Price Vector Research Articles

Earning and Utility Limits in Fisher Markets

Earning limits and utility limits are novel aspects in the classic Fisher market model. Sellers with earning limits have bounds on their income and lower the supply they bring to the market if income exceeds the limit. Buyers with utility limits have an upper bound on the amount of utility that they want to derive and lower the budget they bring to the market if utility exceeds the limit. Markets with these properties can have multiple equilibria with different characteristics. We analyze earning limits and utility limits in markets with linear and spending-constraint utilities. For markets with earning limits and spending-constraint utilities, we show that equilibrium price vectors form a lattice and the spending of buyers is unique in non-degenerate markets. We provide a scaling-based algorithm to compute an equilibrium in time O ( n 3 ℓ log (ℓ + nU )), where n is the number of agents, ℓ ≥ n a bound on the segments in the utility functions, and U the largest integer in the market representation. We show how to refine any equilibrium in polynomial time to one with minimal prices or one with maximal prices (if it exists). Moreover, our algorithm can be used to obtain in polynomial time a 2-approximation for maximizing Nash social welfare in multi-unit markets with indivisible items that come in multiple copies. For markets with utility limits and linear utilities, we show similar results—lattice structure of price vectors, uniqueness of allocation in non-degenerate markets, and polynomial-time refinement procedures to obtain equilibria with minimal and maximal prices. We complement these positive results with hardness results for related computational questions. We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good.

THE ISSUE OF VALUE IN ECONOMICS: PRACTICAL CONSEQUENCES

Value is a standard of the cost, a certain common quality, which makes it possible to compare costs of quite different things. This construct probably cannot be operationalized generically, but in the development of theory operationalization is not imperative. Although neoclassical economics rejects this category ultimately, it is possible to demonstrate that this approach can be well adjusted to it. The issue of value is not merely a theoretical one. The purpose of the work is to show that if a feedback through the market must have an objective basis as an initial standard, that is money must have a benchmark, then the correct choice of a monetary benchmark can result in significant positive macro-economic consequences. Methods of research: scientific and philosophical analysis of texts and theoretical development. Conclusions: The idea that the feedback through the market must have an objective basis as an initial standard - that is money must have a benchmark – is not contradictory theoretically and its realization is desirable in practice. An energy monetary benchmark is probably preferable for a modern economy. The energy monetary benchmark can stabilize currency circulation potentially, optimize the price vector and simplify the valuation of mineral resources.

Wybrane problemy niejednoznaczności ceny dualnej wody w postoptymalizacyjnej analizie systemu wodociągów

In literature it is believed that the dual price of water is an objective premise for shaping the market price of water. However, the authors note that a single vector of dual prices in the distribution of water, when ambiguous, should not become the basis for making decisions both regulating the price of water and affecting the procedures for modernizing the water supply network. This work cautions water management engineers not to duplicate common software errors and indicates how, despite the complete lack of literature tips, the technical problems encountered could be practically solved. The linear dependence of the row vectors of the left-hand parameters of binding constraints in the linear programming model for water consumption is identified here as the reason for the ambiguity of dual price vectors. This ambiguity in the issues of water distribution requires shaping alternative technical scenarios allowing for a variant selection of the method for modifying the water abstraction system. Therefore, the principles for determining the proportionality of simultaneous changes in certain parameters of the right-hand conditions of constraint conditions are described. These principles for the optimal selection of the most productive vectors for the parametric linear programming method were formulated and indicated on a simplified model of water distribution. The methodology developed in the work enables, among others, generating alternative technical scenarios for saving varying amounts of water, resulting in various financial savings

Price vector issue in a choice experiment: A methodological proposal

Price vector issue in a choice experiment: A methodological proposal

Stability in a general oligopoly model

AbstractWe analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.

Discrete choice experiments with multiple price vectors for products sold in a wide price range

The discrete choice experiment is a widely used methodology in consumer studies. However, applying this method to investigate the market of products sold in a wide price range could present issues as to the quality of the estimate of preferences. In fact, for this type of product, frequently consumers may have different behaviours when faced with different price levels. For example, some market segments may refrain from purchasing products below certain price thresholds, considering them of an unacceptable quality, while others choose only below certain prices. To work around this problem area, we propose a methodology in which each respondent declares his own price interval of reference and consequently participates in a choice experiment with a price vector coherent with his habits. In this manner, we are able to grasp and include in the estimations the heterogeneity of consumers with respect to price and thus obtain more accurate willingness to pay estimates.•The method describes a procedure to bypass issues related to identifying the price vector in discrete choice experiments that involve products sold in a wide price range.•We propose a discrete choice experiment with different price vectors for consumer segments with different price preferences.

Price and Assortment Optimization under Choice Models with Anticipated Wait

Customers often face multiple choices when purchasing a product or service. After making a choice, they sometimes have to wait for a while before receiving their purchased item due to the firm’s limited capacity to process orders. This paper incorporates the anticipated wait for receiving purchased products or services into customers’ choice behavior. The resulting choice model shares the same spirit of the rational expectation equilibrium, and captures the effects of negative externality caused by the anticipated wait, because all orders may be processed by a common facility. Our analysis shows that the anticipated wait may change the substitution patterns dramatically. We further investigate the effects of the anticipated wait on the decisions of capacity investment, product pricing and assortment planning. We establish the one-to-one mapping between the price vector and the choice probability vector, and show that the equivalent profit function of the choice probabilities is explicitly defined and more tractable. We characterize the multi-product price optimization problem under the MNL model with waiting. In addition to price competition, we also study the Cournot competition, in which the decision is the choice probability for each firm, and show that there exists a Nash equilibrium. For the assortment optimization, we identify the conditions under which the optimality of the revenue-ordered assortment still holds. Because the assortment problem with waiting is generally NP-hard, we develop efficient approximations with performance guarantee and also provide an easy-to-compute tight upper bound. The new model has the potential to increase prediction accuracy for customers’ choice behavior especially when customers faced with multiple choices are aware of the possible waiting for their purchased products. Failure to take into account the effects of the anticipated wait in customers’ purchase behavior may result in substantial losses to firms.

Skew to win, not to profit – unbalanced bidding among informed bidders

PurposeSeveral sectors, especially the construction industry, use unit price contracting (UPC). This contracting form provides agents, ex ante, with estimated quantities of the work to be done. Competing agents then offer corresponding unit prices i.e. the bid is a price vectors, and most often the lowest vector sum is awarded the contract. This way of procuring is not only transparent but also entails a potential problem of unbalanced bidding. Unbalanced bidding occurs when an informed agent skews unit prices to win the ex ante bid. The concept is not new topic in research, but theoretical models from an economics perspective are not extensive.Design/methodology/approachThis paper will focus on how competition among informed bidders will affect the optimal solution.FindingsIt is shown that skewing is still a dominating strategy under competition. However, competition will decrease, but not necessarily eliminate, information rents.Originality/valueIn this setting, unbalanced bidding could mainly be seen as a way to win the contract and not to extract information rents. Thus, it would not constitute an efficiency problem for the client.

Dynamic Pricing and Learning: An Application of Gaussian Process Regression

We consider the problem of offering an optimal price when demand is unknown and must be learned by price experimentation - a variant of the multi-armed bandit problem. In each period, the retailer must decide on a price while using knowledge already acquired to weigh the benefits of exploring other prices versus maximizing revenue. Other algorithms proposed for such problems either learn the price-demand relation for each price separately or determine the parameters of an assumed parametric demand function. We instead combine Gaussian process regression with Thompson sampling as a nonparametric learning algorithm that can learn any functional relation between price and demand. This GP-TS algorithm scales significantly better with the number of price vectors than do existing approaches, yet it makes no restrictive assumptions on the price-demand relationship's functional form. We show how to apply the algorithm to finite inventory settings that consider both single and multiple products and also to settings in which exogenous contextual information can affect prices. One advantage of the algorithm is that its performance depends not on the number of price vectors over all products but only on the number of products considered. For each setting considered here, we benchmark our approach to existing algorithms. The GP-TS algorithm's learning performance is far superior to that of its peers, especially when there are increases in the number of products to learn concurrently. Finally, we propose extensions that enable the application of our algorithm when demand follows a Bernoulli or Poisson distribution.

Integrating Dynamic Pricing and Inventory Control for Fresh Agriproduct under Multinomial Logit Choice

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh agriproducts (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period the retailer makes ordering decision for new FAP and sets regular and discount price for new and old inventories, respectively. After demand realization, the expired leftover is disposed and unexpired inventory is carried to the next period, continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximize the total expected discount profit over the whole planning horizon. We present a price-dependent, stochastic dynamic programming model taking into account zero lead time, linear ordering costs, inventory holding, and backlogging costs, as well as disposal cost. Considering the influence of the perishability, we integrate a Multinomial Logit (MNL) choice model to describe the consumer behavior on purchasing fresh or nonfresh product. By way of the inverse of the price vector, the original formulation can be transferred to be jointly concave and tractable. Finally we characterize the optimal policy and develop effective methods to solve the problem and conduct a simple numerical illustration.

A Matter of Equality: Linear Pricing in Combinatorial Exchanges

Combinatorial exchanges that allow for package offers to address nonconvexities in demand or supply typically employ linear and anonymous prices because they are simple, tractable, and fair. Despite their prevalence, linear anonymous prices do not necessarily correspond to Walrasian competitive equilibrium prices in such settings, and their impact is not well understood. This paper is the first to analyze the effect of different pricing rules on the efficiency of combinatorial exchanges, using both analytic methods and numerical experiments. Our analysis is motivated by a combinatorial fishery-rights exchange designed to reform the fishing industry in New South Wales (NSW), Australia. We find that when linearity and anonymity are required for only one side of the market, the average efficiency loss is negligible. In contrast, with a single linear price vector for both sides, the efficiency loss is substantial, especially when the market is small. In a formal model, we show that efficiency losses decrease when the number of buyers grows or the size of the submitted packages decreases. Besides the reform of the NSW fishing industry, our results have important implications for other cap-and-trade programs as well as other industries where demand or cost complementarities play a role.

Economic comparison of different electric fuels for energy scenarios in 2035

Electric fuels (e-fuels) enable CO2-neutral mobility and are therefore an alternative to battery-powered electric vehicles. This paper compares the cost-effectiveness of Fischer-Tropsch diesel, methanol and Liquid Organic Hydrogen Carriers. The production costs of those fuels are to a large part driven by the energy-intensive electrolytic hydrogen production. In this paper, we apply a multi-level electricity market model to calculate future hourly electricity prices for various electricity market designs in Germany for the year 2035. We then assess the economic efficiency of the different fuels under various future market conditions. In particular, we use the electricity price vectors derived from an electricity market model calibrated for 2035 as an input for a mathematical model of the entire process chain from hydrogen production and chemical bonding to the energetic utilization of the fuels in a vehicle. Within this model, we perform a sensitivity analysis, which quantifies the impact of various parameters on the fuel production cost. Most importantly, we consider prices resulting from own model calculations for different energy market designs, the investment cost for the electrolysis systems and the carbon dioxide purchase price. The results suggest that the use of hydrogen, which is temporarily bound to Liquid Organic Hydrogen Carriers, is a favorable alternative to the more widely discussed synthetic diesel and methanol.

Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae

We consider the problem of modelling and forecasting the distribution of a vector of prices from interconnected electricity markets using a flexible class of drawable vine copula models, where we allow the dependence parameters of the constituting bivariate copulae to be time-varying. We undertake in-sample and out-of-sample tests using daily electricity prices, and evidence that our model provides accurate forecasts of the underlying distribution and outperforms a set of competing models in their abilities to forecast one-day-ahead conditional quantiles of a portfolio of electricity prices. Our study is conducted in the Australian National Electricity Market (NEM), which is the most efficient power auction in the world. Electricity prices exhibit highly stylised features such as extreme price spikes, price dependency between regional markets, correlation asymmetry and non-linear dependency. The developed approach can be used as a risk management tool in the electricity retail industry, which plays an integral role in the apparatus of modern energy markets. Electricity retailers are responsible for the efficient distribution of electricity, while being exposed to market risk with extreme magnitudes.

Decentralized Control via Dynamic Stochastic Prices: The Independent System Operator Problem

A smart grid connects wind or solar or storage farms, fossil fuel plants, industrialor commercial loads, or load serving entities, modeled as stochastic dynamical systems. In each time period, they consume or supply electrical energy, with the constraint that total generation equals consumption. Each agent's utility is either the benefit accrued from consumption, or negative of generation cost. The Independent System Operator has to maximize their sum, the social welfare, without agents revealing their dynamic models or utilities. It has to announce prices after interacting with agents via bids. If agents observe and know the laws of uncertainties affecting other agents, then there is an iterative price and bid interaction that leads to the maximum social welfare attainable if agents pooled their information. In the important case where agents are LQG systems not even knowing of the existence of other agents, the bid and price iteration is dramatically simple, exchanging time vectors of future prices and consumptions or generations at each time step. State dependent bidding is not needed. This solution of the decentralized stochastic control problem may be of economic importance in power systems, and of broader interest in general equilibrium theory of economics for stochastic dynamic agents.

Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence

We present a general equilibrium model with incomplete financial markets and numeraire assets. We assume that there are 2 periods of time, say today and tomorrow. In period 0, households exchange goods and assets and then consumption takes place; in period 1, one of S possible states of nature occurs. In each of them, assets pay their returns, which are measured in units of a given physical good, i.e., the numeraire commodity; households exchange goods; finally, consumption takes place. We define a consumption, portfolio holding, commodity and asset price vector as an equilibrium vector associated with a given economy, if at those prices and economies households maximize, and market clears. While the existence proof by Geneakoplos and Polemarchakis (Essays in honor of K.J. Arrow, vol 3, Cambridge University Press, Cambridge, pp 65–95, 1986) uses a fixed point argument, we provide an independent existence result in terms of variational inequalities. That approach allows us to get the desired existence result under some different and more general or realistic assumptions than those usually made in the literature.

Freeing long‐period prices from the uniform profit rate hypothesis: A general model of long‐period positions

AbstractModern long‐period literature defines long‐period prices as prices yielding a uniform profit rate. This definition relies on the assumption of free competition, which is not essential in defining long‐period prices, the reproducibility of the economic system being the essential condition. A definition of long‐period prices based only on reproducibility is then proposed and a model developed. The existence of long‐period price vectors is obtained in a variety of situations yielding differential or uniform profits rates. Our analysis shows that the long‐period approach is “robust” with respect to the elimination of the significant but problematic assumption of uniform profit rates. Our model provides also a formalization of Smith’s view of domestic and international division of labour.

Price Determinism in Specialized Producing Economy

In an economy with n kinds of products, producers are specialized to produce one kind of product and exchange for the others. Exchange matrix A consists of supplies and demands. Price vector p is the solution of Ap = 0.When R(A) = n – 1, the price is determined given total money amount. When R(A) = n – m, the economy can be divided into m sub-economies with no exchange of products between any two of them. In each sub-economy the price is determined.

A nonlinear state marginal price vector model for the task of business valuation. A case study: The dimensioning of IT-service companies under nonlinear synergy effects

In the present contribution we present a nonlinear extension of the innovative linear investment-oriented company valuation method and so-called state marginal price vector model of Toll which represents a two-step procedure separated into a base and a valuation approach. As novel aspect we address nonlinear synergy effects in M&A’s. For this purpose we introduce a nonlinear framework within a semi-discrete convex optimization approach. As capital market assumption we simulate an imperfect market. To demonstrate the usefulness of the method, we address a case study of a merger of two IT-service companies. The related valuation and dimensioning of capacities is done by solving a multi-period newsvendor model under stochastic demand. The demonstrated nonlinear framework is shown to be suitable for a wide range of business valuation tasks.

Inventory rebalancing through pricing in public bike sharing systems

This paper presents a new conceptual approach to improve the operational performance of public bike sharing systems using pricing schemes. Its methodological developments are accompanied by experimental analyses with bike demand data from Capital Bikeshare program of Washington, DC (USA). An optimized price vector determines the incentive levels that can persuade system customers to take bikes from, or park them at, neighboring stations so as to strategically minimize the number of imbalanced stations. This strategy intentionally makes some imbalanced stations even more imbalanced, creating hub stations. This reduces the need for trucks and dedicated staff to carry out inventory repositioning. For smaller networks, a bi-level optimization model with a single level reformulation is introduced to minimize the number of imbalanced stations optimally. The results are compared with a heuristic approach that adjusts route prices by segregating the stations into different categories based on their current inventory profile, projected future demand, and maximum and minimum inventory values calculated to fulfill certain desired service level requirements. We use a routing model for repositioning trucks to show that the proposed optimization model and the latter heuristic approach, called the iterative price adjustment scheme (IPAS), reduce the overall operating cost while partially or fully obviating the need for a manual repositioning operation.

Computing pure Nash equilibria in network revenue management games

We present a mixed-integer model to optimize a competitor’s behavior in a network revenue management game. Our model is based on a well-known deterministic linear program for the single-airline network revenue management problem. Assuming that the competitors make decisions based on our model, we present an algorithm to compute a pure Nash equilibrium (NE) in a two-player game through an iterative search for best responses. If the algorithm gets stuck in a loop without finding an NE, additional constraints are added to the models to control the search. The complete algorithm finds an NE with certainty if one exists in the game. The players’ price vectors are modified so that their models have unique solutions, and the search follows a unique path. This makes sure that both players end up in the same NE even if uniqueness is not guaranteed or cannot be proved. A computational study shows the algorithm’s performance which can compute NE in networks of realistic size in acceptable time.