Varian, H.R.: Intermediate Microeconomics. W.W. Norton, New York, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that have CES functions. A production function Q = f(K, L) measures output given inputs consisting of the factors of production (in our case we have 2 factors: labor L and capital K) A simple production function often used in the economic literature is the Cobb Douglas production function [30]. It looks like: 21) Q = #K L A more complicated function that is very well known is the CES production function. CES functions were introduced by [3] and are also called ACMS functions, Figure 4. Contours of CES production function after the authors. For more information on CES functions ....

Hal R. Varian, Intermediate microeconomics. a modern approach, fifth ed., W. W. Norton & Co., 1999.

....the well known optimization problem of utility maximization under a budget constraint. Interesting, non trivial variants can be constructed by assuming some non linear pricing structures actually observed in daily life. 2. Linear budgets A simple model for optimal consumer behavior is as follows [7]. Consider a Cobb Douglas utility function that measures utility for a bundle of goods x: 1) u(x) Kx 1 x an n = K Consumers want to maximize utility subject to their budget function: 2) where p i is the price of good i and m is the available budget. i.e. the optimization ....

Hal R. Varian, Intermediate microeconomics. a modern approach, fifth ed., W. W. Norton & Co., 1999.

....modeling the utility function of Transmission Control Protocol (TCP) algorithms [7] We say that a user u with utility function Ua (x) is greedier than another user u2 with utility function Ua2 (x) if a2 a. One can interpret the notion of greed here using the notion of price elasticity of demand [13]. With the utility functions of the form in eq. 14 one can easily show that the price elasticity of demand decreases with a as follows. Given a price p, the optimal rate x (p) of the 1 user that maximizes the net utility Ua(x) x p is given by p a. The price elasticity of demand, which ....

....a price p, the optimal rate x (p) of the 1 user that maximizes the net utility Ua(x) x p is given by p a. The price elasticity of demand, which measures how responsive the demand is to a change in price, is defined to be the percent change in demand divided by the percent change in price [13]. In our case the price elasticity of demand p dx (p) p 1 p l a 1 x (p) dp p l a l a 1 is given by l a (15) Therefore, one can see that price elasticity of the demand decreases with a, i.e. the larger a is, the less responsive the demand is. 5 In the presence of time delay T ....

Hal R. Varian. Intermediate Microeconomics. Norton, New York, 1996. 14

....their best Q over a and we take the highest W=Q over i. That is, we are only interested in the best possible individual happiness. We are going to start drawing economic analogies to our various approaches. In economic theory, this would be the equivalent of a Nietzschean social welfare function [Varian, 1993, 30] where the value of an allocation depends on the welfare of the best off agent. The counterpart of this method would be: min min (Q(x,a) 89 that is, find the action which leads to the smallest unhappiness for someone and take it. This approach is pointless because it means just obey ....

....agents share the same suite of actions, we can calculate: max i x, a Note that this may produce compromise actions. The winning action may be an action that none of the agents would have suggested. In economics, this method would be equivalent to the classic utilitarian social welfare function [Varian, 1993, 30] the greatest happiness for the greatest number) If the agents don t share the same suite of actions, it s hard to see what we can do. We can t predict the happiness of other agents if one agent s action is taken. We can only try it and observe what happens. This leads to the following ....

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Varian, Hal R. (1993), Intermediate Microeconomics, W.W.Norton and Co.

....MARI uses its internal mathematical approximation of the buyer s and sellers utility functions to calculate bids and asks. MARI attempts to optimize by selecting a pairing whose associated surplus is maximal among all possible pairings. The resultant pairing can be shown to be Pareto optimal [14, 18]. Effectively, the bid ask spread indicates the surplus [17, 18] that the parties can derive from the transaction. As such, the buyer is matched with the seller with the lowest ask, among all sellers whose asks are less than or equal to the buyer s bid. The clearing price is set at the midpoint ....

....and sellers utility functions to calculate bids and asks. MARI attempts to optimize by selecting a pairing whose associated surplus is maximal among all possible pairings. The resultant pairing can be shown to be Pareto optimal [14, 18] Effectively, the bid ask spread indicates the surplus [17, 18] that the parties can derive from the transaction. As such, the buyer is matched with the seller with the lowest ask, among all sellers whose asks are less than or equal to the buyer s bid. The clearing price is set at the midpoint between the original bid and ask prices, equally dividing the ....

[Article contains additional citation context not shown here]

Varian, Hal P 1999. Intermediate Microeconomics. W. W. Norton & Company, New York.

....that have CES functions. A production function Q = f(K, L) measures output given inputs consisting of the factors of production (in our case we have 2 factors: labor L and capital K) A simple production function often used in the economic literature is the Cobb Douglas production function [17]. It looks like: Q = #K # L # (2) A more complicated function that is very well known is the CES production function. CES functions were introduced by [1] and are also called ACMS functions, after the authors. The functional form of a CES production function is: Q = # # #L # (1 #)K ....

H. Varian, Intermediate Microeconomics. A modern approach, fifth edition, 1999, W. W. Norton & Co.

....the base station are all equal. This implies that users who are further from the base station must transmit more power to achieve the same SIR target than those that are closer to the base station. Pareto E#ciency. A classical measure of the e#ciency of an equilibrium solution is Pareto e#ciency [Varian, 1996], which is defined for our wireless system below. Definition 2: A power vector P is Pareto e#cient if and only if there exists no such vector P 0 such that at least one user achieves higher utility while the other users utilities remain the same or improve. In other words there exists no ....

Varian, H. (1996). Intermediate Microeconomics, A Modern Approach. W. W. Norton and Co., New York, NY.

....which is the ultimate goal. A model of user preferences and selection of services was designed with micro economics ideas adapted to the problem. 6.2 Utility Utility is a way to describe preferences and to recognise a product that is better than another one. Hal R. Varian defines it so (see [Var96]) A utility function is a way of assigning a number to every possible consumption bundle 1 such that more preferred bundles get assigned larger numbers than less preferred bundles . This is the ordinal property of the utility function, because the utility value of a service has no significance ....

Hal R. Varian. Intermediate Microeconomics, a modern approach. Norton, 1996.

....of demand curves that increase with price, most of us display skepticism and refer to that remote possibility as to the Giffen paradox. In fact, as one of the most widely used microeconomics textbooks states it, Giffen goods are pretty peculiar, and are primarily a theoretical curiosity [Varian (1987, p.133) 1 On the other hand, positively sloped demand curves vastly populate marketing textbooks, where they are mostly to be found under the heading of prestige pricing [e.g. Gaedeke and Tootelian (1983) The opinion of marketing scholars is that several products are primarily bought ....

Varian, H.R., 1987, Intermediate Microeconomics, Norton, New York.

....by MARI, which evaluates the cost of each potential buyer seller pairing. MARI attempts to optimize by selecting the subset of feasible pairings whose associated surplus is maximal amongst all feasible pairings, as described below. The resultant matchings can be shown to be Pareto optimal [15]. MARI thus acts as an impartial resource brokering intermediary. MARI s interaction model with the user is based on a multi stage or ramping interface heuristic. MARI supports several levels of increasingly sophisticated interaction. At the simplest level, each ontology specific attribute has a ....

....to calculate bids and asks. Then, for each buyer, MARI evaluates the cost that would be incurred if the buyer were to engage in a transaction with any of the qualified sellers. Currently, we take this cost to be equal to bid ask spread, which can be interpreted as the aggregate surplus [14, 15] that the two parties would derive if the transaction were to take place. We use this metric of cost since our indicator of the goodness of an Figure 1: Specifying Ranges for Flexible Attributes allocation is welfare, which, in this case, is measured by the surplus that the allocation ....

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Varian, Hal R. Intermediate Microeconomics. W. W. Norton & Company, New York. 1999.

....of calculating consumer surplus are based on the estimation of a parametric demand curve. Imposing such a restriction on the shape of the demand curve may not be appropriate and may lead to misleading estimates. An alternative is to compute consumer surplus using non parametric methods (see Varian, 1993). The fourth method is based on the idea that consumer welfare is captured by the increase in utility resulting from changes in prices and consumption. Accordingly, instead of relying on a demand function, one may use a utility function to derive a measure of welfare. 34 Consumer surplus based ....

Varian, H., 1993, Intermediate Microeconomics, New York: W.W. Norton and Company.

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Varian, H.R.: Intermediate Microeconomics. W.W. Norton, New York, 1999.

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Hal R. Varian. Intermediate Microeconomics. Norton, New York, 1996.

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