression was run on the results from the choice experiment to estimate the following discretechoice model:Vm =B Bm +I Im + PAYmHere Vm denotes the utility associated with choice option m; Bm and Im denote, respectively, thelevels of birds and insect diversity present in option m on a particular choice card, and PAYm denotesthe actual $ payment associated with option m. The B,I and terms are the parametersestimated by the regression. The results obtained from regression estimation are shown in the tablebelow: AttributeParameterEstimateStatisticallysignificant ?Birds0.77yesInsect Diversity0.21yesPayment-0.035yes B I (a) Using the results shown in the table above, calculate the ‘part worths’ associated with(i) a 20% increase in the size of the bird population(ii) a 5% increase in insect species diversity(b) Use the results shown in the table above to estimate average willingness to pay ($/averagerespondent) for a habitat restoration scenario which would deliver the following combination ofoutcomes:Bird population: current +40%Insect species diversity: current +5%(c) The survey for this choice experiment was conducted on a representative sample of the totalpopulation of 125,000 individuals who would benefit from the proposed habitat restoration.Calculate the population’s total willingness to pay for the habitat restoration scenario proposed inpart (b).814. The following schedule of costs will be incurred in fitting SO2 cleanup equipment to a combustionplant. The equipment will remove 8 tonnes of SO2 annually, and has an operational lifetime of 12years. Using a discount rate of 6% per annum, calculate the present value cost effectiveness of thisequipment for SO2 removal ($/tonne of SO2 removed annually) [Round your answer to the nearest $] YearCost ($)012000245006800082500 15. The schedule below specifies the social costs incurred and the social benefits delivered by aninvestment project. YearCost ($)Benefit ($)03,500013,500022,0005,00032,00035048,000081,0007,0001050010,000 (a) Calculate the social net present value delivered by the project, using a discount rate of 4%per annum.(b) Calculate the benefit : cost ratio achieved by this project(c) Would you recommend that this project is undertaken ? Justify your recommendation.16. A multi-criteria analysis (MCA) is being carried out to support decision making regardingpotential management scenarios for a coral reef off the Queensland coast. Three alternativescenarios are being considered, an environmentally focussed scenario (ENV), a fishery developmentfocussed scenario (DEV) and the existing set of usage priorities (SQ – for ‘Status Quo’). The threealternative scenarios will be evaluated in terms of three criteria:• annual fish catch taken from the reef (tonnes) (CATCH)• area (hectares) of reef retained in excellent condition 5 years in the future (REEF)• size of the resident population key fish species (WILD FISH)9Outcomes for these three criteria under the three different development scenarios are shown in thetable below. DEVENVSQCATCH650250400REEF425700525WILD FISH200425300 The following weightings will be applied to the three criteria: CATCH 40%, REEF, 35%, WILD FISH25%.(a) Carry out an MCA to compare the three scenarios: show your workings, step by step(b) Based on your MCA, which scenario would you recommend ?End of Practice Calculation Examples
