Natural Resources & Efficient Allocation of Resources PDF

Chapter 12 Natural Resources and Efficient Allocation of Resources Ó1 Final Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 4:30 PM There are two kinds of natural resources non-renewable resources and renewable resources. A n...

Chapter 12 Natural Resources and Efficient Allocation of Resources Ó1 Final Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 4:30 PM There are two kinds of natural resources non-renewable resources and renewable resources. A non- renewable resource is like oil. We cannot reproduce it once its stock is exhausted. Forests, water, and fish are examples of renewable resources. We use them up as we consume more of them but we can regenerate renewable resources at some cost. A Non-Renewable Resource: Oil Oil is not a renewable resource. As we use it, our stock of oil reserves decreases. Unless there is as cheap a substitute as oil or more oil reserves are discovered, its price will change to reflect the reduction of its underground reserves. In general, the marginal cost of extracting oil is small relative to its price and the oil market is not competitive precisely because it is not renewable. The oil industry looks like an oligopoly with price leadership. To simplify we treat it like a monopoly. Suppose that the total underground reserves of oil are fixed. Each year the owner of the oil reserves must decide whether to change her price. In the previous year, she could have pumped out one more barrel of oil and sold it at that year’s price say $30. If she did, she could have placed the proceeds in a bank and earned a market interest rate, say of 5%. Thus, she did not pump out an additional barrel of oil last year only because she expected to raise the price in this year by an amount at least equal to the foregone interest. That is Expected Price increase = Price of this year - price of last year = Foregone interest = (0.05) x price of last year = (0.05) x $30 = $1.5 Or Percentage rise in the price of one barrel of oil = Expected Price rise - Price of last year 1.5 x 100 = x 100 = 5% Price of last year 30 However, the interest rate is also equal to 5%. In other words, Percentage Rise in the Price of one barrel of oil = Interest Rate. (1) Thus, if total world reserves do not change the price of oil must rise at a rate equal to the interest rate. Equation (1) is Hotelling’s formula. In practice, the price of oil does rise but does not rise exactly according to equation (1). One important source of deviations is the fact that new reserves keep being discovered and political events can interfere with the conditions of supply. In addition, as the price of oil rises, consumers keep reducing their per capita consumption through a more efficient use of oil such as smaller cars or cars with better engines using less oil to provide more power using less oil. The problem of the Commons A commons is a resource owned by nobody. Air and wild fish are examples of a commons. Another interesting example of a commons is a community grazing land available for each member of the 1 Cartago Research and Development Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 2 4:30 PM community to graze his/her cows. The services of such a natural; resource are rival but hey are excludable. In this section we study the case of community grazing land. Cows produce milk, the price of which is $1 per litre. It follows that Total revenue = $1 x total output of milk. We shall refer to the total revenue as the total social benefit of the herd. Since the size of the grazing land is fixed and the total amount of feed available per year is fixed, each cow has less feed to eat and its milk output decreases as the number of cows rises. It follows that the total social benefit increases as the number of cows in the herd increases but at a slower rate due to overcrowding. Columns (1) and (2) of Table 1 describe the relationship between the number of cows and the total social benefit. Columns (1) and (6) describe the marginal social revenue or marginal social benefit. For simplicity, we also assume that each cow costs a constant amount $5 to maintain. It follows that the marginal private and social cost is constant and equal to $5. Columns (1) and (3) and columns (1) and (7) describe respectively the total social cost and the marginal social cost. Columns (1) and (4) describe total net benefit. Column (4) is the difference between columns (2) and (3). Table 1 Number Total Total Total Net Average Marginal Marginal Of Social social Social Benefit Social Benefit Social Private Cost cows revenue = cost = Total Social = Marginal Benefit of = Marginal Total in $ Benefit Private adding Social Cost of social -Total Social Revenue of one more adding one benefit in $ Cost in $ one cow in $ cow in $ more cow in $ (1) (2) (3) (4) (5) (6) (7) 0 0 0 0 5 11 5 10 110 50 110 –50 = 60 11 5 15 9 5 20 200 100 100 10 5 25 7 5 30 270 150 120 9 5 35 122.5 5 5 40 320 200 120 8 5 45 3 5 50 350 250 100 7 5 55 1 5 60 360 300 60 6 5 65 -1 5 70 350 350 0 5 5 75 -3 5 80 320 400 -80 4 5 In figure 1, horizontal line AD plots the marginal social cost and the marginal private cost of adding one more cow as given by columns (1) and (7) of Table 1. Straight line AB plots the marginal social benefit of adding one more cow as given by columns (1) and (6) of Table 1. This curve is downward sloping to reflect the fact that the total feed available naturally is independent of the number of cows Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 3 4:30 PM grazing on the fixed size commons land. Straight line CD plots the average social benefit of one cow and the marginal private revenue of adding one more cow as given by columns (1) and (5) of Table 1. This curve is downward sloping as well to reflect the fact that the marginal social benefit is falling. The additional cow and the existing cows share a fixed amount of feed. The average output of milk must fall as the number of grazing cows increases. Because the marginal social benefit is falling, we note the following important properties: Property 1 of Commons: The average social benefit is higher than the marginal social benefit. Furthermore, since the marginal private revenue for any individual of adding her/his cow on the grazing commons land is equal to the average social benefit, it follows Property 2 of Commons: The marginal private revenue for a member of the community is greater than the marginal social benefit of adding her/his cow to graze on the commons land. In economics, we are interested in the question of finding out whether members of society guided each by self-interest and freedom to choose would allocate total resources at equilibrium in such a way as to maximize total net social benefit from their productive and consumption activities. To answer this question, first we find the most efficient way a benevolent dictator would allocate resources and organize the productive and consumption activities of the members of society so as to maximize total net social benefit. As before, we call such an allocation of resources an efficient allocation of resources Efficient Allocation of Resources To maximize total net social benefit, the benevolent dictator would choose the number of cows to forage on the commons land so as to equate the marginal social benefit of an additional cow to its marginal social cost. As shown by the intersection of straight lines AB and AD at point A in figure 1, the maximum total net social benefit of $122.5 happens at a number of cows equal to 35 cows. Columns (1) and (4) of Table 1 that the maximum total net social benefit reaches its maximum of $122.5 when the number of grazing cows is equal to 35 cows. Figure 1 Unit Costs and Unit Revenues Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 4 4:30 PM Unit Values in dollars 12 11 Average Social Benefit = 10 Marginal Private Revenue 9 C Marginal Social Cost = 8 Marginal Private Cost 7 6 A D 5 4 3 2 1 B 0 -1 0 10 20 30 40 50 60 70 80 90 100 110 -2 Number of Cows -3 -4 -5 -6 -7 -8 Marginal Social Benefit -9 -10 To achieve the efficient allocation of resources, the benevolent dictator would restrict entry to 35 cows. We assume that the benevolent dictator would divide the efficient total social benefit equally among the members of the collectivity. Equilibrium Allocation of Resources under Free Entry Let us now remove the benevolent dictator and allow for free entry, self-interest, and perfect competition. First, we show that the efficient allocation of resources as determined by the benevolent dictator is not a long run equilibrium of perfect competition as defined in chapter 8. In a long run equilibrium of perfect competition, the economic profit is equal to zero. Thus, at a long run equilibrium under perfect competition, there is no incentive for additional producers to enter or exit even though there is free entry and free exit. At the efficient allocation of resources with a number of foraging cows equal to 35, the marginal private revenue as given by curve CD in figure 1 is $8.5, greater than the marginal private cost of $5 and there is a profit of $3.5 per additional cow. Driven by self-interest a member of the community would bring in an additional cow to graze since he/she would make an additional profit of $3.5. The efficient allocation with only 35 grazing cows is not a long run equilibrium. With no restriction on entry, more cows will be brought to forage on the commons land by members of the community until the marginal economic profit disappears or when the number of cows reaches a level such that the marginal private benefit as represented by curve CD is equal to the marginal private cost as represented by curve AD. According to figure 1 and Table 1, this happens at the intersection point D of the two curves. Under perfect competition, the equilibrium number of cows is 70 cows. Columns (1) and (4) of Table 1 show, that at the perfect competition equilibrium, the total net social benefit is zero, significantly lower than the level achieved under a benevolent dictator. That is the tragedy of the commons. Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 5 4:30 PM Implications for Economic Policy Under perfect competition, the commons land will be overgrazed and society loses. The problem lies not with free entry but with ownership. The renewable natural resource is the feed that grows naturally on the commons land at no cost to anyone. With no owner of the land, a member of the community does not have to pay for the feed. By increasing the number of cows he/she owns, any given member would increase her/his own total output of milk. However, the given member causes a reduction of the milk output of other members. The total milk output of the whole community increases as long as the increase in output of the given member is greater than the total loss of output by all other members. When the number of existing members is large enough and each one does the same, the opposite is true and the total output of milk of the whole community would fall. If every member expects others to do the same, then since there is free entry he/she would introduce more cows to make up for the loss of output caused by others and/or increase her/his own output of milk. Thus, the total output would eventually fall and continue falling until the value of the average quantity of milk produced by one cow just covers the cost of maintaining her. This is the outcome of the equilibrium under perfect competition with free entry and no cost to forage on the commons land. In order to allow for freedom to choose, preserve free entry and achieve an efficient allocation of resources, it is necessary to charge for the use of the natural resource. This is possible when the government assumes the ownership of the commons land and charges for the use of the natural resource. Knowing the efficient allocation of resources, the government would sell the right or license to graze. One license enables its holder to graze one cow for one year if the holder agrees to pay an annual price. For a member of the community who wishes to graze a new cow, the annual price of a license is an additional marginal cost. To achieve the efficient allocation of resources, a member of the community must face a private marginal cost that is equal to the marginal private revenue or the average social revenue of $8.5 at the efficient allocation of resources of 35 cows. Thus, the government would charge a price of $3.5 = $8.5 - $5 for a license to graze one cow. The total marginal private cost is now $8.5. Horizontal line CE in figure 2 represents the new (total) marginal private cost of adding one more cow. It is curve AD shifted upward by $3.5. The marginal private revenue of grazing one more cow beyond 35 cows is now lower than the (total) marginal private cost of $8.5. Although we allow for free entry, no more than 35 cows will be introduced on the commons land. The equilibrium under perfect competition yields now an efficient allocation of resources and society would be able to graze the efficient number of cows and earn the maximum total social benefit. Another way to ensure that perfect competition achieves an efficient allocation of resources is to auction a license to graze one cow. The price of which consists in a fee per cow paid annually to the community government. At a zero fee for a license and when the number of cows is less than or equal to 35, the marginal private revenue from grazing one more cow is greater than $8.5. The marginal private revenue that any additional cow beyond 35 cows would yield is less than $8.5. No one would be willing to pay a fee for a license to graze an additional cow beyond 35 cows higher than $3.5 since the fee is a unit cost that he/she must pay in addition to the private marginal cost of $5 for the upkeep of a cow. Figure 2 Equilibrium under Perfect Competition with a License Fee Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 6 4:30 PM unit Values in dollars 12 Average Social Benefit = Marginal Private Cost including a 11 Marginal Private Revenue license price of $3.5 10 9 C E 8 Marginal Social Cost = 7 Marginal Private Cost 6 5 4 A D 3 2 1 B 0 -1 0 10 20 30 40 50 60 70 80 90 100 110 -2 Number of Cows -3 -4 Marginal Social Benefit -5 -6 -7 -8 -9 -10 On the other hand if any member X of the community wants to graze a cow and offers to pay a fee less than $3.5, he/she knows that, because there is perfect information and free entry and exit in the cow grazing activity, another community member Y would offer to replace X’s cow by her/his cow and pay a fee slightly higher than that offered by X but less than $3.5. The total cost per cow of Y will be less than $8.5. X would lose the licence. Thus, no one would offer to pay an annual fee less than $3.5 to graze one cow. Driven by self-interest, no one would want to pay more either. Since no one wants to pay an annual fee higher or lower than $3.5, the auction would result in an equilibrium annual fee equal to $3.5. We call the annual fee for gracing a cow, the marginal external cost of grazing a cow on the commons land. Thus Private marginal cost cow to graze a cow = Annual license Fee + the unit cost to upkeep a cow Private marginal cost cow to graze a cow = External Marginal Cost + the unit cost to upkeep a cow Thus, Private marginal cost cow to graze a cow = $3.5 + $5 = $8.5 Again, Curve CE in figure 2 represents the private marginal cost = marginal social cost = $8.5. The perfect competition equilibrium number of grazing cows = 35 cows. Again, equilibrium under perfect competition yields an efficient allocation of resources and society would be able to graze the efficient number of cows and earn the maximum total net benefit. We assume that the community government collects the annual fee and distribute it each year fairly among the members of the community. Common Property Renewable Resources: Fish Fish is a natural resource that belongs to everyone. Unlike air or water, it grows if left undisturbed. Its rate of net growth when undisturbed by human fishing activity depends on its stock. The amount of net growth is the excess of births over deaths. Scientists agree that we can represent the relationship between the amount of net growth of the stock of fish when undisturbed and the stock itself by a Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 7 4:30 PM curve called the sustainable yield curve as in figure 3. Two major factors affect the amount of net growth of a fish stock, the size of the stock and the capacity of the environment to sustain the stock. If the stock is large enough the probability of mating and producing offspring is very high. The stock will produce more than enough offspring to replace those fish that die every year of natural causes or fall prey to larger fish. When the stock is not too large, the greater the stock the greater the probability to reproduce and the more offspring it will generate hence the greater the amount of net growth. Figure 3 Sustainable Yield Curve + Positive Net Growth Sustainable Yeild D 12 Curve F 10 C G 6 2.5 A B E H Z 0 40 60 100 140 150 160 Stock of Fish - Negative Net Growth As illustrated in figure 3, when the stock is equal to OA = 40 units on the horizontal axis, the amount of net growth is zero. The probability of mating is just high enough for the number of births to offset the number of deaths. However, when the stock is equal to OB = 60 units on the horizontal axis, the amount of net growth is positive and equal to BC = 6 units. Still, when the stock is larger say equal to OE = 100, the amount of net growth is larger and equal to EF = 10 units. When the fish population is large, its food demands on the environment will be too large. Some of the offspring cannot find enough food and it is easier for non-human predators to catch more of them. As figure 3 shows, beyond a certain size of the fish stock, say 100, the amount of net growth becomes smaller as the stock increases. For example, when the stock is equal to OH = 140 units, the amount of net growth is equal to HG = 6 units, less than the amount of net growth EF when the stock is smaller and equal to OE. When the stock becomes too large, OZ, the amount of net growth drops to zero or becomes negative. The environment cannot support any higher stock. On the other hand, when the stock is too small, the chance of finding a mate will be too small. The number of offspring would be too small compared to deaths and the amount of net growth of the stock is negative. The stock starts shrinking and dwindles to zero. The specie left on its own becomes extinct; the stock of fish converges to zero. When the stock is greater than OA and it is undisturbed by human fishing activity, left to itself, it would grow to OZ and stops growing at that level. In figure 3, an arrow pointing towards Z indicates this fact when the stock is greater than OA. When the stock is less than OA, the stock starts shrinking. When the stock is between 0 and OA, an arrow pointing out toward zero indicates this fact. The marginal social cost curve Fishing, like any other economic activity needs to combine capital and labour to produce its output. Unlike the car industry, its capital stock is composed of two parts: machinery equipment and the fish Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 8 4:30 PM stock. At any given stock, the maximum output that can be harvested every year without reducing the current stock of fish is the equal to the amount of the annual net growth of the fish stock. We assume that the component of the total average cost attributable to machinery equipment and labour is constant independent of the amount of the harvest. Figure 4 Marginal Social Cost Curve Figure 4.a Figure 4.b Unit cost in $ 48 Unit 48 cost in $ 46 Marginal Social Cost if stock of 46 44 Fish is less than 100 units 44 Marginal Social Cost if stock of 42 42 Fish is greater than 100 units 40 40 38 G J 38 36 36 J 34 34 32 32 30 30 28 28 26 26 24 24 22 H 22 H 20 20 18 18 16 Efficient 16 14 14 12 Size of the Efficient 12 10 annual Harvest 10 Size of the 8 8 C 6 annual Harvest 6 4 4 2 2 0 0 0 2 4 6 8 H 10 12 14 16 18 0 2 4 6 8 10 12 14 16 1 H Quantity Harvested Quantity Harvested Z E A B E 40 60 100 140 160 100 Stock of Fish Stock of Fish On the other hand, since fish moves around its natural habitat, the average total cost of fishing is a decreasing function of the stock of fish. If society maintains a fixed stock of fish forever by harvesting exactly the sustainable yield corresponding to that stock, this component of the average total cost is also constant independent of the amount of the harvest. It follows that under those assumptions, the marginal cost is also constant independent of the amount of the harvest a) Stock of Fish Less than or Equal to 100 Units of Fish Curve GHJ in figure 4.a represents the marginal social cost of fishing if society wishes to maintain a sustainable annual harvest at a stock of fish greater than the minimum stock of 40 units of fish- that is necessary to prevent extinction) and lower than the stock of 100 units of fish, at which the sustainable annual harvest is at its maximum. The black continuous horizontal axis is the amount of fish harvested every year. The discontinuous red horizontal axis in figure 4.a represents the corresponding stock of fish that society can maintain indefinitely. The greater is the stock of fish, as we move from the left to the right on the red axis in figure 4.a, the lower is the marginal social cost. The reason is when the stock of fish is larger, it is easier it is to catch fish and the marginal social cost decreases. The higher is the stock of fish above the extinction level, the greater is the sustainable quantity harvested at a lower marginal social cost. Thus, the Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 - 9 4:30 PM marginal social cost curve GHJ in figure 4.a is downward sloping between zero and 10 units of harvested fish as measured on the black continuous horizontal axis.. b) Stock of Fish Greater than or Equal to 100 Units of Fish Curve CHJ in figure 4.b represents the marginal social cost of fishing if society wishes to maintain a sustainable annual harvest at a stock of fish greater than or equal to 100 units but less than the maximum stock of 160 units to which the stock of fish would converge if undisturbed by human activity. The black continuous horizontal axis in figure 4.b is the amount of fish harvested every year. The discontinuous green horizontal axis in figure 4.b represents the corresponding stock of fish that society can maintain indefinitely. Notice its opposite direction of increase. The greater is the stock of fish as we move from the right to the left on the green axis, the lower the marginal social cost of fishing the corresponding sustainable harvest, which is equal to the growth of the stock. In this case, the marginal social cost is increasing with the size of the maximum sustainable harvest of fish (which is equal to the growth of the corresponding decreasing stock of fish). b) The Marginal Social Cost Curves GHJ and CHJ of figures 4.a and 4.b respectively represent the marginal social cost in the sense that the latter takes into consideration the costs to all generations when society allows each generation to inherit the same size of fish stock and harvest the corresponding growth, given that society does not favour any generation over the others. Since the maximum sustainable growth or yield according to figure 3 is 10 units, it follows that an annual harvest of more than 10 units is not indefinitely sustainable since it would lead to the depletion of the stock of fish and the marginal social cost is thus infinite. Thus, at a stock of fish equal to 100 units, the marginal social cost is given by vertical line HJ in each of the panels of figures 4.a and 4.b. At a stock of fish equal to OZ = 160 units (OA = 40 units) in figure 3, the amount of net growth of the stock of fish is equal to zero and each generation can harvest nothing if it chooses to hand over to the next generation the same stock of fish. At OZ (OA) in figure 3, the stock of fish is large (small) and the marginal social cost of fishing is low (high) since it is very easy (difficult) to fish. According to figure 4.b (figure 4.a), at OZ (OA) in figure 3, the marginal social cost is equal to $5 ($37). When the stock of fish is equal to OH = 140 units (OB = 60 units) in figure 3, the maximum annual amount of fish that each generation can harvest while keeping the stock intact is equal to the amount of net growth of the fish stock, equal to 6 units. Figures 4.a (4.b) shows that the corresponding marginal social cost of fishing is $14 ($32) because, in figure 3, the stock of fish OB =60 units is much lower than the stock of fish OH = 140 units. When the stock of fish is OE = 100 units in figure 3, each generation can harvest the maximum sustainable harvest of fish or the maximum sustainable yield of 10 units. However, the marginal social cost is now $20 according to figures 4.a and 4.b. At any stock of fish, every generation cannot harvest more than 10 units without casing the stock to fall. A yearly harvest greater than 10 units must take out not only the net growth but also some of the existing stock of fish, which in a relatively short time would deplete the stock. It follows that the marginal social cost of all generations should be infinite. That is the reason the marginal social cost becomes infinite at 10 units as shown by the vertical segment HJ of the marginal cost curves CHJ and GHJ in figure 4. The marginal social cost curve CHJ (GHJ) corresponds to stocks of fish higher (lower) than or equal to 100 units. The marginal social cost implies that it is inefficient to operate a fishery at a fish stock lower than 100 units when all generations are equally important. Efficient Allocation of resources Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 10 12 - 4:30 PM Suppose that the yearly demand curve for fish is as given by curve DHB in figure 5. We know that the demand curve represents the marginal social benefit. For all units between 0 and 10, the marginal social benefit is greater than the marginal social cost. For any of these units, the marginal net social benefit, which is equal to the distance between the demand curve DHB and the marginal social cost curve CHJ at the corresponding stock of fish or harvest, is positive or zero. The total net social benefit is the sum of all the marginal net social benefits from all units fished. Fishing one more unit between 0 and 10 would add to the total net social benefit and the latter would increase. Figure 5 Efficient Allocation of Resources in a Special Case Unit Costs, Price, in $ 48 Marginal Social 46 Cost Curve J 44 D 42 40 38 Demand Curve = 36 Marginal Social Benefit 34 32 30 28 26 24 Supply Curve 22 L H 20 Private Marginal Cost Curve 18 16 14 12 10 8 C 6 G B 4 2 A 0 E 0 2 4 6 8 10 12 14 16 18 Quantity Harvested 160 140 100 Efficient Quantity Z Stock of Fish The total net social benefit would reach a maximum given by the area of triangle CHD when the marginal net social benefit from an additional unit fished is zero and the harvest size is 10 units at the corresponding stock of fish equal to 100 units. Each generation harvests 10 units, keeping the stock of fish constant and equal to 100 units. Society would achieve the maximum total net social benefit. This is the efficient amount of the yearly harvest and the corresponding stock of fish would maintain itself at a level equal to 100 units indefinitely. Given that society harvests the optimal amount every year, starting from any stock of fish greater than 100 units, the amount of net growth is smaller than the harvest and the stock of fish falls. When the stock of fish falls to 100 units, the amount of net growth is exactly equal to the optimal size of the annual harvest, the stock of fish stops falling, and it remains equal to 100 units forever. If the stock of fish is less than 100 units, society would strive to increase it to 100 units by harvesting less than the net growth of the stock for a certain number of years to enable the stock of fish to grow to reach 100 units and lower the marginal social cost. Perfect Competition Markets Under Ideal Conditions, No Over-Fishing We know that the marginal cost curve in perfectly competitive markets represents the supply curve.. Real World with an Ideal Hypothesis To help us understand better how do real world markets function for products of renewable resources, we start with an imaginary case where human beings satisfy the following assumption: Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 11 12 - 4:30 PM An Ideal Hypothesis Suppose that every person trusts that every person of her generation, including herself, and those of every future generation, fisherperson or consumer, respects the rights of every other member of her generation and those of every future generation to enjoy the consumption of the same amount of fish units. Assume further that all members of every generation know the characteristics of the fish stock population as we have learned about them in this chapter. Under the Ideal hypothesis, every fisherman of every generation knows the marginal social cost curve CHJ as given in figure 5 Thus, curve CHJ in figure 5 represents the market supply curve under perfect competition given the above assumption. Given demand curve DHB, the perfect compet6ion market for fish achieves its equilibrium at the intersection point H of the market supply curve CHJ and the market demand curve DHB. Every year and forever the annual harvest will be equal to 10 units and the price of one unit of fish is $20. The corresponding stock of fish will be equal to 100 units forever. The perfect competition equilibrium is efficient. In this case, the annual total economic profit of all the fishermen of every generation is equal to the area of rectangle AGHL $160 = ($20 - $4) x 10 units. The competitive equilibrium fishing industry would harvest the maximum sustainable yield. This harvest size maintains the stock of fish constant at 100 units. This is exactly the level of harvest and the level of fish stock that would maximize the total net social benefit. In this case an ideal perfectly competitive fishing industry is efficient. The stock will not be depleted and there will be no extinction of the fish specie. A fisherperson would earn an economic profit. The industry would be in long run equilibrium. It would not attract more fishermen. Consumers will enjoy the consumer surplus If the demand curve shifts upwards in the following year, the ideal perfect competition market will maintain the same equilibrium quantity 10 units of fish harvested and equal to the maximum yield. The equilibrium price will increase dollar for dollar with the increase in the willingness to pay for an additional unit at a quantity consumed of fish of 10 units. The ideal perfect competition market will maintain forever the stock of fish constant equal to the corresponding maximum yield stock of 100 units. The total economic profit at equilibrium and the share of every active fisherperson will increase overtime. Real World with Perfect Competition Market, Over-fishing, and the Extinction of the Fish We know that the private marginal cost curve of every producer in perfectly competitive markets represents the supply curve. The private marginal cost corresponds only to a fisherperson’s out of pocket payments plus his normal profit. For simplicity, we assume that the private marginal cost of a single fisherperson is constant equal to $4. Furthermore, suppose that with the current technology, the maximum amount of fish that a fisherperson can fish during a year is 2 units and there are five (5) of them. In the short run, the number of fisherperson cannot change and the market quantity supplied is 10 units. In this case the market supply curve is a vertical line GH at 10 units. The short run equilibrium price is $20. The total economic profit for the industry is the same as in the previous case of an ideal perfect competition market and it is equal to $160. Every fisherperson total economic profit is $32. Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 12 12 - 4:30 PM In this case, straight line AB in figure 5 represents the long run private marginal cost of every fisherperson. Given enough time, the $32 economic profit will attract more fisherperson in the industry. Their number will increase until the total economic profit is wiped out. The market supply curve in the long run is now horizontal line AB. The equilibrium of the perfect competition market moves from point H to point B in figure 5 thanks to free entry and exit and the product is not excludable but rival. The corresponding equilibrium price of a unit of fish is equal to $4 and the equilibrium quantity that is being harvested every year is equal to 16 units, greater than the maximum sustainable yield of 10 units. The economic profit is equal to zero. Every fisherperson is earning only a normal profit. For a while, the stock of fish will not change. However, we know that at any given stock of fish, an annual harvest greater than the maximum sustainable yield of 10 units will eventually cause a fall in the stock of fish. An ever-growing proportion of the fishing industry output will come from a reduction of the stock of fish. The stock of fish will decline continuously. The stock of fish will approach its lowest level when the stock of fish will not be able to have a positive growth and is on its way for extinction. Unemployment Insurance, Improvement in Technology and Government Subsidies During the seventies, the government of Canada offered subsidies to fisherman to purchase new boats and equipment. The government extended also unemployment insurance to fisherman and made it easier for them to qualify for unemployment benefits. These measures reduced the capital costs for fisherman and resulted in a great increase in the number of fishermen and boats, and a more lethal technology that hastened the pace of convergence of the stock of fish to extinction. This is another illustration of the tragedy of the commons. Although these measures lowered the marginal private cost for an individual fisherman, they did not reduce the marginal social cost or shift upwards the sustainable yield curve of figure 3. They only hastened the reckoning day. They caused an increase in the private marginal cost curve as the stock of fish decreased. Finally, the politicians of most developed countries, including Canada, woke up to adopt the economist’s solution. Economist’s Solutions: No Over-Fishing The economist’s solutions are based on the above case of Perfect Competition Markets Under Ideal Conditions. It is impossible to imagine that human beings driven by self-interest will behave like a fisherperson as in the case of an ideal perfect competition model. Let us continue to assume that in the real world a single fisherperson faces a constant marginal cost of $4. Curve AB in figure 6 represents the supply curve based on constant marginal cost for every fisherperson. Furthermore, suppose that the demand curve is now curve MR in figure 6. Furthermore, assume as before that one fisherperson can catch a maximum of 2 units of fish during a year. Suppose further that the current stock of fish is equal to 100 units. We know that the efficient size of a harvest is equal to the maximum sustainable yield of 10 units and the corresponding efficient stock is constant and equal to 100 units as in figure 3. To maintain the stock of fish at 100 units forever, society needs only 5 fisherperson. Suppose that society members agree to confer the ownership of the stock of fish to its government with the requirement that the annual harvest must be equal to 10 units. Solution 1: There are no vested interest in a status quo with too many active fisherperson Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 13 12 - 4:30 PM The government imposes an annual tax equal to $26 per unit of fish harvested. The private marginal cost, including the unit tax, of an active or prospective fisherperson is now a constant equal to $30. In a perfect competition market, the market supply curve is horizontal line LN in figure 6 since the private marginal cost including the unit tax is constant equal to $30. The perfect competition market achieves equilibrium at point N in figure 6, where demand curve MR intersects the market supply curve LN. At this equilibrium, the equilibrium quantity harvested is equal to the efficient size of the yearly harvest, equal to the maximum yield of 10 units. There will be only 5 fisherpersons active, since none can earn a positive economic profit beyond the normal profit and the equilibrium price covers the private marginal cost, the unit tax, and a normal profit. Society will be able to maintain forever the stock of fish equal to ifs efficient size and the market equilibrium of the perfect competition market is efficient. Solution 2: There are politically strong vested interests composed of active fisherpersons The private marginal cost of a prospective fisherperson is still a constant equal to $4. In figure 6, the market supply curve under perfect competition is horizontal line AB and the demand curve is MR.. Without government intervention, the perfect competition equilibrium obtains at point B. At this equilibrium, the equilibrium price is equal to $4, the annual equilibrium quantity harvested equal to 16 units, and the equilibrium number of fisherpersons is equal to 8, each one of them harvesting 2 units of fish, with the economic profit of each one of the 8 fisherpersons equal to zero. These fisherpersons have each a vested interest in the status quo. The perfect competition market left to itself in the hands of the invisible hand will eventually lead to the extinction of the stock of fish. Figure 6 Unit Costs, Price in $ 58 56 J Demand Curve = 54 Marginal Social Cost Curve Marginal Social Benefit 52 50 48 46 Supply Curve, 44 M 42 Private Marginal Cost 40 Curve, Tax = $26 38 36 34 32 N 30 28 L Supply Curve, 26 Private Marginal 24 22 H Cost Curve, No 20 Tax 18 16 14 12 R 10 C 8 G 6 B 4 A 2 0 E 0 2 4 6 8 10 12 14 16 18 Quantity Harvested 160 140 100 Efficient Quantity Z Stock of Fish Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 14 12 - 4:30 PM In this case, the government politicians in power of a democratic society cannot impose a tax as in the economist’s Solution 1, if the group of the eight active fisherpersons is politically strong. Otherwise, they lose the next election. Those eight fisherpersons would oppose the imposition of the tax as in solution 1 since at equilibrium only five fisherpersons are needed, each of them harvesting 2 units fish every year and the corresponding economic profit of every active fisherperson is zero. This implies that three of them would have to quit the fishing business and they will not be able to recover their investment in human capital and physical capital, nor will they be able to capture a portion of the annual total tax imposed on the sale of fish that the government collects if government officials were able to impose the $26 unit tax as in solution 1. The government politicians face a quandary. To placate and appease the group of eight fisherperson, they need a middle ground solution to ensure that the stock of fish will not become extinct, which results in a loss of some total net social benefit, and it makes it even impossible to win the votes of the group of the eight fisherpersons. First, to save the fishery economy from collapsing into the abyss of extinction, the stock of fish has to be allowed to recover and reach an appropriate level. To enable the fish stock to recover, the government politicians in power must impose a moratorium on fishing. This is also impossible to help them win votes in the next election unless the group of eight fisherpersons are promised some form of compensation beyond unemployment insurance. Can the economist deliver the right solution in this case? The answer is yes. The economist’s proposal in this case is the following: Second Economist’s Proposal For simplicity and to use what we learned with the economist’s solution 1, let us assume that the government politicians choose a moratorium on fishing until the stock of fish recovers and reaches the level (=100 units) such that the corresponding annual harvest is equal to the maximum yield (10 units). We know that efficiency requires in this case that the annual harvest should be equal to 10 units. To ensure that this is the case and the group of 8 fisherpersons will accept the deal, let the government politicians offer to issue 8 licences to fish no more than 1.25 units of fish every year thence.. Each one of the eight fisherpersons receives only one such license with the government commitment that no more licences to fish will be issued now or in the future. Analysis of Second Economist’s Proposal The total annual harvest by all fisherperson will be equal to 10 units = 8 x (1.25 units). The stock of fish will remain equal to its efficient level of 100 units The Second Economist’s Proposal does block free entry: the fish product is now rival and excludable. There will be excess productive capacity for a while. In figure 6, the annual supply curve is now vertical line GJ, but the annual demand curve is still Curve MR in figure 6. The “perfect competition” equilibrium occurs at point N where the demand curve MR and supply curve GH intersect. The equilibrium price is $30 and the equilibrium quantity is equal to 10 units. Each fisherperson produces annually 1.25 units. According to this proposal, each one of the group of 8 fisherpersons who got a license to fish will be able to receive annually now an economic profit equal to $32.5 = ($26 x 1.25 units) for ever Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 15 12 - 4:30 PM The group of 8 fisherpersons who got a license to fish, together, they capture the total collected tax that the government would collect on behalf of society according to Economist’s Solution 1. A fishing license has a value. The further the demand curve shifts to the right, the greater the value of the license. Clearly, the group of 8 fisherpersons, who got a license to fish, will support this second economist’s Proposal. Once the Economist’s Second Proposal is implemented, the license has a value and it will be traded in a corresponding market. If the demand curve keeps shifting to the right as a consequence of population growth, the price of a license to fish will keep increasing. In Canada, a similar arrangement is currently in force, although the resulting stock of fish may lower than the efficient stock. Conclusion There are two kinds of natural resources: Non-renewable natural resources and renewable natural resources. Regardless of how the market for a given non-renewable natural resource determines its price, given its equilibrium price in the present and no discovery of additional under ground reserves of the resource or substitutes of it in the future, Hotelling’s Rule states that its equilibrium price between any two future periods will increase at a rate equal to the then future market interest rate When the natural resource is renewable and the market for its product operates under perfect competition, the resource is usually a commonly owned resource. Thus, Its product is rival but non- excludable. Left to itself and if not subject to a fatal disease, fatal attacks by natural predators, and/or excessive harvesting by humankind, the stock of a renewable natural resource will grow overtime until it reaches a certain maximum size that the natural environment can sustain. If its stock is too small then it risks extinction. Biologists inform us that the annual growth of an otherwise healthy stock is a function of the stock itself. Starting at a stock greater than the level below which the stock of the natural resource will become extinct, the annual amount of the growth of the stock is called the sustainable yield corresponding to that stock level. As the stock level of the natural resource increases, the corresponding sustainable yield increases to reach a maximum amount. We call this maximum amount of the sustainable yield the maximum sustainable yield. Past the stock level that corresponds to the maximum sustainable yield, the sustainable yield starts falling until the stock reaches a certain level at which the corresponding sustainable yield is equal to zero. The best example of this natural resource is the fish population in the earth’s oceans and seas. The consumption of fish by human kind gave rise to a fishing industry with a certain number of fisherpersons or fish producers companies. If the fish product operates under perfect competition or monopolistic competition, free entry and exit starting at a given stock of fish leads to an annual equilibrium price of fish and an annual harvest of fish the size of which exceeds the sustainable yield of the given stock. Overtime, the stock of fish in the Earth’s ocean’s and seas will start to fall and continue falling, especially when the world demand curve for fish keeps shifting to the right under the pressure of a growing humankind population.. Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 16 12 - 4:30 PM The marginal cost of a fisherperson or a fish producing company includes only what they pay of additional costs to produce an additional unit of fish. It does not include the marginal external cost suffered by other fish producers of her/his generation or of those of future generations. We call it the private marginal cost of a fisherperson or a fish producing company In contrast, there is a marginal social cost curve that takes into consideration the size of the stock of fish and of the need to limits the annual harvest to the sustainable yield at any level of the corresponding stock of fish. Starting from the smallest stock of fish which ensures no possible risk of extinction of the natural resource of fish, the marginal social cost of harvesting the corresponding sustainable yield and no more falls until it reaches a certain level when the growth of the stock of fish is equal to the maximum sustainable yield. At this level of the stock of fish, the marginal social cost is infinite. This is the efficient level of the stock of fish and the efficient amount of annual harvesting. At this level, the current generation and all future generations will be able to consume the same amount of fish harvested annually. Taking into account the welfare of every present and future generation, efficiency requires that optimal stock of fish to maintain forever is the stock that yields the maximum sustainable yield Most likely, with the current world population size, the market demand curve of fish will intersect the marginal social cost at an annual fish harvest equal to the maximum sustainable yield of the corresponding to stock of fish. The marginal external cost is equal to the difference between the marginal social cost and the private marginal cost Due to population growth and a continuous increase in the average national income, the demand curve for fish keeps shifting right, creating opportunities of earning a short term positive economic profit. Thanks to free entry and earth’s seas and oceans are defacto a common property and starting from any stock of fish, the equilibrium annual harvest of a perfect competition market for fish will eventually exceed the maximum sustainable yield of the stock of fish, causing the stock of fish to fall. If society does not do anything about the situation, the stock of fish is bound for extinction. In contrast, an efficient management of the fishing activity is to allow the stock of fish to recover and reach a level equal to that which yields an annual harvest equal to the maximum sustainable yield. There are two solutions to ensure that at equilibrium a perfect competition fish market will not lead to the extinction of the stock of fish and produce a harvest equal to the maximum sustainable yield. One solution is to impose a moratorium on fishing until the stock of fish increases enough to reach its level, which yields the maximum sustainable yield. Then impose a varying annual unit tax equal to the excess of the corresponding marginal social benefit over the private marginal cost at a total quantity demanded equal to the maximum sustainable yield. In a democratic society, special interests will oppose this solution. A second solution is a middle ground solution. It consists in imposing a moratorium on fishing until the stock of fish reaches an acceptable level to all parties and have the government issue a certain number of licenses to fish a certain annual quantity of fish annually and no more such that the number of licenses is equal to the current number of fisherpersons and the total annual quantity of fish is equal to the sustainable yield at the accepted level of the stock of fish. This scheme blocks free entry and ensures that each holder of the licence makes a profit, which keeps growing as the demand curve keeps shifting right. The licence has an increasing market value overtime.. End Chapter 12: Natural Resources, Chapter 12 Natural resources June 2024 Introductory Microeconomics, 8/20/2024 17 12 - 4:30 PM