Nonlinear Demand Function Research Articles

The demand disruption management problem for a supply chain system with nonlinear demand functions

This paper addresses the problem of handling the uncertainty of demand in a one-supplier-one-retailer supply chain system. Demand variation often makes the real production different from what is originally planned, causing a deviation cost from the production plan. Assume the market demand is sensitive to the retail price in a nonlinear form, we show how to effectively handle the demand uncertainty in a supply chain, both for the case of centralized-decision-making system and the case of decentralized-decision-making system with perfect coordination.

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms.

Nonlinear dynamics in the Cournot modelwithout full information

A Cournot model with an arbitrary nonlinear demand function and where firms do notobserve their rival's actions directly is shown to allow mistaken beliefs to persist. Thesealter the original equilibrium state and, in a range of beliefs, destroy its stability and createcycles. The dynamics of the Cournot model are therefore fundamentally affected.

Inventory Model for Damagable Items with Stock-Dependent Demand and Shortages

Items made of glass, ceramics, etc. get damaged during the storage due to accumulated stress of stocked items. Inventory models of these items are developed here with finite rate of replenishment and inventory level-dependent demand. Both linear and non-linear damage and demand functions are considered, shortages are allowed and fully backlogged. Optimum order quantities are determined using the profit maximization principle in integral form. The models are illustrated with numerical examples and a sensitivity analysis is presented.

Product differentiation and cartel stability: Chamberlin versus Hotelling

This paper contrasts the implications, for cartel stability, of the non-spatial (‘Chamberlinian’) and the spatial (‘Hotelling’) models of product differentiation. Using the special case of a linear demand framework, we show that whereas the former approach suggests that cartel stability is non-monotonic but predictable in the degree of differentiation, the outcome is very much more ambiguous when the latter formulation is employed. We examine also the implications for stability when demand shocks occur, and show that even in the case of linear demand, when differentiation is modelled in spatial terms the results are consistent with non-linear non-spatial demand functions, as well as with those obtained in more complicated models of firm behaviour.

Optimal market segmentation of hotel rooms—the non-linear case

The optimal market segmentation pricing strategy for rooms of hotels is investigated to determine the optimal number of segments to be used and the accompanying number of rooms and price prevailing in each segment, under the assumption of an aggregate non-linear demand function. A single state-variable dynamic programming model is formulated to maximize profit, and an efficient reduction in the range of search for the solution of the model is outlined. A numerical example is provided for a 400 room hotel with an exponential demand curve.

Sensitivity analysis of tax incidence in a spatial equilibrium model

In this paper, we show that the impact of an ad valorem tax on demand prices is the same for all interrelated spatial regions regardless of sizes of their price elasticities. In the case of a degenerate spatial equilibrium model in which several independent submarkets develop, the tax incidence is identical within a submarket; but varies between different submarkets. In the case of non-linear and/or non-separable demand and supply functions, the same results hold as long as (i) the tax does not affect unit transportation costs and (ii) a unique equilibrium commodity flow solution exists.

On Parametric Medians of Trees

In this paper we consider the optimal location of a single facility with respect to a set of demand points on a tree network. The demands of the points to be served are dynamic and our model takes into account predictable changes in these demands. We study problems with both linear and nonlinear demand functions. We make use of the analytical properties of tree networks and sensitivity analysis, and devise efficient algorithms to construct the optimal trajectory of the parametric location problem. We also give theory that exploits the network topology.

Transformation and weighting in recreation demand regressions

Transformation is the appropriate way to treat non-linear recreation demand functions, such as the logically and empirically desirable negative exponential. Transformation, however, affects the error variance of data, bringing a need for a different set of data weights in regressions. The appropriate weights for logarithmically transformed data are numbers of visits from each zone of origin. A two-stage weighting process is theoretically preferable and empirically effective in determining consumers' surplus per visit, compared with either unweighted or simple weighted protocols.

Excessive exchange rate variability: A possible explanation using nonlinear economic dynamics

This paper seeks to show that a possible explanation of excessive exchange rate variability is that the dynamics of exchange rates are being driven by nonlinearities in the underlying economic relationships. The Dornbusch model, which is the theoretical underpinning of many models of exchange rate dynamics, is the starting point. A nonlinear demand function for foreign assets is introduced into the model. Small time lags, in the adjustment of exchange rates to the differential between domestic and foreign interest rates, and, in the formation of expectations of exchange rate changes are both introduced. The dynamics of the model are governed by a set of three nonlinear differential equations. The system is analysed using concepts and techniques from the theory of noninear differential equations. The model exhibits various dynamic regimes as the expectations lag decreases, moving from global asymptotic stability (long lag), through limit cycle behaviour to a discontinuous oscillation (short lag). The behaviour for short time lags, and in the perfect foresight limit, is consistent with highly variable exchange rates.

Comparative Statics for Utility Maximization Models with Nonlinear Budget Constraints

This paper investigates the properties of demand functions generated by budget constraints, and relates them to those of demand functions generated by budget constraints. The analysis shows that the properties of nonlinear and linear demand functions in some respects are similar, but in other respects differ substantially. The study gives conditions under which properties of the linear demand functions carry over to the nonlinear ones. The implications for the nonlinear demand functions of various separability assumptions are also studied. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Optimal pricing and production in an inventory model

This paper deals with the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon. For nonlinear demand functions and convex inventory and shortage cost functions the optimal solution paths are derived by using optimal control theory. The treatment of linear nonsmooth cost functions requires the use of a generalized maximum principle. The solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as the resulting inventory paths. Moreover, it is shown that in the case of nonsmooth piecewise linear cost functions the equilibrium is approached within finite time although the model is nonlinear in the control variables. Finally it is illustrated that exogenous fluctuations in the demand rate (seasonal demand pattern) amount to cyclical optimal solutions.

Competition Versus Optimal Control in Groundwater Pumping When Demand is Nonlinear

This article considers the issue of optimal control versus no control in groundwater pumping under the assumption of a nonlinear demand function for water use. We confirm for the case of the nonlinear demand function what had been demonstrated for the case of a linear demand function: namely, if water rights are properly defined and if the storage capacity of the aquifer is relatively large, the difference between a strategy of no control and a strategy of optimal control is small and thus can be ignored for practical policy considerations. Furthermore, we demonstrate that even if simulated optimal control yields slightly better results than no control, a strategy of no control is likely to yield better results than optimal control, unless we can be sure that the estimated demand for groundwater is very close to the true demand.

Solving the generalized transportation problem

This paper advocates a mathematical programming approach for solving the classical transportation problem generalized to include non-linear demand and supply functions and non-linear transport costs. Such an approach is made possible by the recent public availability of a powerful optimizing system called MINOS, assembled for the solution of large programming problems for which the constraint set is linear and spatial. Primal and dual program formulations for this generalized transportation problem are set out in the paper, and brief computational experience with the software system in solving several illustrative problems is recorded.

The nature of substitution between transport modes

In this paper, we have derived a non-linear demand function for gasoline by means of a two-stage optimization of the S-2 branch utility function. The demand function was simplified by employment of the Kuhn-Tucker optimization conditions and the Shephard-Samuelson theorem.