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Q1:1. (14 total points) Suppose a consumer has a utility functiongiven by U(X,Y)= MIN(X, 3Y). The consumer has $60 to spend(M = $60). The Price of Good Y is Py = $1.a) (10 points) Draw the consumer's Price Consumption Curve forthe following prices for Good X: Px = $1, Px = $2, Px = $3. Foreach set of prices, make sure to accurately draw each budgetconstraint, and also identify the consumer's optimal bundle oneach budget constraint. Make sure your graph is neat, accurate,scaled properly, and fully labeled to receive full credit.b) (4 points) Using a graph, sketch the consumer's demand curvefor Good X. Make sure to identify three points on the demandcurve. Make sure your graph is neat, accurate, scaled properly, andfully labeled to receive full credit.See Answer
Q2:Exercise 2- Attitudes towards risk and fair betsThe following graph represents Mike's marginal utility of income (not the utility but the marginal utility):Marginal UtilityMU(I)IncomeWe know that Mike's income I is greater than $20, but we do not know his exact income. Alejandro offers Mikethe following bet: Alejandro will roll a 6 sided dice (all numbers equally likely). If it is 1 or 2, Mike pays Alejandro$20. Otherwise, if it is 3, 4,5 or 6, Alejandro pays Mike $10.a) Is this a fair bet?b) Will Mike accept or reject the bet? Do your answer depend on Mike's initial wealth? (assuming he canalways pay the $20 if he loses)See Answer
Q3:Question 1: Auctions a. Using the second-price, sealed-bid auction model described in Lecture 1, but assuming buyers' valuations are privately drawn from a uniform distribution over [0, 0], show that: i. The optimal bidding strategy for any buyer is to bid their true valuation and so: ii. Explain how the expected revenue to the seller will increase with u. b. Suppose instead that the seller implements a first-price, sealed-bid auction. i. Show that the bidding strategy b' : = - (1)u, is u, is an equilibrium bidding strategy when there are two bidders in the auction (N = 2). ii. What is the expected revenue in this auction? c. Would a risk-averse seller prefer one auction-type over the other? d. Consider a Position Auction discussed in lectures, with each buyer's valuation known to all other buyers: i. Show that the strategy b³ (as defined in lectures) is a best response to b¹ and, similarly, that b² is a best response to b³ and b. ii. Will a seller necessarily increase revenue by increasing the number of positions available for advertising on a webpage?See Answer
Q4:Question 2: Networks and Platforms There is a mass M = 1 of consumers uniformly distributed along a straight (Hotelling) road of length 1. A single games platform is located at one end of the road and consumer i's "willingness to pay" from playing on the platform is given by: u₂ (di) = 1 - di (1) Here, d; is the distance consumer i must travel to reach the console store. Assume that consumers who do not participate on the platform receive zero utility. The platform charges a price p for the access and faces costs C(x) = x², where is the proportion of consumers using the platform. The platform sets prices to maximise profits. a. Determine the demand curve and inverse demand curve faced by the platform. b. What is the profit-maximising price charged by the store? c. What price would a welfare-maximising social planner choose? d. What is the dead-weight loss associated with the monopoly price? Now assume that a new multi-player game is introduced that allows the platform users to gain utility by interacting with others using the same platform, so the "willingness to pay" of each consumer is now given by: 7 ui (di, 9) = 1 + 1/2 − di - 8 (2)/n7 == u,(di,q) +1/12-di Here, q is the proportion of consumers agent i expects to use the platform. e. Recalculate parts b., c., and d. above for the new situation. f. How did the introduction of the multi-player game impact on the profits of the platform? The firm realises that there is actually a mass N of advertisers willing to advertise on the platform. Each advertiser j expects to receive profit ; (Pa, 9) from advertising, where: (2) Tj (Pasq) = 2q-cj- Pa (3) Here, c; is a random variable drawn from a uniform distribution over [0, 1], pa is the price charged by the console manufacturer to the advertiser, and q is the proportion of consumers expected to use the platform. The platform faces additional costs Ny² from adding advertisers, where y is the proportion of adver- tisers advertising on the console. g. Given your solutions to part e., calculate the price på the platform should charge advertisers. h. Should the platform vary the price p charged to consumers? If so, how? i. Compare the profit-maximising prices charged with the marginal costs for the games platform in the two markets. Comment on your answers. j. What prices would a social planner charge if it were able to set prices on the platform? k. How large is the Spence distortion?See Answer
Q5: What was the main objective and motivation behind Gordon 1954? What was the author trying to prove/ disprove/ show and why? Explain economic rents and describe what type of market structure (pure competition vs. monopoly) would provide the highest rents. Draw a diagram and identify the optimal harvest level, cost, and rent or profit made under this harvest level. Explain how the effort will be allocated in a simple two fishery ground model (**hint** think of marginal productivity). Show why this environment will never reach a steady state (**hint** how will fisherman shift their effort between the two grounds?). Draw a diagram if necessary. What is the functional form we assume for the production function (aka the landings' function) and why do we use this functional form? Is it realistic? Which more optimal, sole ownership or open access? Why? Do you think Gordon is implying that we only give one fisherman the right to fish? Explain. If not, what do you think are policy implications of the findings?/n | CHICAGO JOURNALS The Economic Theory of a Common-Property Resource: The Fishery Author(s): H. Scott Gordon Source: The Journal of Political Economy, Vol. 62, No. 2 (Apr., 1954), pp. 124-142 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1825571 Accessed: 22/02/2010 20:04 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Political Economy. STOR http://www.jstor.org THE ECONOMIC THEORY OF A COMMON- PROPERTY RESOURCE: THE FISHERY¹ H. SCOTT GORDON Carleton College, Ottawa, Ontario I. INTRODUCTION T HE chief aim of this paper is to ex- amine the economic theory of nat- ural resource utilization as it per- tains to the fishing industry. It will appear, I hope, that most of the prob- lems associated with the words "con- servation" or "depletion" or "overex- ploitation" in the fishery are, in reality, manifestations of the fact that the natu- ral resources of the sea yield no economic rent. Fishery resources are unusual in the fact of their common-property nature; but they are not unique, and similar problems are encountered in other cases of common-property resource industries, such as petroleum production, hunting and trapping, etc. Although the theory presented in the following pages is worked out in terms of the fishing industry, it is, I believe, applicable generally to all cases where natural resources are owned in common and exploited under conditions of individualistic competition. II. BIOLOGICAL FACTORS AND THEORIES The great bulk of the research that has been done on the primary production phase of the fishing industry has so far been in the field of biology. Owing to the ¹ I want to express my indebtedness to the Canadian Department of Fisheries for assistance and co-operation in making this study; also to Pro- fessor M. C. Urquhart, of Queen's University, Kingston, Ontario, for mathematical assistance with the last section of the paper and to the Econo- mists' Summer Study Group at Queen's for afford- ing opportunity for research and discussion. lack of theoretical economic research,² biologists have been forced to extend the scope of their own thought into the eco- nomic sphere and in some cases have penetrated quite deeply, despite the lack of the analytical tools of economic the- ory.³ Many others, who have paid no specific attention to the economic as- pects of the problem have nevertheless recognized that the ultimate question is not the ecology of life in the sea as such, but man's use of these resources for his own (economic) purposes. Dr. Martin D. Burkenroad, for example, began a recent article on fishery management with a section on "Fishery Management as Po- litical Economy," saying that "the Man- agement of fisheries is intended for the benefit of man, not fish; therefore effect of management upon fishstocks cannot be regarded as beneficial per se.”4 The 2 The single exception that I know is G. M. Gerhardsen, "Production Economics in Fisheries," Revista de economía (Lisbon), March, 1952. 3 Especially remarkable efforts in this sense are Robert A. Nesbit, "Fishery Management" (“U.S. Fish and Wildlife Service, Special Scientific Re- ports," No. 18 [Chicago, 1943]) (mimeographed), and Harden F. Taylor, Survey of Marine Fisheries of North Carolina (Chapel Hill, 1951); also R. J. H. Beverton, "Some Observations on the Principles of Fishery Regulation," Journal du conseil permanent international pour l'exploration de la mer (Copen- hagen), Vol. XIX, No. 1 (May, 1953); and M. D. Burkenroad, "Some Principles of Marine Fishery Biology," Publications of the Institute of Marine Sci- ence (University of Texas), Vol. II, No. 1 (Septem- ber, 1951). 4 "Theory and Practice of Marine Fishery Man- agement," Journal du conseil permanent international pour l'exploration de la mer, Vol. XVIII, No. 3 (January, 1953). 124 THEORY OF A COMMON-PROPERTY RESOURCE great Russian marine biology theorist, T. I. Baranoff, referred to his work as "bionomics" or "bio-economics," al- though he made little explicit reference to economic factors.5 In the same way, A. G. Huntsman, reporting in 1944 on the work of the Fisheries Research Board of Canada, defined the problem of fisheries depletion in economic terms: "Where the take in proportion to the effort fails to yield a satisfactory living to the fisherman";6 and a later paper by the same author contains, as an incidental statement, the essence of the economic optimum solution without, apparently, any recognition of its significance.7 Upon the occasion of its fiftieth anniversary in 1952, the International Council for the Exploration of the Sea published a Rap- port Jubilaire, consisting of a series of papers summarizing progress in various fields of fisheries research. The paper by Michael Graham on "Overfishing and Optimum Fishing," by its emphatic recognition of the economic criterion, would lead one to think that the eco- nomic aspects of the question had been extensively examined during the last half-century. But such is not the case. Virtually no specific research into the economics of fishery resource utilization has been undertaken. The present state 5 Two of Baranoff's most important papers- "On the Question of the Biological Basis of Fisher- ies" (1918) and "On the Question of the Dynamics of the Fishing Industry" (1925)-have been trans- lated by W. E. Ricker, now of the Fisheries Re- search Board of Canada (Nanaimo, B.C.), and issued in mimeographed form. 6 "Fishery Depletion," Science, XCIX (1944), 534. 125 of knowledge is that a great deal is known about the biology of the various com- mercial species but little about the eco- nomic characteristics of the fishing in- dustry. The most vivid thread that runs through the biological literature is the effort to determine the effect of fishing on the stock of fish in the sea. This discus- sion has had a very distinct practical orientation, being part of the effort to design regulative policies of a “conserva- tion" nature. To the layman the problem appears to be dominated by a few facts of overriding importance. The first of these is the prodigious reproductive po- tential of most fish species. The adult female cod, for example, lays millions of eggs at each spawn. The egg that hatches and ultimately reaches maturity is the great exception rather than the rule. The various herrings (Clupeidae) are the most plentiful of the commercial species, accounting for close to half the world's total catch, as well as providing food for many other sea species. Yet herring are among the smallest spawners, laying a mere hundred thousand eggs a season, which, themselves, are eaten in large quantity by other species. Even in in- closed waters the survival and reproduc- tive powers of fish appear to be very great. In 1939 the Fisheries Research Board of Canada deliberately tried to kill all the fish in one small lake by poi- soning the water. Two years later more than ninety thousand fish were found in the lake, including only about six hun- dred old enough to have escaped the poisoning. 7"The highest take is not necessarily the best. The take should be increased only as long as the extra cost is offset by the added revenue from sales" (A. G. Huntsman, "Research on Use and Increase of Fish Stocks," Proceedings of the United Nations Scientific Conference on the Conservation and Utiliza- tion of Resources [Lake Success, 1949]). The picture one gets of life in the sea is one of constant predation of one spe- cies on another, each species living on a narrow margin of food supply. It re- minds the economist of the Malthusian law of population; for, unlike man, the 126 fish has no power to alter the conditions of his environment and consequently cannot progress. In fact, Malthus and his law are frequently mentioned in the biological literature. One's first reaction is to declare that environmental factors are so much more important than com- mercial fishing that man has no effect on the population of the sea at all. One of the continuing investigations made by fisheries biologists is the determination of the age distribution of catches. This is possible because fish continue to grow in size with age, and seasonal changes are reflected in certain hard parts of their bodies in much the same manner as one finds growth-rings in a tree. The study of these age distributions shows that com- mercial catches are heavily affected by good and bad brood years. A good brood year, one favorable to the hatching of eggs and the survival of fry, has its effect on future catches, and one can discern the dominating importance of that brood year in the commercial catches of suc- ceeding years. Large broods, however, do not appear to depend on large num- bers of adult spawners, and this lends support to the belief that the fish popu- lation is entirely unaffected by the ac- tivity of man. 8 H. SCOTT GORDON There is, however, important evidence to the contrary. World Wars I and II, during which fishing was sharply cur- tailed in European waters, were followed by indications of a significant growth in 8 One example of a very general phenomenon: 1904 was such a successful brood year for Norwegian herrings that the 1904 year class continued to out- weigh all others in importance in the catch from 1907 through to 1919. The 1904 class was some thirty times as numerous as other year classes during the period (Johan Hjort, "Fluctuations in the Great Fisheries of Northern Europe," Rapports et procès- verbaux, Conseil permanent international pour l'ex- ploration de la mer, Vol. XX [1914]; see also E. S. Russell, The Overfishing Problem [Cambridge, 1942], p. 57). fish populations. Fish-marking experi- ments, of which there have been a great number, indicate that fishing is a major cause of fish mortality in developed fisheries. The introduction of restrictive laws has often been followed by an in- crease in fish populations, although the evidence on this point is capable of other interpretations which will be noted later. General opinion among fisheries biolo- gists appears to have had something of a cyclical pattern. During the latter part of the last century, the Scottish fisheries biologist, W. C. MacIntosh, and the great Darwinian, T. H. Huxley, argued strongly against all restrictive measures on the basis of the inexhaustible nature of the fishery resources of the sea. As Huxley put it in 1883: “The cod fishery, the herring fishery, the pilchard fishery, the mackerel fishery, and probably all the great sea fisheries, are inexhaustible: that is to say that nothing we do seri- ously affects the number of fish. And any attempt to regulate these fisheries seems consequently, from the nature of the case, to be useless."¹⁰ As a matter of fact, there was at this time relatively little re- striction of fishing in European waters. Following the Royal Commission of 1866, England had repealed a host of restrictive laws. The development of steam-powered trawling in the 1880's, which enormously increased man's pred- atory capacity, and the marked improve- ment of the trawl method in 1923 turned the pendulum, and throughout the inter- war years discussion centered on the problem of "overfishing" and "deple- tion." This was accompanied by a con- siderable growth of restrictive regula- ⁹ See his Resources of the Sea published in 1899. 10 Quoted in M. Graham, The Fish Gate (London, 1943), p. 111; see also T. H. Huxley, "The Herring," Nature (London), 1881. THEORY OF A COMMON-PROPERTY RESOURCE tions." Only recently has the pendulum begun to reverse again, and there has lately been expressed in biological quar- ters a high degree of skepticism concern- ing the efficacy of restrictive measures, and the Huxleyian faith in the inex- haustibility of the sea has once again begun to find advocates. In 1951 Dr. Harden F. Taylor summarized the over- all position of world fisheries in the fol- lowing words: Such statistics of world fisheries as are avail- able suggest that while particular species have fluctuated in abundance, the yield of the sea fish- eries as a whole or of any considerable region has not only been sustained, but has generally in- creased with increasing human populations, and there is as yet no sign that they will not con- tinue to do so. No single species so far as we know has ever become extinct, and no regional fishery in the world has ever been exhausted.¹2 In formulating governmental policy, biologists appear to have had a hard struggle (not always successful) to avoid oversimplification of the problem. One of the crudest arguments to have had some support is known as the "propagation theory," associated with the name of the English biologist, E. W. L. Holt. 13 Holt advanced the proposition that legal size limits should be established at a level that would permit every individual of the species in question to spawn at least This suggestion was effectively de- molished by the age-distribution studies whose results have been noted above. Moreover, some fisheries, such as the "sardine" fishery of the Canadian At- lantic Coast, are specifically for imma- ture fish. The history of this particular fishery shows no evidence whatever that once. 11 See H. Scott Gordon, "The Trawler Question in the United Kingdom and Canada," Dalhousie Review, summer, 1951. 127 the landings have been in any degree re- duced by the practice of taking very large quantities of fish of prespawning age year after year. 12 Taylor, op. cit., p. 314 (Dr. Taylor's italics). 13 See E. W. L. Holt, "An Examination of the Grimsby Trawl Fishery," Journal of the Marine Biological Association (Plymouth), 1895. The state of uncertainty in biological quarters around the turn of the century is perhaps indicated by the fact that Holt's propagation theory was advanced concurrently with its diametric opposite: "the thinning theory" of the Danish biologist, C. G. J. Petersen.¹4 The latter argued that the fish may be too plentiful for the available food and that thinning out the young by fishing would enable the remainder to grow more rapidly. Petersen supported his theory with the results of transplanting experiments which showed that the fish transplanted to a new habitat frequently grew much more rapidly than before. But this is equivalent to arguing that the reason why rabbits multiplied so rapidly when introduced to Australia is because there were no rabbits already there with which they had to compete for food. Such an explanation would neglect all the other elements of importance in a natural ecol- ogy. In point of fact, in so far as food alone is concerned, thinning a cod popu- lation, say by half, would not double the food supply of the remaining individuals; for there are other species, perhaps not commercially valuable, that use the same food as the cod. Dr. Burkenroad's comment, quoted earlier, that the purpose of practical policy is the benefit of man, not fish, was not gratuitous, for the argument has at times been advanced that commercial fishing should crop the resource in such a way as to leave the stocks of fish in the sea completely unchanged. Baranoff was largely responsible for destroying this 14 See C. G. J. Petersen, "What Is verfish- ing?" Journal of the Marine Biological Association (Plymouth), 1900-1903.See Answer
Q6:Question 1 (50 pts) Consider a rational addiction model with flow utility u(e₂, h. y) where e is consumption of the additive good, h is health, and y is consumption of the non-addictive good. The flow utility is increasing in all three inputs. The present value of lifetime income is A, the discount factor is 3, and the prices of the addictive and non-addictive goods are pe and 1, respectively. Health depends on prior consumption of the addictive good as follows: h=h(₁-2) a. (10 pts) What does the flow utility need to satisfy for the tolerance property to be satisfied? Explain your answer. b. (10 pts) What does the flow utility need to satisfy for the reinforcement property to be satisfied? Assume tolerance is satisfied. Explain your answer./nc. (8 pts) Write the setup of the maximization problem. d. (5 pts) Write the Lagrangian of the problem./ne. (17 pts) Compute the first order condition with respect to the addictive good at t. Assume tolerance is satisfied. Explain your FOC.See Answer
Q7:Vlad lives in Siberia. It gets really cold there. He has $1,000 in monthly income. He pays $500 of his income in rent for his apartment and spends the remaining $500 on two things: Fuel for heating the apartment (H) and all other goods (Y). Vlad's utility function is quasilinear and non-monotonic: u(H,Y) = -0.01(H — 100)² + Y. Note that it is non-monotonic because too much heat makes Vlad worse off (there's a 'right' temperature). Let Y be the numeraire (py = $1) and, for simplicity, also suppose that PH = $1. With rent fixed at $500, Vlad's budget constraint is then simply: H+ Y = 500. a) How much H does Vlad consume? b) Suppose the landlord is considering including heat in the rent. She offers Vlad a heat-included rental contract of $560 per month (under this contract, heat would be free to Vlad). Should Vlad take the deal? c) Suppose heating fuel costs the landlord the same as the tenant (PH = $1). How much would the landlord have to charge for a heat-included rental contract to break even, i.e., to make as much money as with the old heat-not-included contract? d) Would Vlad be better or worse off under the 'breakeven' heat-included contract from part c) compared to paying $500/month in rent and buying heating fuel separately (part a)? What's the maximum Vlad would be willing to pay in rent for a heat-included contract?See Answer
Q8:TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-4000 TOPICS IN ADVANCED MICROECONOMIC THEORY ASSIGNMENT 1 DUE: FEBRUARY 12, 2024 Answer all questions. Each is equally weighted. Question 1: Consider a consumer whose utility function is given by U(x₁, x₂) = x₁x2, where x and y represent quantities of consumption of two consumer goods. and x2. 3/41/4 (a) Derive and interpret this consumer's Marshallian demand functions for X1 (b) Derive and interpret this consumer's indirect utility function. (c) Derive and interpret this consumer's Hicksian demand functions for x₁ and x2. (d) Derive and interpret this consumer's expenditure function. (e) Suppose the consumer's income is $1000 and the prices of x, and x2 are both $5. How should the consumer maximize her utility? What is her maximum level of utility? (d) Now suppose the price of x, rises to $10. The price of x2 remains at $5. (i) Derive, explain, and illustrate the income and substitution effects of this price change on the consumption of x₁. (ii) Derive, explain, and interpret the income and substitution effects of this price change on the consumption of x2. (iii) What are the effects of this price change on the consumer's maximum utility? +See Answer

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