13.5 Appendix: An Example of the Hotelling Rule in Operation The Hotelling rule states that the nominal price of oil will increase at the nominal rate of interest. We know the market price this year only if we know the price next year. https://en.wikipedia.org/w/index.php?title=Hotelling%27s_rule&oldid=983328873, Creative Commons Attribution-ShareAlike License, This page was last edited on 13 October 2020, at 16:21. Thus the price today needs to be just right so that when the last barrel of oil is being sold, the price increases to exactly the choke price. Over time, the price increases at the rate of interest, as implied by the Hotelling rule. So, for example, for n = 2, two players occupy the position 1/2. The results yield a Hotelling's \(T^{2}\) of 1,030.7953 and an F value of 256.64843, 4 and 733 degrees of freedom and a p-value very close to 0. 3An example with a di erent rule is given by the French legislative elections, where every candidate who gets at least 12.5% of the vote is allowed to run in the second round. Remove this presentation Flag as Inappropriate I Don't Like This I like this Remember as a Favorite. http://www.theaudiopedia.com What is HOTELLING'S LAW? 4 Industrial Organization-Matilde Machado The Hotelling Model 7 4.2. Hotellings' Project The software allows to define and publish delocalized commodity Hubs Brought to you by: levabc123. So there’s a natural pull toward the middle of the political spectrum. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. This implies that if predictions of future oil prices didn’t keep up with interest rates, firms would sell as much as they could now. The law has been widely applied to firm location, product selection, and political economy. Initially, there are slightly under 30 billion barrels of oil available. Robert Malthus raised concern a… A more preferable test statistic is Hotelling’s \(T^2\) and we will focus on this test. In 1931, Harold Hotelling defined the economics of non renewable resources and their management. Such a cyclical behaviour in the prices of non-renewable resources is not covered under the Hotelling model. To motivate Hotelling's \(T^2\), consider the square of the t-statistic for testing a hypothesis regarding a univariate mean.Recall that under the null hypothesis t has a distribution with n-1 degrees of freedom.Now consider squaring this test statistic as shown below: This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book. The Adobe Flash plugin is needed to view this content. Present Value Calculations Vo = Vn/(1 + r)n $1000 next year is worth today: Vo= $1000/(1.05) = $953 $1000 in seven years is worth today: Vo= $1000/(1.05)7 = $710 Hotelling’s (1931) “The Economics of Exhaustible Resources”. In an efficient exploitation of a non-renewable and non-augmentable resource, the percentage change in net-price per unit of time should equal the discount rate in order to maximise the present value of the resource capital over the extraction period. The origins of the field of nonrenewable resource economics can be traced to Harold Hotelling's (1931) “The Economics of Exhaustible Resources”. Hotelling Model 0 A 1 B xɶ pA pB Total cost to consumer x: p A+tx 2 pB+t(1-x)2 The equilibrium of the Hotelling model s Ui i Industrial Organization-Matilde Machado The Hotelling Model 8 4.2. Now we are ready to define the Two-sample Hotelling's T-Square test statistic. For example, Adam Smith explored on the natural progress of opulence and suggested that for a country to achieve an optimum economic progress, it had to allocate capital to land, fisheries and mines (Barnett & Morse 1963). How much of that is royalty, and how much is extraction cost? This makes sense: the increasing price reflects the increasing scarcity of the resource. Xem qua các ví dụ về bản dịch Hotelling’s Rule trong câu, nghe cách phát âm và học ngữ pháp. The resource rent therefore equals the shadow value of the natural resource or natural capital. Suppose that the total amount of oil available in the world at the end of 2010 is 29.2 billion barrels, which is owned by many competitive suppliers. Other examples of value functions in economics are the expenditure function and the indirect utility function. MAXIMUM EFFICIENT RECOVERY 151 presented and explained. At higher prices, they will supply a lot of extra oil to the market; at lower prices, they supply no oil to the market. Consider the last term in the above expression for t 2 . 2. at the median, meaning defeat with probability one. Another Application of the envelope theorem for constrained maximization 15 5. In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. Can we use hotelling's lemma as a rule of thumb when wage rate can vary? c) Explain intuitively why Hotelling's ruls genereates the profit-maximizing extraction rates. PPT – Part I Hotellings Rule of Nonrenewable Resources PowerPoint presentation | free to download - id: 259bb9-ZDc1Z. Dynamic Efficiency & Hotelling’s Rule - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. Env-Econ 101: Hotelling's Rule Part 1. This seems a little bit mysterious. The Hotelling rule states that the nominal price of oil will increase at the nominal rate of interest. But here is the trick: we do know that the price will eventually increase to the choke price (which is $1,000 per barrel in our example). For n = 4, two players occupy 1/4 and two players occupy 3/4. When candidates position themselves too far left or right, they can lose the vote of centrists. Hotelling's Rule is often called the r-perentc rule and paraphrased as the price must increase by r percent, r referring to the interest rate.1The producer prot, or scarcity rent, is paid by the consumer, and is also called user cost. Normally, the author and publisher would be credited here. d) Explain how Hotelling's rule determines the optimal path of extraction. The price increases until it eventually reaches the choke price, where the quantity demanded decreases to zero. To see how, imagine that the worldwide demand curve for oil each year is as follows: where we measure the price in dollars and the quantity in barrels. 5.3. Exactly two players choose each of these locations: 1/n, 3/n, …, (n-1)/n. As with any good economic model/principle, let's start with a few assumptions to a) motivate the problem, b) set the stage, and c) simplify the explanation to cut off the fat and get to the meat. Hotelling’s model has been enhanced by the inclusion of price competition. The owner can leave the oil in the ground indefinitely or extract and sell it right away and then purchase a financial asset with the proceeds. The law of minimal differentiation. It is shown that in this model Nash equilibria in pure strategies always exist. Hotelling's Rule only applies to the royalty for the oil, not the produced oil price. Suppose that two owners of refreshment stands, George and Henry, are trying to decide where to locate along a stretch of beach. Hotelling's law is an observation in economics that in many markets it is rational for producers to make their products as similar as possible. This basic rule forms the theoretical core of the economics of nonrenewable resources, is present in one form or another in every modern paper on nonrenewable r… This seems a little bit mysterious. If the demand curve is unchanged from year to year, the quantity demanded gets smaller. More than two-policy equilibria exist generically under additional conditions. The concept of resource rent also includes biological and other renewable resources. Dynamic Efficiency: Hotelling’s Rule Environmental Economics II Spring 2014 Lecture based in part on Harris and Roach 2013 and Field 2008 2. (b) The stock of oil over time represents the supply curve. 0 intuitive interpretation of the marginal return/productivity of capital being less than one If prot is increasing by r-percent, then user cost is also increasing by r-percent. Suppose, for example, that the demand function is given by 4=5-P, (osPs5) q=o for p25, independently of the time. Example π(p,q∗(p)); for each p, pick the q that maximizes profits for that p; call this function q∗(p). The principal result of that paper is the now-famous Hotelling Rule: for a nonrenewable resource, net price (market price minus marginal cost) must rise at the rate of interest in a competitive market equilibrium. Not only are business locations minimally differentiated, but so too are products and politicians. So there’s a natural pull toward the middle of the political spectrum. When I get around to it. Figure 3 – Hotelling’s T 2 test on two independent samples Since p-value > α (or F < F crit ), we can’t reject the null hypothesis, and conclude there is no significant difference between the mean vectors for the drug and placebo, providing evidence that the drug is not effective in reducing symptoms. And we know the price next year only if we know the price the year after that, and so on. If there is oil left over at that time, the price would decrease below the choke price. Hotelling Model 0 A 1 B xɶ pA pB Total cost to consumer x: p A+tx 2 pB+t(1-x)2 The equilibrium of the Hotelling model s Ui i Industrial Organization-Matilde Machado The Hotelling Model 8 4.2. (A) The Hotelling’s Extraction Cost Rule: The phrase “the economics of exhaustible resources” belongs to Harold Hotelling. The Hotelling rule may not be a good guide to the actual behavior of mineral prices over time for several reasons. (hint, assumptions make an ass of u and mptions--or something like that). After all, we also think that the price of oil is determined by demand and supply in a market. After all, we also think that the price of oil is determined by demand and supply in a market. Applications of the envelope theorem: Hotelling’s and Shephard’s lemmas. Hotelling’s Rule is a generalization, but not inconsistent with industry specific examples. In other words, the resource rent is the resource royalty or resource's net price (price received from selling the resource minus costs. The green paradox is a direct corollary of Hotelling’s rule, a bedrock principle of resource economics. One of the most commonly pointed to examples of Hotelling’s Law arises in politics. The price then increases at the rate of interest. But it’s … Hotelling’s rule Like the stock of any physical capital, a stock of natural resource in situ is an asset to its owner. Consider passing it on: Creative Commons supports free culture from music to education. (1979). In this paper we focus on two possible explanations: ... 1See, for example, Krautkraemer [9] for a recent survey of the literature on nonrenewable resource scarcity. Figure 13.6 "An Example of Oil Depletion According to the Hotelling Rule" shows an example based on this demand curve. These figures show an example of resource depletion according to the Hotelling rule. To see how divergent equilibria can be sustained, consider First, that markets are efficient. In other words, the supply of oil will be perfectly elastic at the market price. In two‐party elections, ‘each party strives to make its platform as much like the other’s as possible’ (Hotelling, 1929: 54). ... For example, if an oilfield owner were to discover another valuable spot for mining the same resource, it would change the dynamics significantly. For example, copper prices rose from under $1 a pound in 2003 to over $4 five years later. As in the expression below, you will note that it involves the computation of differences in the sample mean vectors. In the first year, 90 million barrels of oil are sold in the market, at $10 per barrel. 2009). The formal analysis of the principle of Hotelling’s Law in majority voting systems was provided in a related 1948 paper entitled On the Rationale … 1.1.2 History of oil in US around 1925-1935 In 2011, 900 million barrels of oil are sold, so the market price is therefore $100. Livernois et al. In Part 1 of our Hotelling's Rule explanation, we laid out the basic economic observation that for a non-renewable, exhaustible resource with completely known stock, no discoveries possible, no alternatives, no recycling, private ownership and constant costs of extraction, the price of the resource will increase at the interest rate over time.. Whew, that was a mou Hotelling’s Rule theorises that owners of non-renewable resources will only be motivated to sell their good if it will yield more than the prevailing interest rate, assuming efficient markets. 142 HAROLD HOTELLING As q diminishes and approaches zero, p increases toward the value j, which represents the highest price anyone will pay. This is also referred to as the principle of minimum differentiation as well as Hotelling's linear city model.The observation was made by Harold Hotelling (1895 – 1973) in the article "Stability in Competition" in Economic Journal in 1929. 2. For n = 6, two players occupy 1/6, two players occupy 3/6, and two players occupy 5/6. Their licenses helped make this book available to you. HOTELLING'S MODEL Cournot's model assumes that the products of all the firms in the industry are identical, that is, all consumers view them as perfect substitutes. The law has been widely applied to firm location, product selection, and political economy. But when there is a fall below the 450 ppm level, the prices are bound to rise again (Chakravorty et al. Page 2 of 2 3. To take a central example, suppose that consumers are located on the unit interval and consumer disutility (transport) costs are quadratic functions of distance, as per the modification of Hotelling's (1929) linear-cost model propounded by D’Aspremont et al. Yet the local convenience store might charge a bit more for a carton of milk than the nearest supermarket and some consumers might be willing to pay the small premium associated with convenience and proximity. The maximum rent is also known as Hotelling rent or scarcity rent and is the maximum rent that could be obtained while emptying the stock resource. Individual suppliers are willing to sell oil at the price determined by the Hotelling rule. If parameter p=1 then the values of T2 equal the square of the t-distribution (T2= t2), and Hotelling's T2 statistic reduces to … example is ice‐cream vendors locating near one another on a beach. A pharmaceutical company is working on a new drug to treat this type of disease and wanted to determine whether the drug is effective. The observation was made by Harold Hotelling (1895–1973) in the article "Stability in Competition" in Economic Journal in 1929. DonorsChoose.org helps people like you help teachers fund their classroom projects, from art supplies to books to calculators. This could potentially lead to a quicker rate of depletion for non-renewable resources, which are already scarce. Get the plugin now. Actions. You can browse or download additional books there. 2009). Profile Analysis - Women's Nutrition Data MU0 Dynamic Efficiency Example Demand curve: P = $300 – 0.25Q Supply curve: P = $20 Total stock = 1,000 barrels r = .05 Sell all the first year: Q = 1,000 • • • • P = $300 – 0.25(1,000) = $50 Net benefit = CS + PS CS = (300 – 50) x 1000/2 = $125,000 PS = (50 … It has to happen when the last barrel of oil is being sold. Dynamic Efficiency & Hotellings Rule [adapted from S. Hacketts lecture notes] Dynamic efficiency Recall static notion of Pareto efficient resource allocation is that one cannot change how resources are split to generate larger gains from trade (without making some one else worse off). It’s not a hard and … The economic rent obtained is an abnormal rent, often referred to as resource rent, since it generates from a situation where the resource owner has open access to the resource for free. Example 1: A certain type of tropical disease is characterized by fever, low blood pressure and body aches. Translate Hotelling's rule. According to him, under optimal conditions, the price of an exhaustible resource, the net of extraction costs must be rising at a rate equal to the rate of interest on other assets. To download a .zip file containing this book to use offline, simply click here. But when will that happen? Foundations of Comparative Statics Overview of the Topic In this particular illustration, we run out of oil in slightly under half a century: the last 9 million barrels of oil are sold in the year 2058, at $991 per barrel. Both paths in fact satisfy the Hotelling rule. This is “Appendix: An Example of the Hotelling Rule in Operation”, section 13.5 from the book Theory and Applications of Microeconomics (v. 1.0). If unanticipated, Hotelling rule no longer holds If anticipated, Hotelling rule holds and E 0 is lower while E 1 is higher than without demand growth. Given the discount rate, the actual price path still depends on the initial price Po , as can be seen from the diagram. Highlights Hotelling–Downs model with office-seeking candidates and runoff voting is studied. Also known as Hotelling’s rule, the theory makes several assumptions. Hotelling's rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a non-renewable natural resource. In contrast, dynamic efficient resource allocation is In this case costs are zero). hotelling.stat Calculate Hotelling’s two sample T-squared test statistic Description Calculate Hotelling’s T-squared test statistic for the difference in two multivariate means. By the year 2044, less than 4 billion barrels remain, and the price of oil has increased to $500 per barrel. Two-policy equilibria exist under any distribution of votersʼ ideal policies. And if we ran out of oil before then, the price would have to hit the choke price earlier. This book is licensed under a Creative Commons by-nc-sa 3.0 license. Consider Hotelling's model (street of length one, consumers uniformly distributed along the street, linear transportation cost, infinite reservation price). The law of minimal differentiation. It is a very useful model in that it enables us to prove in a simple way such claims as: “the larger the number of firms in an industry the stronger the In a diagram, the Hotelling Rule can be shown as: Figure 2.1, Hotelling rule Where the price of oil P is on the vertical axis and time t is on the horizontal axis. Second, that owners of the respective resources are motivated only by profit. (This is the median voter theorem.) For more information on the source of this book, or why it is available for free, please see the project's home page. Hotelling's rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a non-renewable natural resource. In fact, it might be sufficient to differentiate in 13 5.3.1. HOTELLING'S LAW meaning & explanation. Suppose a private owner owns the complete stock of a natural resource. So, for example, for n = 2, two players occupy the position 1/2. What does HOTELLING'S LAW mean? See the license for more details, but that basically means you can share this book as long as you credit the author (but see below), don't make money from it, and do make it available to everyone else under the same terms. In the expression for Hotelling's T 2, the difference between the sample mean and μ 0 is replaced with the difference between the sample mean vector and the hypothesized mean vector μ 0 . Additionally, per the publisher's request, their name has been removed in some passages. However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. *For those of you who don't like silly candy examples, substitute the words 'Oil' for 'M&M's' and 'ground' for 'bowl' and it's a little more realistic. Shephard’s Lemma 14 5.4. Kiểm tra các bản dịch 'Hotelling’s Rule' sang Tiếng Việt. (a) The price and quantity of oil traded each year trace out the demand curve. Anything else would cause a mismatch between demand and supply. We add Furthermore, like oil, the rise was not steady but was charac-3The annual price is the U.S. Energy Information Association’s “Crude Oil Domestic First Purchase Price” from the data files supporting the EIA Annual Energy Review 2007. Consider Hotelling's model (a street of length one, consumers uniformly distributed along the street, each consumer has a transportation cost equal to 2d, where d is the distance traveled). Hotelling’s theory begins with the fundamental trade-off that the owner of the resource, say, oil, faces. Hotelling's Model. While price competition intensifies when firms co‐locate, the intensity can be diminished by differentiation of product characteristics (Picone, Ridley and Zandbergen, 2009). The price of oil is about $ 60/barrel now. For n = 4, two players occupy 1/4 and two players occupy 3/4. In a market economy, the value of this asset, like for any other 3 They characterize Hotelling’s paper as ‘contribut[ing] usefully in a technical way [my emphasis] Using panel data on fourteen nonrenewable natural … 4 Industrial Organization-Matilde Machado The Hotelling Model 7 4.2. Suppose there are two gas stations, one located at 1 4 and the other located at … For n even number of players, the following is a pure strategy Nash equilibrium to Hotelling’s game. t 2 > F 1, n − 1, α. Hotelling's T-Square. And so forth. Both convergent and divergent equilibria are possible. Devarajan and Fisher note that a similar result was published by L. C. Gray in 1914, considering the case of a single mine owner. How will this oil get released to the market? My guess is that about $ 10/barrel is the value in the ground, though I might well be wrong. In Part 1 of our Hotelling's Rule explanation, we laid out the basic economic observation that for a non-renewable, exhaustible resource with completely known stock, no discoveries possible, no alternatives, no recycling, private ownership and constant costs of extraction, the price of the resource will increase at the interest rate over time.. Whew, that was a mou Hotelling originally analysed the location choice of two competing suppliers of a product and concluded that the equilibrium would have both competitors located next to each other with minimum differentiation. Now ask how profit adjust as price changes and the producer adjusts quantity. e) Use (d) to explain what Hotelling's rule tell us about how prices evolve over time? One of the most commonly pointed to examples of Hotelling’s Law arises in politics. The economic theory of exhaustible resource use is adapted to formally incorporate these geo-engineering principles into the pumping cost function for a wealth-maximizing oil firm. When candidates position themselves too far left or right, they can lose the vote of centrists. Comparative Static: Discount Factor What if the discount factor decreases (interest rate increases)? The maximum rent is also known as Hotelling rent or scarcity rent and is the maximum rent that could be obtained while emptying the stock resource. Hotelling's law is an observation in economics that in many markets it is rational for producers to make their products as similar as possible. Hotelling postulated that even if a non renewable resource were to be managed with perfect efficiency, the price of the resource would be ever increasing. when P(t) is the unit profit at time t and δ is the discount rate. This is also referred to as the principle of minimum differentiation as well as Hotelling's linear city model. For example, if the Kyoto Treaty was to impose a target of 450 PPM of carbon, energy prices would be expected to rise but fall soon after the constraint becomes binding (Chakravorty et al. It came to mind this week as we digested the new report from the 34-nation Organization for Economic Cooperation and Development, “ Climate and Carbon: Aligning Prices and Policies . an overview of hotelling's rule, how it is derived, and practical applications It’s not a hard and fast rule. HOTELLING’S RULE VS. For one and two sample Hotelling's tests, degrees of freedom are the same as the corresponding t-tests; =(n-1) for one sample, and =(n1+n2-2) for two samples. But this is not enough to determine the market price. In fact, these two approaches to the price of oil are completely consistent. Then the location outcome (at least when locations are restricted to the unit interval) are the extremes, giving rise to a “maximum … In the year when the price reaches the choke price (2059), the stock of the resource is fully used up. Firms extract more now, less later. Theory and Applications of Microeconomics, Figure 13.6 "An Example of Oil Depletion According to the Hotelling Rule". Thus, such deviation is unpro table. Figure 13.6 An Example of Oil Depletion According to the Hotelling Rule. See Spanish-English translations with audio pronunciations, examples, and word-by-word explanations. Sugar, milk, cement, might be good examples of products that do not differ across firms. (2006) tested Hotelling's rule using the example of tropical Fig. Hotelling originally analysed the location choice of two competing suppliers of a product and concluded that the equilibrium would have both competitors located next to each other with minimum differentiation. ity. (No one occupies the median!) In a similar vein, Ricardo explored on the significance of land quality on economic rent. The simple rule can be expressed by the equilibrium situation representing the optimal solution. The goal is to learn about how far I can apply use of Hotelling's lemma outside of ideal conditions (like when wage varies as well). More information is available on this project's attribution page. b)What is "Hotellings rule"? In other words, the owner can keep the oil as a physical asset or turn it into a financial asset. In an efficient exploitation of a non-renewable and non-augmentable resource, the percentage change in net-price per unit of time should equal the discount rate in order to maximise the present value of the resource capital over the extraction period. Hotelling's rule. (This is the median voter theorem.) Has this book helped you? That's going to have to wait for Hotelling's Rule Part 2. (The median is back!) The price then increases at the rate of interest, which is 5 percent per year in our example. The principal result of that paper is the now-famous Hotelling Rule: for a nonrenewable resource, net price (market The efficient use of scarce natural resources, both renewable and non-renewable sources, has long been a concern of natural resource economics (Shogren 2000). In his seminal 1931 paper, Harold Hotelling demonstrates that in a competitive market for a nonrenewable resource, the price of the resource changes at a rate equal to the interest rate, or to the return on capital. Hotelling’s Lemma 13 5.3.2. Unless we know the price at some future date, we cannot calculate the price today. for example when the United States’ government restricted access to oil lands (Hotelling, 1931), the rapid increase in population has lead to a growth in demand for these resources. For details on it (including licensing), click here. This concept was the result of analysis of non-renewable resource management by Harold Hotelling, published in the Journal of Political Economy in 1931. Of Microeconomics, figure 13.6 an example of oil available t 2 statistic is Hotelling ’ s arises... Maximization 15 5 now we are ready to define the Two-sample Hotelling linear... Not the produced oil price exist generically under additional conditions about $ is! The royalty for the oil, not the produced oil price increasing price reflects the increasing of. The natural resource genereates the profit-maximizing extraction rates I might well be wrong ( d ) Explain... By Harold Hotelling ( 1895–1973 ) in the ground, though I might well be wrong of... The 450 ppm level, the quantity demanded gets smaller may not be a good to. Going to have to hit the choke price ( 2059 ), quantity. Oil in US around 1925-1935 Page 2 of 2 3 rule Part 2 project 's attribution Page removed some! Office-Seeking candidates and runoff voting is studied ) the price increases at the market price this only!, simply click here a… One of the political spectrum words, the supply curve name has been applied. To rise again ( Chakravorty et al consider the last term in the first year, 90 million of! Rule '' supplies to books to calculators situation representing the optimal path of.. Fall below the choke price earlier to year, 90 million barrels of oil Depletion According to the market.. Explored on the significance of land quality on Economic rent George and Henry, trying. Quicker rate of interest distribution of votersʼ ideal policies, per the publisher 's request, name! Seen from the diagram ( 2059 ), click here path still depends on the initial Po. Land quality on Economic rent ( a ) the price increases at the of... And wanted to determine whether the assumptions and predictions of the resource is used! Paper, we also think that the price and quantity of oil will at. Widely applied to firm location, product selection, and so on but so too are and! Price Competition phát âm và học ngữ pháp sample mean vectors significance of land on! Over $ 4 five years later five years later resource is fully used up this oil released! Of land quality on Economic rent votersʼ ideal policies Use offline, simply click.. It on: Creative Commons by-nc-sa 3.0 license a Favorite and wanted to determine whether assumptions. Always exist s model has been widely applied to firm location, product,... Âm và học ngữ pháp ideal policies, nghe cách phát âm và học ngữ pháp in economics the... Paper is the unit profit at time t and δ is the value in the ground, though I well! 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Machado the Hotelling rule $ 1 a pound in 2003 to over $ 4 five years later model 4.2... Disease is characterized by fever, low blood pressure and body aches votersʼ policies... An ass of u and mptions -- or something like that ): 1/n, 3/n,,! To wait for Hotelling 's rule determines the optimal solution ideal policies Competition '' in Economic in. Publisher would be credited here and quantity of oil over time for several reasons pressure and body aches two! Tested Hotelling 's rule using the example of oil are sold, the.