Linear Demand Research Articles

Too Much of a Good Thing: Quality-Differentiated Demand and Monopoly Bias

Previous teaching notes focused on the logic and mechanics of a quality-differentiated linear demand structure. This note takes up the question of potential bias in how markets respond to quality-related aspects of consumer choice. Earlier examples demonstrated instances where monopoly interests might conflict with those of consumers in matters of quality choice. Here the question concerns a more general propensity toward excessively high or low levels of quality under monopoly market structures.

Linear Demands and Third-Degree Price Discrimination with Some Caveats

This note shows that compared to uniform pricing, third-degree price discrimination can be neutral. For linear demands, having all price intercepts of submarkets’ inverse demands to be the same is the necessary and sufficient condition for third-degree price discrimination to be neutral. For general demands, when all submarkets’ demands are proportional to each other, not only will all the submarkets be served under uniform pricing, but all prices before and after price discrimination will be the same.

Neutrality of third-degree price discrimination

This note shows that compared to uniform pricing, third-degree price discrimination can be neutral. For linear demands, having all price intercepts of submarkets’ inverse demands to be the same is the necessary and sufficient condition for third-degree price discrimination to be neutral. For general demands, when all submarkets’ demands are proportional to each other, not only will all the submarkets be served under uniform pricing, but all prices before and after price discrimination will be the same.

An analysis of retailer’s inventory in a two-echelon centralized supply chain co-ordination under price-sensitive demand

As the industrial environments become more competitive, managing specific inventory levels and coordination between channel members of a companies supply chain is very much crucial. In this paper, we have analyzed a two-echelon supply chain containing a manufacturer and a retailer in which the manufacturer offers a single product to the retailer and the retailer takes the responsibility of managing the inventory of the product. The products deteriorate at the retailer warehouse at a constant deterioration rate. We have generalized our model for two different demand functions faced by the retailer from the customers’ side. The demand functions are (a) a linear function of price (b) an iso-elastic function of price. The shortage is also allowed and partially backlogged with a constant backlogging rate. Total profit of the supply chain under two different demand scenarios is evaluated for a joint centralized coordination. The prime objective of our paper is to compare the total profit under two different demand functions in joint centralized coordination such that the channel member can decide their optimal sales price, inventory scheduling of retailer, ordering lot size to maximize the total profit. A numerical example has been illustrated to validate the theoretical results. Also, sensitivity analysis of some key parameters is carried out which gives some managerial applications. The findings of this paper demonstrate that linear demand would increase the joint profit of a centralized system. This analysis has an important guiding significance for the supply chain coordination of deteriorating items under linear and iso-elastic demand.

Return Decision Model of the Manufacturer-Leading Dual-Channel Supply Chain

According to the manufacturer-leading dual-channel supply chain return problem, a linear demand function considering the change rate of product interaction between the two channels and the change rate of market demand on the return price was established. Under the premise of no cross-return, this paper analyzes the changes of the optimal profit value of the manufacturer, retailer, and supply chain of the dual-channel supply chain in the context of centralized and decentralized decision-making and through the establishment of the price discount decision model and compensation strategy to coordinate the whole supply chain profit. This paper has shown that the use of the price discount decision model and compensation policy model could make the whole supply chain profit optimum value in decentralized decision-making situations equal to profit optimum value in the centralized decision-making situations, and price discount model could make manufacturers better to maximize profit considering the same return scenario, and that compensation policy model could be more helpful to maximize profits for retailers.

Tractatus Optimo-Linearis Demandandus: The Demandments (Treatise on Optimality and Linear Demand)

The linear demand curve and the consumer optimization problem are treated as separate, mutually exclusive manifestations in economics texts, leading to oversights and spurious results. We introduce a Revised Demand Framework (RDF) elucidating the underlying consumer optimization problem within the linear demand framework with its results. Income increases do not shift the demand curve but rotate it clockwise around the x-intercept as demand converges at all prices to its unconstrained optimum where p = 0. Thus, increases in income make the demand curve more price inelastic; income elasticity and price elasticity are additive inverses in equilibrium. Changes in income exhibit a quasi-Slutsky Decomposition; direct effects rotate the demand curve around the x-intercept while indirect effects shift it with the demand curve. Hence, the Law of Demand is inviolable as each purported violation is associated with a change in the unconstrained optimum shifting the demand curve. Convergence of demand to a finite level as income increases suggests that expansionary macroeconomic policy targeting consumer income could have a more limited impact than expected. Similarly, models employing Cobb Douglas preferences should justify isoelastic demand or nonfinite convergence in income when relying on these properties. Finally, we present a model of demand that is liner in price.

Is cultural taste in Finland acquired from mother, father or both

The main goal of this paper is to address the importance of parental cultural taste in explaining cultural participation among older adults in Finland. The study considers the intergenerational transfer hypothesis and asks: Do middle-aged or older consumers inherit cultural tastes from their parents? How stable are these intergenerational transfer effects? Which parental hobbies are the most influential? A constant elasticity of substitution (CES) utility function is used to describe the structure of consumer preferences. The linear demand system to be estimated uses the seemingly unrelated systems (SUR) method with two equations. If the intergenerational transfer hypothesis is valid, parental interest in movies, pop music, classical music and visual arts should have a positive impact on their children’s demand for movies, rock or jazz music, classical music and art gallery visits, respectively. The results indicate that the intergenerational transfer hypothesis is valid. Children do indeed inherit their cultural habits and taste from their parents. We seem to visit similar cultural events to those that our parents do or did. The youngest age cohort is by far the most influenced by parental interest in classical music. The visual arts and pop music interests of parents seem to be second and third most influential hobbies but only when the youngest age cohorts are considered. Parental pop music and sport hobbies are the most influential sources when the cultural and sports participation of the middle-aged are studied. A mother’s visual arts interests and father’s sports interests are most important determinants of the cultural and sports participation decisions of the oldest age cohort. In general age, gender and education are important determinants of cultural participation. The youngest, who have less family constraints, are more active than the middle-aged and those over 55 are more active participants – except for filmgoing or rock music. Theatre attendance, arts gallery visits and classical music concert visits increase after age 45. Attending musicals is not dependent on education while all other cultural events are elite in terms of education, except rock music concerts, which well-educated parents, attend less than the reference group, which is students. Women are more active in all cultural activities studied here. Most of the intergenerational transfer effects are not stable throughout the child’s age. Only a mother’s classical music or visual art habits seem to have a stable and positive effect on the classical music concert participation and on the art gallery visits of the child regardless of age. However, a father’s corresponding classical music or visual art habits have a positive effect on their children, when they are aged between 15 and 35, attending classical music concerts and going to art galleries. Keywords : Intergenerational transfer, Cultural participation, Finland, CES. DOI: 10.7176/JCSD/62-07 Publication date: November 30 th 2020

Food Security Assessment in Azad Jammu and Kashmir: Empirical Analysis of Dietary Diversity, Current and Project Food Demand and Supply-Demand Gap

This study attempts to determine the dietary diversity score for different food groups and estimates the current demand for different food groups in AJK. Data for this study was collected from 1250 households covering all 10 administrative districts of AJK by following multi-stage sampling techniques through a comprehensive interview schedule. Ten commodity groups (Wheat, Rice, Milk, Meat, Vegetables, Fruits, Pulses, Oil/Ghee, Tea and Other food were developed for analysis. Linear Approximate-Almost Ideal Demand System (LA-AIDS) model was used for estimating food demand elasticities through Zellner’s Seemingly Unrelated Regression by using STATA software. All the 10 food groups were found normal goods, except milk and fruits (income elasticity higher than unity). This implies that in future demand for milk and fruits would increase more proportionately as income would increase. The own price elasticities of all 10-food groups were also found congruent to economic theory (Wheat-0.28, Rice-0.65, Milk-0.92, Meat-0.34, Fruits-0.61, Vegetables-0.21, Pulses-0.29, Oil and ghee-0.04, Tea-0.35 and Other food-0.32). The income and own price elasticities depicted that wheat, vegetables, pulses and oil and ghee are necessities as compared to other food groups. The cross-price elasticity illustrated that rice could be a substitute for wheat and wheat for rice in the State of AJK. The Berry’s Index (82.43) depicted that food was diverse on average with a minimum Index value of 61.31. The study of different factors in relation to Berry’s Index depicted that education and income significantly and positively affect Berry’s Index while location of household in urban or rural area do not affect diversification of food. Inclusion of all necessities in Food Stamp program and Ramadan package and efforts by agriculture and livestock department regarding improved production of food commodities are recommended.

Stability of cartels in Multimarket Cournot oligopolies

AbstractWe investigate the stability of cooperation agreements, such as those agreed by cartels, among firms in a Cournot model of oligopolistic competition embedded in a multimarket contact setting. Our analysis considers a broad array of 64 potential market structural configurations under linear demand and quadratic production costs. We establish that for an appropriate range of parameter values there exists a unique core stable market configuration in which an identical two‐firm cartel is sustained in both markets. Our result highlights the significance of multimarket presence for cartel formation in light of the well‐known result from the single‐market setting where cartels are non‐profitable.

Linear demand systems for differentiated goods: Overview and user’s guide

Linear demand systems and quasi-linear quadratic utility models are widely used in industrial economics. We clarify the link between the two settings and explain their exact origin as it seems to be little known by practitioners. We offer practical recommendations to achieve consistency, tractability and a reasonable degree of generality when using the linear demand framework. We show that all tractable versions of the model used in practice are (almost) identical and have a mean-variance structure. We provide concise, ready-to-use formulae for the symmetric model. Finally, we revisit and extend the asymmetric model of Shubik and Levitan.

Approximate Calculation of Equilibria in the Nonlinear Stackelberg Oligopoly Model: A Linearization Based Approach

The game-theoretic problem of choosing optimal strategies for oligopoly market agents with linear demand functions and nonlinear cost functions is considered. Necessary conditions for the existence of a solution of a system of nonlinear equations with power functions are established. The system of equations for the optimal responses of agents is linearized by expanding the power functions in Taylor series. As a result, the linearized system depends on the vector of linearization parameters, and the calculation of game equilibria is reduced finding fixed points of nonlinear mappings. The deviations of the approximate equilibrium from the exact solution are investigated. Analytical formulas for calculating equilibria in the game of oligopolists under an arbitrary level of Stackelberg leadership are derived. Analysis of duopoly and tripoly demonstrates that the game equilibrium is determined by two factors as follows. First, the concavity of the agent’s cost function (the positive scale effect) leads to an increase in his payoff compared to the agents with convex cost functions (the negative scale effect). Second, the agent’s payoff increases if he is a Stackelberg leader; however, the advantage of his environment by the type of cost function reduces the effect of the second factor.

Efficiency and Revenue in Linear-Quadratic Double Auctions

We study uniform-price double auctions augmented with a class of subsidy schemes. Using these subsidies, any profile of linear demand schedules can be implemented as an equilibrium outcome. By revenue equivalence, all other mechanisms which implement linear auction equilibria are essentially equivalent to some subsidy scheme in our class. We show that, under a linear dependency condition on primitives, fully efficient, budget balanced, and individually rational trade is possible. Thus, the welfare loss from equilibria in uniform-price auctions without subsidies is a non-fundamental distortion, which can be fixed with better mechanism design. However, we show that monopolist trading platforms have incentives to reduce allocative efficiency to increase revenue, even as the number of traders becomes large.

Equilibrium existence in games with a concave Bayesian potential

We establish existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games that have a continuous and concave potential at all states of nature, without assuming absolute continuity of information. As an application, we show that Bayesian Nash equilibrium exists in many well-known games that have semi-quadratic payoffs (including Bertrand and Cournot oligopolies with linear demand), for general information structures.

On the welfare impact of mergers of complements: Raising rivals’ costs versus elimination of double marginalization

A common view in antitrust analysis is that mergers of complements can have raising rivals’ costs and elimination of double marginalization effects, with the net effect on consumer welfare thus unclear. We revise this view in the context of a merger between a monopolist in one market and a duopoly producer of a complement good. With linear demand and imperfect substitutability, while such a merger increases the price of the monopolized component, elimination of double marginalization dominates any raising rivals’ costs effects, increasing consumer welfare. We discuss a variety of extensions.

Entry mode selection and its impact on the competition between organic and conventional agricultural products

As the global organic food market continues to grow, so too will the challenges associated with managing organic food supply chains. We consider an entry mode selection problem facing an organic farmer. Specifically, an incumbent conventional farmer is selling its product through an independent retailer on the market. An organic farmer aiming to enter the market faces the problem of selecting between the conventional farmer’s retailer and an organic-only retailer. Consumers are heterogeneous in their purchasing valuation of the conventional agricultural product and its organic alternative. Horizontal competition between the two competing farmers is considered under different scenarios. Multiple-stage games are analyzed to study the impact of different cases on the pricing decision and profit of each player. The results show that when the organic agricultural product enters the market through the incumbent conventional retailer, two types of products are sold through a common retailer, the competition between the two farmers will be intensified, and the profit at the retail end will increase. It is always better for the organic farmer to sell an organic agricultural product through an independent organic-only retailer than to sell it through the incumbent conventional retailer. The paper makes two contributions. First, we derive the explicit equilibrium under chain-to-chain competition with piecewise linear demand functions. Second, we link the analytical marketing literature on channel structures with the supply chain literature on chain-to-chain competition and apply them to the food supply chain.

Stackelberg Independence*

The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. However, this Stackelberg independence property relies on all standard assumptions’ being satisfied. It fails to hold whenever the demand function is non‐linear, marginal cost is not constant, goods are differentiated, firms are non‐identical, or there are any externalities. I show that small deviations from the linear demand assumption may make the leaders’ choices completely uninformative.

When Crowd-Based Resources and Capabilities Generates Radical Innovation? It Depends on the Network Effects

Peer-to-peer or digital multi-sided platform (MSP) startups have created disruptions in various industries in the past few years. In this matter, the crowds within the platform ecosystem have significant contribution for digital MSP startups’ growth. However, there are limited studies that examine the crowd-based resource and capabilities as the source of radical innovation performance since it still conducts the perspective of linear product-market supply and demand. By using network theory, this research proposal wants to examine the role of network effects toward the development of the radical innovation. The findings of PLS-SEM analysis with 70 respondents from digital MSP startups show that crowds-based resources and capabilities manifested by integrative capabilities can generate radical innovation performance through decent network effect that enables to produce high incremental innovation performance beforehand. It shows the importance interaction between digital MSP startups with the crowds for innovation purposes. Hence, the findings contribute in open innovation literatures especially in finding the contributing factors to generate radical innovation

Reflexion Processes and Equilibrium in an Oligopoly Model with a Leader

An oligopoly model with a leader in the class of linear demand and cost functions of agents is considered, and the dynamic processes of reflexive behavior in this model are analytically studied. Dynamic decision-making processes with the inaccurate beliefs of agents about the choice of competitors are implemented not through the optimal responses to their expected actions, but as repeated static games on a range of admissible responses. Such an approach to decision-making is demonstrated to be justified. Observing the current state of the market and considering current economic restrictions (competitiveness and profit), agents refine their outputs in game-to-game dynamics and take steps towards the current position of their goal. A Stackelberg leader and other agents with the Cournot response choose step sizes independently of each other. Sufficient conditions on the step sizes under which the dynamics converge to an equilibrium are established.

A fuzzy inventory model for Weibull deteriorating items under completely backlogged shortages

<p style='text-indent:20px;'>In this paper, a fuzzy stock replenishment policy implemented for inventory items that follows linear demand and Weibull deterioration under completely backlogged shortages. Moreover, to minimize the aggregate expense per unit time, the fuzzy optimal solution is obtained using general mathematical techniques by considering hexagonal fuzzy numbers and graded mean preference integration strategy. Finally, the complete exposition of the model is provided by numerical examples and sensitivity behavior of the associated parameters.

Decentralized Supply Chains under Random Price-Dependent Demand: Noncooperative Equilibria vs. Coordination with Cost-Sharing Contracts

It is common for a supplier to sell products to multiple retailers. In this paper, we investigate the equilibrium behavior of a decentralized supply chain with multiple retailers facing a random price-dependent demand in the additive form. Here, we consider two kinds of demand functions: the distribution of the demand depends only on the retailer’s own retail price (noncompeting retailers) and not only on his own retail price but also on that of the other retailers (competing retailers). We present appropriate wholesale price, buy-back, and lost-sales cost-sharing contracts to coordinate the total supply chain, so that when all the retailers adopt their equilibrium response, the supply chain system coordination is also achieved. Furthermore, the coalition formation among retailers is also analyzed. We find that with buy-back and lost-sales cost-sharing contracts and linear price-dependent demand function, retailers always prefer being in the grand coalition to forming any other coalition.