The Broad Picture

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Demand Function ◽  
Exchange Model ◽  
Natural Projection ◽  
Demand Functions ◽  
Regular Economies

This chapter shows that the m-tuple (fi) of demand functions defining the exchange model belongs to ε‎r, i.e., the demand function fi is bounded from below (B) for every consumer and satisfies desirability (A) for at least one consumer. These additional properties will give to the natural projection the very important property of properness. The combination of smoothness and properness will suffice to yield what is now known as the theory of regular economies.

The Fine Picture

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Demand Function ◽  
Terms Of Trade ◽  
Exchange Model ◽  
Full Measure ◽  
Revealed Preferences ◽  
Trade Intensity ◽  
Demand Functions ◽  
Regular Economies ◽  
Uniqueness Of Equilibrium ◽  
Weak Axiom

This chapter restricts the m-tuple (fi) of demand functions defining the exchange model to belong to ε‎c. In addition to the assumptions made in the previous chapters (recall that ε‎c is a subset of ε‎r), the demand function fi satisfies the weak axiom of revealed preferences for every consumer, and the slightly stronger negative definiteness of the Slutsky matrix for the consumer whose demand function satisfies desirability (A). These stronger assumptions are aimed at giving more economic flesh to the exchange model. As a consequence, the natural projection inherits much stronger properties that give a specificity of its own to the exchange model. The most important properties of the exchange model with (fi) ɛ ε‎c are the regularity of the no-trade equilibria, the openness and full measure (a.k.a., the genericity) of the set of regular equilibria as a subset of the equilibrium manifold, the inclusion of the set of equilibrium allocations in one and only one connected component of the set of regular economies, the uniqueness of equilibrium for all economies belonging to that component, and the interpretation of that property in terms of trade intensity.

scholarly journals Regular Infinite Economies

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Enrique Covarrubias
Keyword(s):  
Demand Function ◽  
Excess Demand ◽  
Natural Projection ◽  
Banach Manifold ◽  
Equilibrium Manifold ◽  
Equilibrium Set ◽  
Regular Economies

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.

scholarly journals LEARNING TO PLAY BEST RESPONSE IN DUOPOLY GAMES

2004 ◽  
Vol 06 (03) ◽  
pp. 443-459 ◽  
Author(s):  
JAN WENZELBURGER
Keyword(s):  
Demand Function ◽  
Optimal Strategies ◽  
Market Demand ◽  
Response Behavior ◽  
Estimation Errors ◽  
Demand Functions ◽  
Best Response ◽  
Game Theoretic ◽  
Payoff Functions ◽  
Duopoly Market

We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response behavior of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, a firm is able to play best response in the usual game theoretic sense.

The Exchange Model

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
General Equilibrium ◽  
Smooth Manifold ◽  
Comparative Statics ◽  
Exchange Model ◽  
Natural Projection ◽  
Equilibrium Models ◽  
Manifold Structure ◽  
Equilibrium Manifold ◽  
Complex Models ◽  
Smooth Map

The exchange model is the simplest of all general equilibrium models. Studying it will show us the directions to follow when studying more complex models like those that include production or take explicitly into account time and uncertainty. This chapter introduces the exchange model defined by the equilibrium manifold and the natural projection. It presents proof that the equilibrium manifold is indeed a smooth manifold. The smooth manifold structure implies that the natural projection is a smooth map. In terms of comparative statics, this tells us that equilibrium prices can be considered as depending linearly on the fundamentals defining an economy in sufficiently small neighborhoods of regular equilibria.

Framework for Deriving Macroscopic Demand Functions from Microscopic Acceleration Models

2017 ◽  
Vol 2623 (1) ◽  
pp. 40-48 ◽  
Author(s):  
Anupam Srivastava ◽  
Wen-Long Jin
Keyword(s):  
Demand Function ◽  
Transmission Model ◽  
Acceleration Process ◽  
Cell Transmission Model ◽  
Traffic Demand ◽  
Macroscopic Models ◽  
Demand Functions ◽  
Integral Role ◽  
Vehicle Acceleration ◽  
Traffic Systems

Vehicle acceleration plays an integral role in determining the operational capacity of roadway sections. Traditional first-order macroscopic models of traffic do not capture the boundedness of vehicle acceleration. In a recent study, it was shown that the cell transmission model could capture critical macroscopic effects of bounded acceleration if one modified the demand function such that traffic demand (sending flow) decreased in density for congested traffic. However, such a modified demand function was calibrated only with data. This paper introduces a framework for deriving such macroscopic demand functions corresponding to well-known microscopic acceleration models. Two mechanisms are explored for deriving the demand function with varying assumptions on how vehicles accelerate within a single discretized cell. The first mechanism is based on the assumption that vehicles within a single cell begin accelerating at the same time and that this information of the trigger of acceleration propagates instantaneously. The second mechanism assumes that the information for the trigger propagates within the cell at a finite speed such that following vehicles begin their acceleration process later than the leading vehicles. The derived demand functions are consistent with those calibrated with data. This study explicitly bridges macroscopic and microscopic models of bounded acceleration and can lead to more efficient evaluation of the effects of bounded acceleration on traffic systems.

scholarly journals Demand functions and demand manifolds

2021 ◽  
Author(s):  
Alan Beggs
Keyword(s):  
Demand Function ◽  
Firm Behavior ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Static Properties ◽  
Demand Functions ◽  
Necessary And Sufficient ◽  
The Relationship

AbstractMrázová and Neary (2017) introduce the notion of the Demand Manifold which expresses the relationship between the elasticity and curvature of a demand function. They argue that this determines many important comparative static properties of firm behavior. This paper gives necessary and sufficient conditions for two demand functions to have the same demand manifold and so to have similar comparative static properties.

scholarly journals Consistent Conjectural Variations Equilibrium in a Mixed Duopoly

2011 ◽  
Vol 15 (4) ◽  
pp. 425-432 ◽  
Author(s):  
Nataliya I. Kalashnykova ◽  
◽  
Vladimir A. Bulavsky ◽  
Vyacheslav V. Kalashnikov ◽  
Felipe J. Castillo Pérez ◽  
...  
Keyword(s):  
Demand Function ◽  
Market Price ◽  
Mixed Duopoly ◽  
Demand Functions ◽  
Interior Equilibrium ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Influence Coefficients ◽  
Conjectural Variations ◽  
Conjectural Variations Equilibrium

In this paper, we consider a model of mixed duopoly with Conjectured Variations Equilibrium (CVE). The agents’ conjectures concern the price variations depending on the increase or decrease in their production outputs. We establish existence and uniqueness results for the conjectured variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function derivative with respect to the market price.

Equilibrium with Decreasing Returns

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
General Equilibrium ◽  
Equilibrium Model ◽  
Exchange Model ◽  
General Equilibrium Model ◽  
Private Ownership ◽  
Demand Functions ◽  
Individual Demand

This chapter discusses an approach to the study of the general equilibrium model with private ownership of smooth production with decreasing returns by adjusting consumers’ individual demand functions for production. The “exchange model” defined by these production adjusted demand functions is then shown to be equivalent to the original general equilibrium model with private ownership of production. The production adjusted demand functions are very close to satisfy the properties considered in the first part of this book, properties that guarantee that the main properties of the exchange model are satisfied. As a result, the general equilibrium model with private ownership of smooth production with decreasing returns features exactly the same properties as the standard smooth exchange model.

scholarly journals Stability of Money Demand Function in Nepal

2013 ◽  
Vol 3 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Siddha Raj Bhatta
Keyword(s):  
Money Demand ◽  
Demand Function ◽  
Annual Data ◽  
Money Demand Function ◽  
Data Set ◽  
Monetary Aggregates ◽  
Demand Functions ◽  
Real Gdp ◽  
Long Run ◽  
Stability Issue

This paper examines the long-run stability issue of money demand function in Nepal using the annual data set of 1975-2009 by using the recently developed ARDL modelling to cointegration popularized by Pesaran and Shin (1999). The bounds test shows that there exists the long-run cointegrating relationship among demand for real money balances, real GDP, and interest rate in case of both narrow and broad monetary aggregates. Further, the CUSUM and CUSUMSQ test reveal that both the long-run narrow and broad money demand functions are stable. The results show that demand for money balance in Nepal is a stable and predictable function of a few variables and the central bank can rely on the monetary aggregates as intermediate targets for achieving the broad economic objectives.DOI: http://dx.doi.org/10.3126/bj.v3i1.7508 Banking Journal Vol.3(2) 2013 pp.1-27  

scholarly journals Uncapacitated Pricing Optimization for Mobile Broadband Services

2018 ◽  
Vol 20 (1) ◽  
pp. 49-58
Author(s):  
Fransiscus Rian Pratikto
Keyword(s):  
Demand Function ◽  
Estimation Method ◽  
Bayes Estimation ◽  
Plausible Assumption ◽  
Mobile Broadband ◽  
Demand Functions ◽  
Price Response ◽  
Broadband Services ◽  
Data Points ◽  
The Impact

The success of revenue management starting in the mid-1980s has been driving pricing decision to be more tactical and operational. Since then, statistics and operations research have been important tools in pricing and revenue optimization. This research seeks to determine optimal price for mobile broadband services of a particular service provider. The case study is mobile broadband services in Indonesian market. We made a plausible assumption that there is no capacity constraint. We used choice-based conjoint with hierarchical Bayes estimation method to derive individual part-worth utilities, based on which market simulation was run to obtain the price-response function. By combining this with information about market size, we came up with a number of data points representing the demand function. Instead of fitting the data points with some theoretical demand functions, we used monotonic cubic splines to interpolate the demand function. Accordingly, we did not use explicit demand functions in the optimization, but a numerical interpolation function to estimate demand for any particular price level. Using enumeration, we then came up with a recommended contribution-maximizing prices under one, two, and three fare-classes segmentation. We assumed a perfect segmentation where cannibalization and arbitrage were not present. Further, we discussed a generalized optimal segmentation problem under that assumption. We also investigated the impact of the changes in competitors’ service attributes on the optimal prices.

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