September 29, 1895 december 26, 1973 was an american mathematical statistician and an influential economic theorist, known for hotellings law, hotellings lemma, and hotellings rule in economics, as well as hotellings tsquared distribution in statistics. Hotelling model graphically 0 1 1 location of firm a location of firm b mass of consumers 1 1 0 0. Hotellings lemma, mathematical analysis by ignou jitendra kumar economics. The various units of the mineral are then to be thought of as being at any time all equally valuable, excepting for varying costs of placing them upon the market. Winner of the standing ovation award for best powerpoint templates from presentations magazine. Consumers differ in their tastes for the two products. Hotellings game and the median voter theorem duration. For the profit function of the firm n terms of the goods price. A basic decomposition identifies subspaces of the parameters in which one model is.
Similar models with a larger number of firms have been analyzed by lancaster 1979, salop 1979, novshek 1980, and economides 1983,1989, among others. Hotellings 1929 duopoly model of locationally differentiated products has been recently reexamined by daspremont, gabszewicz and thisse 1979 and economides 1984, among others. Hotellings lemma is the heart of duality theory, it is instructive to begin with a graphical presentation of this theorem and the relationship between the indirect profit function, lr 7rp, r, and the direct profit function, r py rx. Using the shephards lemma to obtain demand functions. It was first shown by harold hotelling, and is widely used in the theory of the firm the lemma can be stated as. We show the slightly unusual case of an input demand. Minimise expenditure subject to a constant utility level. In this video ill attempt to explain hotellings lemma and prove it mathematically. Kumar aniket 29 may 20 hicksian demand function and shepards lemma. Worlds best powerpoint templates crystalgraphics offers more powerpoint templates than anyone else in the world, with over 4 million to choose from. I general mathematical theory of depreciation, by harold hotelling, jolrrnal of the american statistical association, september, 192 j.
Foundations of comparative statics overview of the topic 1 implicit function theorem. Some properties of profit functions and supply functions. Hicksian demand function hicksian demand function is the compensated demand function. Dixon april 23, 2012 hotelling s rule is the observation that the exploitation of a nonrenewable resource can only be economically e cient if the resource owner s marginal pro t increases at the prevailing discount rate. A competitive firms profit function is convex in prices, while cost and expenditure functions are concave. Of buying from seller a are of buying from seller b are s. He also developed and named the principal component analysis method widely used in statistics and. Hotellings lemma is a result in microeconomics that relates the supply of a good to the profit of the goods producer. If pp is twice differentiable, hotellings lemma and convexity ofpp together imply y ip p i. Hotellings lemma says that the derivative of this profit. For the test that the means of k variables are 0, let x be a 1 k matrix of the means and s be.
Then we can say that the point with coordinates az,afz 2y. We suppose that the two products are located at the extremes of the segment 0,1 and, following hotellings classical model hotelling 1929 and daspremont et al. Use the definitions of all these functions to show that hotellings lemma is really just a special case of. Another application of the envelope theorem for constrained maximization 15 5. Ppt bertrand and hotelling powerpoint presentation. The original formulation was by hotelling1931 and mahalanobis 1930,1936. Using the shephards lemma to obtain demand functions dr. The envelope theorem in an optimization problem we often want to know how the value of the objective function will change if one or more of the parameter values changes. Independence often fails, yet the need to identify outliers. He also developed and named the principal component analysis method widely used in. Foundations of comparative statics overview of the topic.
Hotellings rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a nonrenewable natural resource. At a profit maximum, the marginal effect of adjusting production on profits is zero. Hotellings main street with more than two competitors. For differentiable functions, these properties, with hotellings or shephards lemmas, imply weakinequality ownprice effects on net supplies or demands. All it does is to scale up the amount of the resulting pro. Finally, one of the most used of hotellings economic insights is contained not in a paper but in a letter to the director of the national park service hotelling, 1947. In a nash equilibrium every player chooses a best response. Since the entrance free is relatively small, it is clear that people are probably get. Yet, hes perhaps best known for some simple yet profound observations, one of which is now known as hotellings law. Ec 720 math for economists samson alva department of economics, boston college october 12, 2011 problem set 3 solutions 4.
Theyll give your presentations a professional, memorable appearance the kind of sophisticated look that todays audiences expect. The change in profits from a change in price is proportional to the quantity produced. Conventional usage enjoins hotellings t 2 i diagnostics, derived and applied under the mutual independence of y 1. The old quantities are still feasible and yield pro. It says that the net supply function of good i is the derivative of the pro. Hotelling model the transportation costs of consumer x. Paul schweinzer school of economics, statistics and mathematics birkbeck college, university of london 715 gresse street, london w1t 1ll, uk email. This theory proposes that owners of nonrenewable resources will only produce a supply of their product if it will yield more than instruments available to them in the markets.
Hotellings lemma is a famous result of duality theory. Persuasive advertising in hotellings model of product. Duality, net supply, and the directional distance function. Hotellings law is also referred to as the principle of minimum differentiation or hotellings linear city model. Harold hotelling 18951973 who described the idea in an economics journal article, stability in competition 1929. Trained in mathematics, he participated in the early twentieth century movement to mathematize economics. A regularized hotellings t2 test for pathway analysis in. To strengthen this we may make further assumptions about the hessian of pp. Hotellings lemma solves the problem as both parties become. 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.
The director had asked him and others how to measure the economic value of national parks. Application of separating hyperplane theorem for convex sets. Convexity and hotellings lemma are proved together. Profit maximization lectures in microeconomic theory fall 2009, part 3 01. Alternative scale models are compared with regard to the pitman efficiency of hotellings t2 in tests for means. Proof of hotellings lemma suppose y is a maximizing output at p, w. Hotellings lemma just tells us that the latter effect is zero for a profitmaximizing firm, which need not do much adjusting. September 29, 1895 december 26, 1973 was a mathematical statistician and an influential economic theorist, known for hotellings law, hotellings lemma, and hotellings rule in economics, as well as hotellings tsquared distribution in statistics. Hotellings lemma athe lagrangian for the rms problem is. The economics of exhaustible resources harold hotelling. Assumptions i and ii from the previous slide are enough to use brouwers theorem. Hotellings lemma says that the derivative of this profit function with respect to the output price coincides with the supply function and that the derivatives of the profit function with respect to each input price, multiplied by1, coincide with the associated factor demand curves.
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