Form Of Demand Function Research Articles

The existence, uniqueness and stability of steady state for a class of first-order difference equations with application to the housing market dynamic

We study the existence, uniqueness and stability of the steady state for the dynamic described by a class of first-order difference equations. We then apply the result to analyse a housing market where the supply is linear and demand is a bounded and monotone decreasing function of price, derived from households’ optimization behaivour. Under two linear price adjustment mechanisms, we prove the existence and uniqueness of an equilibrium, which is independent of the mechanisms. That is, the house price converges to a same steady state where it clears the market under both mechanisms. The result is general in the sense that we do not need to specify a particular form of demand function. Besides, the same approach can be utilized to analyse the dynamics of other markets.

Carbon tax pass‐through in Canadian retail gasoline markets

AbstractA carbon tax's pass‐through is one factor influencing its effectiveness in internalizing the externality created by greenhouse gas emissions. This paper measures the pass‐through of carbon taxes introduced in retail gasoline markets of four Canadian provinces that did not meet the carbon pollution pricing federal benchmark stringency requirements. Those four provinces are Saskatchewan, Manitoba, Ontario and New Brunswick. Using daily retail gasoline prices for 40 treated cities and nine control cities we find the pass‐through rates are city‐specific and vary from 0% to over 140%. City‐specific pass‐through rates imply that estimations at a higher level of geographical aggregation assume homogeneous effects where heterogeneous effects might be present. Our results also suggest it would be difficult for a government to impose an optimal and nationwide carbon tax on automotive greenhouse gas emissions. Although the degree of competition can explain city‐specific pass‐through rates, it cannot explain over‐shifting. Over‐shifting can be explained, however, by the demand functional form.

Endogenous thresholds in energy prices: Modeling and empirical estimation

Spot prices or front-month futures prices for energy commodities can exhibit occasional sharp peaks and drops (even to negative values), accompanied by large backwardations or contangos and unusually low or high levels of working stocks. We present a model of storage arbitrage that rationalizes such episodes, relevant for markets for energy commodities such as petroleum, natural gas, or storable electricity, where free disposal is not available. Based on price data only, we offer an empirical approach to estimate key parameters that determine the dynamics of prices, including endogenous price thresholds that indicate lower and upper bounds on discretionary stocks. Price movements in the regime within these bounds are moderated by responses of speculative storage. In the two regimes where price is respectively above or below threshold prices, sharp price jumps are more likely. We are the first to prove consistency and asymptotic normality of a method of estimating this model on prices with endogenous jumps. We explore the behavior of our estimator for small samples, and illustrate its application using petroleum prices. Although the model structure and the distributions of the disturbances in the Euler equation are quite complex, a nice feature of our estimator is its simplicity; it is straightforward non-linear least squares. Moreover, our estimation approach is robust to the demand functional form and the distribution of the shocks.

Finite-horizon joint inventory-pricing optimization with non-concave demand and lost sales

In this paper, we study a periodic-review joint inventory and pricing optimization problem in a stochastic price-sensitive demand framework with lost sales. We contribute to the existing literature from three aspects: generalizing the form of demand functions, developing the technique of proving concavity preservation, and extending the scope of optimality conditions. Specifically, we set the demand in our model as a general function. In order to obtain the optimality condition under general demands, we first introduce the concept of Price Elasticity of the Slope (PES) and transform the original PES condition between sales and profit in literature into a PES condition between sales and demand. Then, we obtain the lower bound of the PES difference between sales and profit by utilizing our transformed condition. With the non-negativity of the lower bound, we obtain two groups of easy-to-verify conditions which consist of the mean demand and the probability distribution of the demand. Under specific demand forms, the obtained conditions are reduced to constraints on the distribution of price-free uncertainty and the deterministic functions of price, respectively. Compared with the existing literature, our study therefore extends the scope of optimality conditions and includes non-concave demand functions when adapting a base-stock list-price (BSLP) policy in a joint inventory-pricing problem. Our conditions ensure that more types of products (e.g., the products of which the price elasticity of demand is constant) meet the optimality of the BSLP strategy, and more retailers can make pricing and replenishment decisions based on this strategy.

Financing Product Development Projects in the Blockchain Era: Initial Coin Offerings Versus Traditional Bank Loans

Nowadays, supported by the blockchain technology, initial coin offering (ICO) has emerged as a way to finance projects via crowdfunding. In this article, by building stylized theoretical models, we examine the product development project financing problem under the traditional bank case (Model TBK) and ICO case (Model ICO). Under a commonly used demand function in which product quality scales the price-dependent market demand, we theoretically derive and compare the optimal pricing and quality decisions for the project under both models. We identify the feasible conditions, which govern the feasibility of each financing model. We then develop the optimal rule, in the form of an algorithm, to determine the optimal financing choice. To show the robustness of the results and test the impacts of having a different form of demand function, we examine in the extended models the case when demand function is linear-additive to both price and quality. We find that the major results derived from the main models scenario remain valid in the extended models scenario. Some interesting subtle differences between the two models are also revealed. We conclude by highlighting that the two financing modes (TBK and ICO) are very different and have a substantial impact on the optimal pricing and quality decisions as well as the start-up company's profitability.

Optimal decision in a green supply chain: Bank financing or supplier financing

The optimal procurement decision of a two-echelon green supply chain with options under capital constraints and financing credit support is studied. At the beginning of the order lead time, the retailer with capital constraints purchases fixed order quantity and options, and exercises all or part of the options during the sales period. We consider two types of credit financing methods: supplier financing and bank financing. At the same time, the non-financing situation is used as a benchmark model, where we find that there is a threshold for the retailer’s working capital. That is, the retailer only purchases a fixed order when the working capital is less than the threshold. When working capital gradually increases, the retailer will reduce fixed order quantity and increase option order quantity, which shows that options are a risk hedging tool for the retailer. In addition, we find that the benefits of supply chain members are higher than those of the benchmark model regardless of supplier financing or bank financing, and cleaner production will bring more benefits to supply chain members. We find that the retailer is a free rider in the green supply chain. Given the corresponding parameters and the form of demand function, we can decide whether to choose supplier financing or bank financing. Finally, numerical examples are given.

An implementable optimization of airfare structure

Pricing and especially fare structures have received little attention within the revenue management literature. For an airline, well-designed fare structures segment customers properly, selling to correct customers at intended prices. For a given origin and destination, the pricing manager seeks to maximize revenue by jointly optimizing all price levels in the airline’s menu of fares. Deterministic demand is modeled using booking periods as primary customer segments; inventory management is integrated as a secondary segmentation tool. Analytical solutions are attained under various demand functional forms, and comparative statics are juxtaposed to reveal characteristics of each demand type.

Optimal production, pricing, and substitution policies in continuous review production-inventory systems

We consider the optimal production, pricing, and substitution policies of a continuous-review production-inventory system with two products: a high-end product and a low-end product. Each product has its associated customer stream; however, the demands for the low-end product may be satisfied by the high-end product. We formulate the problem as a Markov decision process and characterize the structure of the optimal control policy, which specifies when to produce for each product, when to use the high-end product as a substitute, and how to set the optimal prices. We show that a base-stock production policy is optimal; however, the optimal base-stock level for each product depends on the inventory level of the other product and it features a monotonic property. We also demonstrate that the optimal substitution policy is a rationing policy with the rationing level depending on the total inventory amount. We find that the optimal prices can be either decreasing or increasing in the inventory levels, depending on the forms of demand functions. Furthermore, we utilize numerical experiments to investigate the impact of different system characteristics on the benefits of using substitution and dynamic pricing. Finally, we investigate when the dynamic pricing strategy and the substitution strategy are complements or substitutes.

Sequential experimental approach for congestion pricing with multiple vehicle types and multiple time periods

This paper develops a sequential experimental approach for the optimal congestion pricing problem on a general transportation network with multiple vehicle types and multiple time periods. The approach explicitly considers the interaction among different types of vehicular flow and the interdependence of demand among various origin–destination (O–D) pairs and in different time periods. Toll charge on each link in each period is differentiated across vehicle types on the basis of their observable differences to reflect their different congestion externalities. The evolutionary pricing scheme updates link tolls from only observed link flows without requiring explicit forms of demand functions. Given a trial of toll pattern, the revealed link flows can be observed easily; then a new set of tolls can be determined based on the observed flow volume and sequentially used for next trial. The detailed implementation procedure is examined with both theoretical analyses and numerical experiments.

DIFFERENTIAL OUTPUT ELASTICITY OF EMPLOYMENT DURING POST-ECONOMIC REFORM PERIOD IN THE INDIAN ECONOMY

This paper investigates the sign and size of the differential output elasticity of employment for different industries in the private and public organized sectors of the Indian economy during post-economic reform period. A logarithmic form of demand function for employment, derived from the constant elasticity of substitution production function is estimated. An interaction variable is introduced after having ensured that the employment function has a structural shift by Chow break test. The results based on the time series data from the period 1969–1970 to 2004–2005, show that the positive magnitude of elasticity of employment with respect to output in transport, storage and communications industry is relatively very high, as the differential output elasticity of employment is not only positive but also more than unity followed by wholesale and retail trade and financing, insurance and real estate industries in the private organized sector during the post-economic reform period. This reflects the fact that the labor absorption capacity in the industries of transport, storage and communications, wholesale and retail, financing, insurance and real estate is relatively high. The magnitude of output elasticity of employment in financing, insurance and real estate is relatively high during the post-economic reform period as the differential output elasticity of employment is relatively small as compared to output elasticity of employment during the pre-economic reform period. The labor absorption capacity in private sector during the post-reform period is found to be relatively high as compared to public sector as the differential employment elasticity during the post-reform period in private sector is low. Further the results for the organized sector as a whole illustrate that the output elasticity of employment during the post-reform period is negative on account of negative differential output elasticity of employment showing that the economic growth during the post-reform period is not labor intensive in the Indian economy. Therefore, there is a need to review the sectoral policies to generate additional employment opportunities in the organised sector of the Indian economy.

DEMOGRAPHIC DEMAND SYSTEMS WITH APPLICATION TO EQUIVALENCE SCALES ESTIMATION AND INEQUALITY ANALYSIS: THE AUSTRALIAN EVIDENCE

This paper proposes and applies an alternative demographic procedure for extending a demand system to allow for the effect of household size and composition changes, along with price changes, on expenditure allocation. The demographic procedure is applied to two recent demand functional forms to obtain their estimable demographic extensions. The estimation on pooled time series of Australian Household Expenditure Surveys yields sensible and robust estimates of the equivalence scale, and of its variation with relative prices. Further evidence on the usefulness of this procedure is provided by using it to evaluate the nature and magnitude of the inequality bias of relative price changes in Australia over a period from the late 1980s to the early part of the new millennium.

An integrated production-inventory-marketing model under inflationary conditions for deteriorating items

The integration of production and marketing policies is one of the key factors of successful business operation. Moreover, inventory policies for deteriorating items are very sensitive to different marketing strategies and rising inflation rate directly affects the financial situation of industries. Realising the importance of such scenario, an integrated production-inventory-marketing model has been developed under inflationary conditions for deteriorating items; where demand is considered as a function of insertions in a media, as it is well-established fact that 'marginal effect of advertisement on sales is proportional to the unrealised potential of the market'. The model jointly optimises the production lot size and the number of insertions by maximising the net profit. A simple to use solution procedure has been developed to determine these parameters. Further, the model has been extended for multiple media case and a general form of demand function has been developed. The model is then formulated as a mathematical programming problem. The results have been validated with numerical examples followed by sensitivity analysis.

Beyond Illinois Brick: The Law and Economics of Cost Pass-Through in the ADM Price Fixing Case

This article reviews the legal standards and theeconomics of pass-through to indirect purchasers andillustrates these principles with a case involving ADMin the market for high fructose corn syrup (HFCS).With three assumptions about production technologies,buyers of HFCS experience a 100 percent pass throughof the direct overcharge. The extent of pass throughof the increase by buyers is shown to dependcritically upon the market structure of the purchasingindustry and the shape of the retail demand curve. Flexible demand functional forms are needed to avoidconstraining estimated pass through rates.

Vertical Strategic Interaction: Implications for Channel Pricing Strategy

This paper examines two strategic pricing decisions within channels: using foresight (i.e., price leadership) and considering category implications (i.e., product line pricing). Are price leadership and product line pricing always the best pricing strategies for a channel member? If not, when does this occur and why? By investigating these questions, we address some major concerns of both marketing practitioners and scholars interested in channel management issues. In addition, this study provides an indepth discussion on why previous analytic studies produced answers to these questions that depend upon the choice of the form of demand functions. As such, this study should significantly resolve the debate among analytic marketing modelers about the “right” demand specification. At the core of our discussion lies the concept of vertical strategic interaction, which is defined in terms of the direction of a channel member's reaction to the actions of its channel partner within a given demand structure. Specifically, if a channel member's best reaction is to reduce its margin when its channel partner increases its margin, the type of vertical strategic interaction is referred to as vertical strategic substitutability (VSS). If the best reaction is to increase the margin, the environment is referred to as vertical strategic complementarity (VSC). If the best reaction is no margin change, it is referred to as vertical strategic independence (VSI). Using a game theoretic approach, we demonstrate that these three types of vertical strategic interactions represent a key driving force for optimal decisions on channel price leadership and product line pricing. Our investigation involves mathematical analyses of an industry model composed of two manufacturers selling competing products, both carried by two competing retailers. As such, the model allows for retailer product line pricing as well as manufacturer and retailer level competition. In addition, this general model can be used to analyze three more restrictive industry settings often found in the channels literature, i.e., a bilateral monopoly (Jeuland and Shugan [Jeuland, Abel, Steven M. Shugan. 1983. Managing channel profits. Marketing Sci. 2(Summer) 239–72.]), two competing manufacturers selling through competing franchised retailers (McGuire and Staelin [McGuire, Timothy W., Richard Staelin. 1983. An industry equilibrium analysis of downstream vertical integration. Marketing Sci. 2(Spring) 161–92.]), and two competing manufacturers selling through one common retailer using product line pricing (Choi [Choi, S. Chan. 1991. Price competition in a channel structure with a common retailer. Marketing Sci. 10(Fall) 271–96.]). Unlike many other channel studies, most of our analyses are performed without assuming particular functional forms of demand curves. Thus, this paper provides greater assurance that the insights from this stream of research are broadly applicable, not only across industry structures but also across demand conditions. The paper starts out by defining three different rules for how prices are set: The manufacturer uses foresight, the retailer uses foresight, and neither channel member uses foresight. We then show a one-to-one mapping between the type of vertical strategic interaction and the optimality of channel price leadership. Specifically, a channel member finds it profitable to be a price leader for VSS but prefers to be a follower for VSC. For VSI, channel members are indifferent to the channel price leadership issue, as it has no effect on channel member profits. We also show that there exist conditions under which a retailer might see a reduction in profits when it changes its policy from non-product line pricing to product line pricing. Such conditions arise when the retailer is not a price leader and the environment is characterized by VSS or VSC. At a more general level, this study suggests not only the value but also the cost to a firm for using superior knowledge (i.e., foresight and/or product line pricing) in making strategic marketing decisions. In this way, “ignorance can be bliss.” We also explore the link between demand characteristics and the three types of vertical strategic interaction. We show that the type of vertical strategic interaction present in a given environment is closely related with the convexity of the demand curve and the level of demand for a given price. Interestingly, we find that linearity of demand is not a necessary condition for any of the three types of vertical strategic demand function. Consequently, in evaluating the robustness of analytic analyses, it may be more important to determine the type of vertical strategic interaction assumed instead of whether the demand is linear or nonlinear. Finally, our results are limited to situations where the channels are not coordinated and the retailer's precommitment to particular pricing policy and decision is credible. Although such situations still capture a significant portion of reality, we acknowledge that the insights from this study might not be applicable in all situations.

Demographic variables in demand systems: The case for generality

This paper provides evidence in favour of greater generality in the demographic demand literature. We propose two demographic demand procedures. One extends the Gorman model by allowing non additive interaction between ‘overheads’ and ‘Barten scaling’. The other extends ‘Price Scaling’, by allowing the equivalence scale to vary with utility, and offers a test of ‘Equivalence Scale Exactness’ (ESE). The rejection of ESE is robust to the assumed demand functional forms (RNLPS, QAIDS), to items chosen, and the estimation method (MLE, GMM). The results show that published cell averages yield well determined estimates of the demographic generalisation parameters.

A simple model of international joint venture distributorships: the American-Kuwaiti experience

The paper develops an analytical model for analyzing international joint venture distributorships in marketing channels selling highly differentiated industrial products. Regarding four alternative forms of demand functions, profits of channel members and consumer welfare under the joint venture arrangement are compared with those under the classic vertical integrated and decentralized structures. Furthermore, optimal allocation of joint venture benefits is discussed and the influence of attitude towards risk and bargaining power have been examined. A case study from international marketing is presented in relation to the theoretical work developed herein. It describes the events that have lead to the formation of a joint venture between an American manufacturer and a Kuwaiti distributor as well as the factors that have contributed to its termination. Implications of the research and its findings to management are also discussed.

Expenditure Patterns and Aggregate Consumer Behaviour: Some Experiments with Australian and New Zealand Data*

This paper analyzes expenditure patterns in Australia and New Zealand by estimating ‘complete’ demand systems on budget data. Tests of linear Engel curves and separable preferences are carried out on both data sets. The study also exploits the information on household composition to test for demographic effects. Several new demographic ally extended demand functional forms are proposed and estimated, and their behavioural and welfare implications in terms of equivalence scales compared. The study yields plausible estimates of price and expenditure elasticities, and shows that relevant price information can be used successfully to estimate the ‘cost’ of a child.

A Computational Procedure for Calculating Optimal Commodity Taxes with Illustrative Evidence from Indian Budget Data

A simple procedure for calculating optimal commodity taxes is proposed, which takes into account the simultaneous interdependence of taxes, expenditure, and price levels/responses. The method also allows for the social marginal utility of income to depend on prices, besides expenditures, in a manner implied by the assumed preference functional form. Illustrative calculations on Indian budget data provide evidence not only in favor of the procedure, but of considerable sensitivity of directions of marginal tax reforms to the data set (rural or urban) used, and of optimal tax estimates to demand functional form. Copyright 1989 by The editors of the Scandinavian Journal of Economics.

Elementos de teoria de demanda de mercado

This paper explores implications on the market demand stemming from the inequality of income distribution, based on the more usual assumptions made by microeconomics with respect to consumers, as independent deciders who present well-behaved utillty functions. The analysis presents no assumption about income distribution, its continuity, or its shape; nor is it restrieted to specific forms of demand functions, but rather deals with aggregation on consumers in more general conditions. The market demand founded on the equilibrium of a set of consumer units with differing incomes focuses on the need of defining an inequality effect (difference between the average demand for a good and the respeetive demand of the typical consumer unit, the one who receives the average income) and the existence of limit functions of income-consumption to be used when there is inadequate information to determine the collective incomeconsumption function. The study presents an expansion of the Slutsky equation to include the price effect on the market demand for a good. The expanded Slutsky equation represents the adjusting movement of the typical consumer unit in terms of the demand for a good in the face of the change in one of the prices, to which are added the effects of this change on the inequallty effect. These added effects are a pure substitution effeet, all consumer units (including the typical) being held at their respective satisfaction levels, and an income effect on the inequality effect. The study shows that aggregated demand functions ean be treated, with respect to the price effect, in a way similar to the analytical treatment usually applied to individual demand functions.

OPTIMALLY UNIFORM COMMODITY TAXES IN A NON LINEAR DEMOGRAPHIC DEMAND MODEL

ABSTRACTThis paper derives a sufficient condition for optimally uniform commodity taxes within the demographically generalized RNLF'S demand functional form framework. This paper, besides admitting child subsidies, allows for non linear equivalence scales and demographically varying utility and demand functions. The derived condition is shown to yield some recent uniformity results as special cases.