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PROBLEM Chapter (page 37) One convenient way to express the willingness-to-pay relationship between price and quantity is to use the inverse demand function In an inverse demand function, the price consumers are willing to pay is expressed as a function of the quantity available for sale Suppose the inverse demand function (expressed in dollars) or a product is P = 80 – q, and the marginal cost (in dollar) of producing it is MC = lq, where P is the price of the product and q is the quantity demanded and/or supplied (a) How much would be supplied in a static efficient allocation? (b) What would be the magnitude of the net benefits (in dollars)? In the numerical example given in the text the inverse demand function for the depletable resource is P = – 0,4q and the marginal cost of supplying it is $2,00 (a) If 20 units are to be allocated between two periods, in a dynamic efficient allocation how much would be allocation to the first period and how much to the be in the two period when the discount rate is zero? (b) What would the efficient price be in the two periods? (c) What would be marginal user cost be in each period? Assume the same demand condition as stated in question 2, but for this question let the discount rate be 0,10 and the marginal cost of extraction be $4,00 How much would be produced in each period in an efficient allocation? What would the marginal user cost be in each period? Would the static and dynamic efficiency criteria yield the same answer for this problem? Why? Compare two versions of the two-period depletable resource model which differ only in the treatment of marginal extraction cost Assume that in the second version the constant marginal extraction cost is lower in the second period than the first (perhaps due to the anticipated arrival of a new, superior extraction technology) The constant marginal extraction cost is the same in both periods in the first version and is equal to the marginal extraction cost in the first period of the second version In a dynamic efficient allocation how would the extraction profile in the second version differ from the first? Would relatively more or less be allocation to the second period in the second version than in the first version? Would the marginal user cost be higher or lower in the second version? APPENDIX………………………………………………………………………… The Simple Mathematics od Dynamic Efficiency* Assume that the demand curve for a depletable resource is linear and stable over time Thus the inverse demand curve in year t can be written as Pt = a - bqt The total benefits from extracting and amount q t in year t is then the integral of this function (the area under the inverse demand curve): (Total benefits)t = ∫ qt b (a − bq )dq = aqt − q t 2 Further assume that the marginal cost of extracting that resource is a constant c and therefore the total cost of extracting amount qt in year t can be given by (Total cost)t = cqt If the total available amount of this resource is Q , then the dynamic allocation of a resource over n year is the one which satisfies the maximization problem: b aqi − qi − cqi n   Max qt ∑ + λ Q − qi  ∑ i-1  i =1 i =1   (1 + r) n Assuming that Q is less than would normally be demanded, the dynamic efficient allocation must satisfy a − bqi − c (1 + r) i-1 −λ = 0, i = 1, …, n, n Q − ∑ qi = i =1 We can illustrate the use of these equations with the two-period example dealt with in the text The following parameter values are assumed in that problem: a = 8, c = $2, b = 0,4, Q = 20; and r = 0,10 Using these, we obtain – 0,4q1 – – λ = 0, 8- 0, 4q1 – −λ = 0, 1,10 q1 – q2 = 20 It is now readily verified that the solution (accurate to the third decimal place) is q1 = 10,238, q2 = 9,762, λ= $1,905 We can now demonstrate the propositions discussed in the text Verbally, equation (7) states that in dynamic efficient allocation the present value of the marginal net benefit in period (8 – 0,4q1 – 2) has to equal λ Equation (8) states that the present value of the marginal bet benefit in period 2sould also equal λ Therefore, they must equal each other This demonstrates the proposition shown graphically in Figure 2.7 The present value of marginal user the cost is represented by λ Thus equation (7) states that price in the first period (8 – 0,4q1) should be equal to the sum of marginal extraction cost ($2) and marginal use cost (1,905) Multiplying (8) by + r, it becomes clear that price in the second period (8 – 0,4q2) is equal to the marginal extraction cost ($2) plus the higher marginal user cost [λ (1 + r) = (1,905).(1,10) = $2,095] in period These results show why the graphs in Figure 2,8 have the properties they They also illustrate the point that, in this case, marginal user cost rises over time Chapter (page 65) Suppose the state is trying to decide how many miles of a very scenic river it should preserve There are 100 people in the community, each of whom has an identical inverse demand function given by P = 10 – 0,1q, where q is the number of miles preserved and P is the per mile price he or she is willing to pay for q miles of preserved river (a) If the marginal cost of preservation is $500 per mile, how many miles would be preserved in an efficient allocation? (b) How large are the net benefits? (a)- Compute the consumer surplus and producer surplus if the product described by the first problem in Chapter were supplied by a competitive industry Show that their sum is equal to the efficient net benefits (b)- Compute the consumer surplus and the producer surplus assuming this same product was supplied by a monopoly (Hint: The marginal revenue curve has twice the slope of the demand curve) (c)- Show that when this market is controlled by a monopoly, producer surplus is larger, consumer surplus is smaller, and net benefits are smaller than when it is controlled by competitive industry 3 Suppose you were asked to comment on a proposed policy to control oil spills Since the average cost of an oil spill has been computed as $X, the proposed policy would require any firm responsible for a spill to immediately pay the government $X Is this likely to result in the efficient amount of precaution against oil spills? Why or why not? “In environmental liability cases, courts have some discretion regarding the magnitude of compensation polluters should be forced to pay for the environmental incidents they cause In general, however, the large the required payments the better” Discuss (page 90) In Mark A Cohen “The Costs and Benefits of Oil Spill Prevention and Enforcement”, Journal of Environmental Economics and Management 13 (June 1986), an attempt was made to quantify the marginal benefits and marginal costs of U.S Coast Guard enforcement activity in the area of oil spill prevention His analysis suggests (p 185) that the marginal per gallon benefit from the current level of enforcement activity is $ 7,50 while the marginal per gallon cost is $ 5,50 Assuming these numbers are correct, would you recommend that the Coast Guard increase, decrease, or hold at the current level their enforcement activity? Why? In his book Reducing Risks to Life: Measuring the Benefits, Martin Bailey estimates that the cost per life saved by current government risk-reducing programs ranges from $72.000 for kidney transplants to $624.976.000 for a proposed standard to reduce occupational exposure to acrylonitrile (a) Assuming these values to be correct, how might efficiency be enhanced in these two programs? (b) Should the government strive to equalize the marginal costs life saved across all life-saving programs? Chapter (page 197) Suppose a product can be produced using virgin ore at a marginal cost given by MC1 = 0,5q1 and with recycled materials at a marginal cost given by MC2 = + 0,1q2 (a) If the inverse demand curve were given by P = 10 – 0,5(q1 + q2), how many units of the product would be produced with virgin ore and how many units with recycled materials? (b) If the inverse demand curve were P = 20 – 0,5(q2 + q1), what would your answer be? When the government allows private firms to extract minerals offshore or on public lands, two common means of sharing in the profits are bonus bidding and production royalties The former awards the right to extract to the highest bidder, while the second charges a per ton royalty on each ton extracted Bonus bibs involve a single, up-front payment, while royalties are paid as long as minerals are being extracted (a) If the two approaches are designed to yield the same amount of revenue, will they have the same effect on the allocation of the mine over time? Why or why not? (b) Would either or both be consistent with an efficient allocation? Why or why not? (c) Suppose the size of the mineral deposit and the future path of prices are unknown How these two approaches allocate the risk between the mining company and the government? “As society’s cost of disposing of trash increases over time, recycling rates should automatically increase as well” Discuss Chapter 12 (page 297) Assume that the relationship between the growth of a fish population and the population size can be expressed as g = 4P – 0,1P2, where g is the growth in tons and P is the size of the population (in thousands of tons) Given a price of $100 a ton, the marginal benefit of smaller population size (and hence, large catches) can be computed as 20P – 400 (a) Compute the population size that is compatible with the maximum sustainable yield What would be the size of the annual catch if the population were to be sustained at this level? (b) If the marginal cost of additional catches (expressed in term of the population size) is MC = 2(160 – P), what is the population size which is compatible with the efficient sustainable yield? Assume that a local fisheries council imposes an enforceable quota of 100 tons of fish on a particular fishing ground for one year Assume further that 100 tons per year is the efficient sustained yield Once the 100th ton has been caught, the fishery would be closed for the remainder of the year (a) Is this an efficient solution to the common-property problem? Why or why not? (b) Would your answer be different if the 100-ton quota were divided up into 100 transferable quotas, each entitling the holder to catch one ton of fish, and distributed among the fishermen in proportion to their historical catch? Why or why not? In the economic model of the fishery developed above, compare the effect on fishing effort of an increase in cost of a fishing license with an increase in a per-unit tax on fishing effort that raises the same amount of revenue Assume the fishery is private property Repeat the analysis assuming that the fishery is a free-access common-property resource Chapter 14 (page 350) Two firms can control emissions at the following marginal costs: MC1 = $200q1, MC2 = $100q2, where q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms Assume that with no control at all, each firm would be emitting 20 units of emissions or a total of 40 units for both firms (a) Compute the cost-effective allocation of control responsibility if a total reduction of 21 units of emissions is necessary (b) Compute the cost-effective allocation of control responsibility if the ambient standard is 27 ppm, and the transfer coefficient which translate a unit of emissions into a ppm concentration at the receptor are, respectively, a1 = 2,0 and a2 = 1,0 Assume that the control authority wanted to reach its objective in (a) by using an emission charge system (a) What per unit charge should be imposed? (b) How much revenue would the control authority collect? APPENDIX…………………………………………………………………………… The Simple Mathematics of Cost-Effective Pollution Control Suppose that each of N polluters would emit un of emission in the absence of any control Furthermore suppose that the pollutant concentration KR at some receptor R in the absence of control is: N KR = ∑a u n =1 n n +B Where B is the background concentration and an is the transfer coefficient This KR is assumed to be greater than ɸ, the legal concentration level The δ Cn ( qn ) − P ° an = δ qn N ∑a Ω n =1 ∫ qt n n +B= b (a − bq )dq = aqt − q t 2 Q b aqi − qi − cqi n   + λ Q − qi  ∑ ∑ i-1  i =1 i =1   (1 + r) n a − bqi − c (1 + r) i-1 −λ = n Q − ∑ qi = i =1 0, 4q1 – −λ = 1,10 Regulatory problem therefore is to choose the cost-effective level of control qn for each of the n sources Symbolically this can be expressed as minimizing the following Lagrangian with respect to the Nqn control variables:  N N  ∑ Cn ( qn ) + λ ∑ an ( un – qn ) − φ  ,  n =1 n =1  Where Cn(qn) is the cost of achieving the qn level of control at the nth source and λ is the Lagrangian multiplier The solution is found by partially differentiating (2) with respect to λ and the Nqn’s This yields δ Cn ( qn ) − λ °an ≥ , n = 1, …, N, δq N ∑a ( u n =1 n n – qn ) + B − φ = Solving these equations produces the N-dimensional vector qo and the scaiar λo Notice that this same formulation can be used to reflect both the uniformly mixed and non-uniformly mixed, single-receptor case In the uniformly mixed case the an’s all = This immediately implies that the marginal cost of control should be equal for all emitters who are required to engage in some control (The first N equations would hold as except for any source where the marginal cost of controlling the first unit exceeded the marginal cost necessary to meet the target) For the nonuniformly mixed, single-receptor case, in the cost-effective allocation the control responsibility would be allocated so as to ensure that the ratio of the marginal control costs for two emitters would be equal to the radio of their transfer coefficients For J receptors both λo and ɸ would become J-dimensional vectors Policy Instruments A special meaning can be attached to λ If transferable permits were being used, it would be the market clearing price of a permit In the uniformly mixed case λ would be the price of a permit to emit one unit of emission In the non-uniformly mixed case λ would be the price being allowed to raise the concentration at the receptor location one unit In the case of taxes, λ represents the value of the costeffective tax Notice how firms choose emissions control when permit price or tax is equal to λ Each firm want to minimize its costs Assume that each firm is given permits of Ω n where the regulatory authority ensures that N ∑a Ω n =1 n n +B =ɸ for the set of all emitters Each firm would want to Cn(qn) + Po[Ωn – an(un – qn)] The minimum cost is achieved by choosing the value of qn (qno) that satisfies δ Cn ( qn ) − P ° an = δ qn This condition (marginal cost equals the price of a unit of conventration reduction) would hold for each of the N firms Because Po would equal λo and the number of permits would be chosen to ensure the ambient standard would be met, this allocation would be cost-effective Exactly the same result achieved by substituting To, the cost-effective tax rate, for Po Chapter 15 (page 378) The marginal control cost curves for two air pollutant source affecting a single receptor are MC1 = $0,3q1 and MC2 = $0,5q2, where q1 and q2 are controlled emissions Their respective transfer coefficients are a1 = 1,5 and a2 = 1,0 With no control they would emit 20 units of emission apiece The ambient standard is 12ppm (a) If an ambient permit system were established, how many permits would be issued and what price would prevail? (b) How much would each source spend on permits if they were auctioned off? How much would each source ultimately spend on permits if each source were initially given, free of charge, half of the permits? Chapter 16 (page 403) Explain why an acid-rain policy using emissions charge revenue to provide capital and operating subsidies for scrubbers is less cost-effective than an emission charge policy alone The transfer costs associated with an emissions charge approach to controlling chlorofluorocarbon pollution are unusually large in comparison to other pollutants What circumstances would be favorable to high transfer costs? Chapter 18 (page 456) Consider the situation posed in Problem 1(a) in Chapter 14 (a) Compute the allocation which would result if 10 emission permits were given to the second source and were given to the first source What would be the market permit price? How many permits would each source end up with after trading? What would the net permit expenditure be for each source after trading? (b) Suppose a new source entered the area with a constant marginal cost of control equal to $1600 per unit of emission reduced Assume further that it would add 10 units in the absence of any control What would be the resulting allocation of control responsibility? How much would each firm clean up? What would happen to the permit price? What trades would take place? Problem Set Answers CHAPTER (page 576) a Net benefits are maximized where the demand curve intersects the marginal curve-cost curve Therefore, the efficient q would occur when 80 – lq = lq Thus the efficient q = 40 units b Draw the diagram Draw a horizontal line from the place where the demand curve intersects the marginal cost curve to the vertical axis This intersection will take place at a price of 840 The net benefits can now be computed as the sum of the upper right triangle (the area under the demand curve and over this line) and the lower right triangle (the area under the demand curve and over this line) The area of a right triangle is benefits are x 840 x 40 + x base x height Therefore, the net x 840 x 40 = $1600 a Ten units would be allocated to each period b P = 88 – 0,4q = $8 - $4 = $4 c User cost = P – MC = $4 – = $2 Because in this example the static allocations to the two periods (those which ignore the effects on the other period) are feasible within the 20 units available, the marginal user cost would be zero With a marginal cost of $4,00, the net benefits in each period would independently be maximized by allocating 10 units to each period In this example no intertemporal scarcity is present, so price would equal $4,00 marginal cost Refer to Figure 2.7 In the second version of the model the lower marginal extraction cost in the second period would raise the marginal net benefit curve in that period (since marginal net benefit is the difference between the unchanged demand curve and the lower MC curve) This would be reflected in Figure 2.7 as a parallel leftward shift out of the curve labeled “present value of marginal net benefits in period 2.” This shift would immediately have two consequences: it would move the intersection to the left (implying relatively more would be extracted in the second period), and the intersection would take place at a higher vertical distance from the horizontal axis (implying that the marginal user cost would have risen) CHAPTER (page 577) a This is a public good, so add the 100 demand curves vertically This yields P = 1000 – 100q This demand curve would intersect the marginal cost curve when P = 500, which occurs when q = miles b The net benefits are represented by a right triangle where the height of the triangle is $500 ($1000, the point where the demand curve crosses the vertical axis, minus $500, the marginal cost) and the base is miles The area of a right triangle is x base x height = x 8500 x = $1250 a Consumer surplus = $800 Producer surplus = $800 Consumer surplus plus producer surplus = $1600 = net benefits b The marginal revenue curve has twice the slope of the demand curve, so MR = 80 – 2q Setting MR = MC yields q = 80/3 and P = 160/3 Using Figure 3.8, producer surplus is the area under the price line – FE) and over the marginal cost line (DH) This can be computed as the sum of a rectangle (formed by FED and a horizontal line drawn from D to the vertical axis) and a triangle (formed by DH and the point created by the intersection of the horizontal line drawn from D with the vertical axis) The area of any rectangle is base x height The base = 80/3 and the Height = P – MC = 160/3 – 80/3 = 80/3 Therefore, the area of the rectangle is 6400/9 The area of the right triangle is 1/2 x 80/3 x 80/3 = 3200/9 Producer surplus = 3200/9 + 6400/9 = $9600/9 Consumer surplus = 1/2 x 80/3 x 80/3 = $32000/9 c $9600/9 > 800 $3200/9 < $800 $12800/9 < $1600 The policy would not be consistent with efficiency As the firm considers measures to reduce the magnitude of any spill, it would compare the marginal costs of those measures with the expected marginal reduction in its liability from reducing the magnitude of the spill Yet the expected marginal reduction in liability would be zero Firms would pay $X regardless of the size of the spill Since the amount paid cannot be reduced by controlling the size of the spill, the incentive to take precautions which reduce the size of the spill will be inefficiently low If “better” means efficient, this common belief is not necessarily true Damage awards are efficient when they equal the damage caused Assuring that the award reflects the actual damage will appropriately internalize the external cost Larger damage awards are more efficient only to the extent they more closely approximate the actual damage Because they promote an excessive level of precaution that cannot be justified by the damages, awards which exceed actual cost are inefficient CHAPTER (page578) In order to maximize net benefits, Coast Guard oil spill prevention enforcement activity should be increased until the marginal benefit of the last unit equals the marginal cost of providing that unit Efficiency requires that the level of the activity be chosen so as to equate marginal benefit with marginal cost When marginal benefits exceeds marginal cost (as in this example), the activity should be expanded a According to the figures given, the per life cost of kidney transplants lies well under the implied value of life estimates given in the chapter, while per life cost implied by the proposed standard for acrylonitrile lies well over those estimates In benefit-cost terms the allocation of resources to kidney transplants should be increased, while the acrylonitrile standard should be relaxed somewhat to bring the costs back into line with the benefits b Efficiency requires that the marginal benefit of a life saved in government programs (as determined by the implied value of a human life in that context) should be equal to the marginal cost of saving that life Since the data given in the problem indicate that the marginal costs would be beneficial, should all marginal costs be equals? Only if the marginal benefits are equal and, as we saw in the chapter, risk valuations (and hence the implied value of human life) depend on the risk context, so it is unlikely they are equal across all government programs CHAPTER (page 578) According to the microeconomic theory of fertility the impact would be greater for tuition – funded education With tuition funding, the cost of education for an additional child would be the present value of all tuitions paid With property tax funding, the cost of education for an additional child would be miniscule: the amount the family would pay would depend on the value of their property, not on the number of children in the family Hence, the marginal cost of an additional child is higher with tuition funding, so the impact on the desired number of children would be larger It is a positive feedback loop The rich typically have low fertility rates, while the poor typically have high fertility rates High fertility rates among the poor tend to widen the gap between rich and poor by increasing the supply of labor (placing downward pressure on wages, particularly unskilled wages) and by reducing the amount of resources committed to each child, thereby limiting future earning capacity) Industrialization does lower population growth in the third stage (when birthrates fall), but it increases population growth in the second stage (when death rates fall but birthrates remain high) Therefore the statement provides an accurate description of the long run but not the short run CHAPTER (page 579) From the hint MNB1/MNB2 = (1+k)/(1+r) Notice that when k = 0, this reduces to MNB2 = MNB1(1+r), the case we have already considered When k = r, then = MNB1= MNB2; the effect of stock growth exactly offsets the effect of discounting, and both periods extract the same amount If r > k, then MNB > MNB1 If r < k, then MNB2 < MNB1 a With a demand curve shifting out over time, the marginal net benefits from a given future allocation increase over time This raises the marginal user cost (since it is the opportunity cost of using the resource now) and, hence, the total marginal cost Thus, the initial user cost would be higher b Less of the resource would be consumed in the present: more would be saved for the future a This turns out to have the same effect as the environmental cost pictured in Figures 6.6a and 6.6b The tax serves to raise the total marginal cost and, hence, the price This tends to lower the amount consumed in all periods compared to a competitive allocation b The tax also serves to reduce the cumulative amount extracted because it raises the marginal cost of each unit extracted Some resources which would have been extracted without the tax would not be extracted with the tax; their after – tax cost to the producer exceeds the cost of the substitute The price would be higher with the tax in all periods prior to the without – tax switch point After that time the price would be equal to the price of the substitute with or without the tax The cumulative amount ultimately taken out of the ground is determined by the point at which the marginal extraction cost equals the maximum price consumers will pay for the depletabe resource In this model the maximum price is the price of the substitute Neither the monopoly nor the discount rate affect either the marginal extraction cost nor the price of the substitute so they will have no affect on the amount ultimately extracted The subsidy, however, has the effect of lowering the net price (price minus subsidy) of the substitute The intersection of marginal extraction cost and the net price will therefore occur when a smaller cumulative amount has been extracted than would be the case in the absence of the subsidy CHAPTER (page 580) During a recession the demand curve shifts inward If price is held constant, then the quantity demanded is reduced Since the burden of holding the price up falls on the cartel, while the competitive fringe can keep on producing, the demand reduction causes production to fall most heavily in OPEC nations This causes the cartel market share to fall To protect their individual market shares, members start cutting prices In growing markets cartel markets shares can be protected without cutting prices a Producer surplus = Consumer surplus = P = MC = q= b This is the mirror image of the monopoly allocation The net benefits are identical in the two allocations, but they are distributed among producers and consumer surplus is larger and the producer surplus is smaller than the corresponding concepts when the allocation is governed by a monopoly Essentially, the rectangle discussed in the answer to part (b) of the second problem in Chapter goes to consumers with price ceiling and to producers in a monopoly The paper company The high-cost energy is appropriately assigned to the five paper machines because that is the energy cost that would be eliminated if the machines were shut down The company would not shut down all energy sources in proportion; it would shut down the most expensive sources In making a shutdown decision, therefore, it is essential that the machines in question cover the cost of the energy which would be saved if the machines were shut down; otherwise the company is losing money Peaking plants run only a small percentage of the time, so the capital expenditures remain unused most of the time Operating costs are incurred only when they are needed It makes sense, therefore, for utilities to design peaking plants so as to keep capital costs as low as possible, even if it means incurring higher operating cost Base – load plants, on the other hand, run almost continuously, so the capital costs are prorated over a very large number of kilowatt – hours and therefore are less of a burden CHAPTER (page 581) a Assume that only virgin ores are used In this case P = MC1, so 10 – 0.5q1 = 0.5q1 or q1 = 10 This implies MC1 = The marginal cost of producing any units using recycled products is clearly higher than 5, so none will be used Therefore, 10 units would be produced, and all of them would be produced using virgin ores b With the higher demand curve the price will be high enough to stimulate the producer to make some of the product with recycled materials The key to solving this problem is provided by Figure 8.4, where it can be seen that the producer will equate the marginal costs of products made with recycled materials and those made with virgin ores Using this fact, we can set 0,5q1 = + 0,1q2 or q1 = 10 + 0,2q2 Substituting this into the demand function yields P = 20 – 0,5 (10 + 0,2q2 + q2 ) or P = 15 – 0,6q2 Solving for P = MC yields 15 – 0,6q2 = + 0,1q2 or q2 = 100/7 And q1 = 10 + 0,2 x 100/7 = 90/7 The solution can be verified by showing P = MC1 = MC2 = 45/7 a They will not have the same effect Because the royalty is a per –ton fee, it raises the marginal cost of extraction to the firm, but the bonus bid, which does not affect the marginal cost of extraction, does not If the mineral has an increasing marginal cost of extraction, less will be extracted with a royalty system than with a bonus bid system because the marginal cost of extraction (including the royalty payment) will hit the back – stop price at a smaller cumulative extracted b The bonus bid is consistent with efficiency because it does not distort the allocation over time The allocation which maximized firm profits before the bonus bid will still maximize it after the bonus bid While the government shares the profits, it does so without distorting incentives By raising the marginal cost of extraction, royalty schemes distort incentives c With a bonus bid scheme the firm bears the risk The government gets a fixed payment The firm can either win big or lose big depending on how valuable the deposit turns out to be with the royalty scheme, the risk is shared If the mine turns out to be very valuable, profits and government fees both go up If the deposit turns out not to be very valuable, the firm gains little but so does the government Rising societal disposal cost is certainly one of the factors which should stimulate higher recycling rates, but it is by no means the only one And as long it is not the only factor, recycling rates will not automatically increase in response First, this higher social cost must be reflected in increasing marginal disposal costs facing individuals in order to provide the incentive to recycle: rising social costs not automatically result in rising individual marginal costs Second, markets must exist for the recycled materials Collecting them does no good if they can’t be put to good use CHAPTER (page 582) Since the amount of capacity needed would depend on the maximum flow during the year, the extra cost of expanding capacity during this high-flow period should be reflected in higher prices charged to users during these periods Assuming the rate was correct, the flat rate would be more efficient because it would confront the user with a positive marginal cost of further consumption The marginal cost of further consumption with a flat fee is zero CHAPTER 10 (page 582) Norland has the comparative advantage in producing A For every unit of A it produces Norland gives up units of B This is a lower opportunity cost than incurred by Souland, which gives up units of B for each unit of A produced Souland has a comparative advantage in producing B Food stamp programs give the poor more money to spend on food, thus shifting their demand curve for food to the right Only if supply is perfectly inelastic would this shift in demand increase price without increasing quantity sold On the other hand, prices would normally rise somewhat unless the supply curve was perfectly elastic In general, the more elastic the supply curve, the larger would be the increase in quantity sold and the smaller would be the increase in prices for a given shift in demand 3 Soil erosion diminishes future productivity, but its prevention requires current outlays If the renter has a long-term lease, and hence would be able to recoup the investment, he or she might well take efforts to prevent soil erosion If, however, the renter has a short-term lease, he or she would not be likely to prevent soil erosion The losses would accrue to the absentee landlord, who would be less knowledgeable about the extent of the problem CHAPTER 11 (page 583) The plot being turned into a housing development would have the shortest rotation period because the cost of delaying the harvest would be greatest in this case It would include an additional cost-the cost of delaying the construction of the housing development- that would have to be factored in, causing net benefits to be maximized at an earlier harvest age The cost trend is the result of two offsetting trends Harvesting cost is a function of the volume of wood, so it increase as the volume of wood increases Since these costs are discounted, however, costs further in the further are discounted more When the tree growth gets small enough, the discounting effect dominates the growth effect and the present values of the cost decline CHAPTER 12 (page 583) a The maximum sustainable yield is obtained when the marginal benefit of an additional reduction in the population size is zero: 20P – 400 = or P = 20.000 tons The maximum sustainable yield can then be calculated using the g equation: g = 4(20) – 0,1(20)2 = 40 tons b The efficient sustained yield can be found by setting marginal cost equal to marginal benefit: 20P – 400 – 2(160 – P); therefore, P = 32,7, which…