Set Of Demand Functions Research Articles

Multi-Product Price and Assortment Competition

We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The products are substitutes in the sense that the demand volume of each product weakly increases whenever the price of another product increases. The cost structure is linear, with arbitrary cost rates.Our demand model is the unique regular extension of a set of demand functions that are affine in a limited polyhedral subset of the price space. A set of demand functions is regular if it satisfies the following conditions: under any given price vector, when some product is priced out of the market, i.e., has zero demand, any increase of its price has no impact on the demand volumes. Depending on the set of prices selected by the competing firms, a different product assortment is offered on the market.We characterize the equilibrium prices, product assortment and sales volumes in the price competition model, under this demand model. Under minimal conditions, we show that a pure Nash equilibrium always exists; while multiple price equilibria may arise, they are equivalent in the sense of generating an identical product assortment and sales volumes.

New models for locating a moving service facility

In this paper we analyze a new location problem which is a generalization of the well-known single facility location model. This extension consists of introducing a general objective function and replacing fixed locations by trajectories. We prove that the problem is well-stated and solvable. A Weiszfeld type algorithm is proposed to solve this generalized dynamic single facility location problem on Lp spaces of functions, with p ∈(1,2]. We prove global convergence of our algorithm once we have assumed that the set of demand functions and the initial step function belong to a subspace of Lp called Sobolev space. Finally, examples are included illustrating the application of the model to generalized regression analysis and the convergence of the proposed algorithm. The examples also show that the pointwise extension of the algorithm does not have to converge to an optimal solution of the considered problem while the proposed algorithm does.

Analysis of demand for fish in Bangladesh

An analysis of fish consumption patterns, and how they are likely to change as income and relative price changes, is required to assess the welfare impact of technological and policy changes in the fisheries and aquaculture sectors. This analysis is based on a matrix of price and income elasticities of demand for fish by type, as fish is a heterogeneous product and consumption patterns may differ by type of product. This paper presents estimates of fish demand elasticities by fish type for Bangladesh, using individual household expenditure data (5,667 households) collected by the Bangladesh Bureau of Statistics in 1988/89. It uses a multistage budgeting framework that estimates a demand function for food in the first stage, a demand function for fish (as a group) in the second stage and a set of demand functions for fish by type in the third stage. Estimated demand elasticities vary across fish type and across income class. Among the various types of fish, carp have the highest (in absolute terms) own‐price elasticity. Income elasticities of all fish types consistently fall with the increase in per capita expenditure level of households, but none of the fish types become an inferior good at the highest income quartile. Dried fish has the lowest income elasticities for the richest quartile of the population.