Price Dispersion and Consumer Reservation Prices

We describe firm pricing when consumers follow simple reservation price rules. In stark contrast to other models in the literature, this approach yields price dispersion in pure strategies even when firms have the same marginal costs. At the equilibrium, lower price firms earn higher profits. The range of price dispersion increases with the number of firms: the highest price is the monopoly price, while the lowest price tends to marginal cost. The average transaction price remains substantially above marginal cost even with many firms. The equilibrium pricing pattern is the same when prices are chosen sequentially.     

Optimizing the credit term decisions in supply chain finance

We study a credit term determination problem in the context of a supplier-buyer supply chain. The supplier's credit term decision is simultaneously made with its production and inventory decisions, and most importantly, it is impacted by the buyer's order quantity. We present a new game-theoretic framework to model this problem, which captures the interaction between the supplier's credit term decision and the buyer's order decision in a multi-period setting. An exact method based on nonlinear programming is implemented to obtain the optimal solutions. We apply our methodologies on a real world case. The computational results show that our approach significantly outperforms the heuristics with fixed credit terms, and either a short or a long credit term can be sub-optimal for the supplier in profitability. Our work offers the first data-driven model and solution approach that assists purchasing and supply managers to make optimal dynamic credit term decision in conjunction with production, ordering and inventory decisions in a game-theoretic setting.     

Apple's disaster: Linking two‐sided markets and strategic delegation

Asymmetric pricing structure and different intergroup network externalities are characteristics of two‐sided markets not captured in the analysis of one‐sided markets. Focusing on Cournot duopoly where membership decision may be delegated to a manager, several equilibrium regimes are sustained depending on the fixed cost of managerial hiring and strength of the network externality exerted by the side whose demand is more price sensitive. The change from null to full delegation sharpens the asymmetric pricing structure and reduces the price level in two‐sided markets. Contrary to one‐sided markets with direct network effects, the prisoner's dilemma holds for sufficiently strong indirect network externalities. Imperfect interside discrimination of managerial incentives ensures profit maximization and efficient consumers' allocation. Private hiring should occur when the two‐sided market exhibits symmetric pricing structure. An explanation for Apple's unprecedented event is provided. The reduction of revenue and managerial bonus in 2016 may be justified by the dissemination of full delegation in the Chinese information technology industry. Apple's upcoming strategy may consist on reducing both access prices, although the side whose demand is more price sensitive should have a greater price reduction. Alternatively, improving the content quality may constitute Apple's corporate strategy, thereby inducing a skimming pricing strategy on Chinese rivals.     

Trade spends and profitability of promotions

This paper examines the prevalent mechanism of financing advertising and temporary price reductions through trade spend budgets. A manufacturer and a retailer interact for a number of periods with a plan to hold a sale in the last period. During the nonpromotional periods, the retailer accumulates the funds in this budget in proportion to the size of its order from the manufacturer. In the sale period, the budget is used to finance the discount offered by the manufacturer and advertising. I find that the manufacturer drops its price in the sale period to increase the profitability of promotions for the retailer. To be able to sell more units during the sale period, the retailer needs to accumulate a larger trade spend. This is accomplished by setting a smaller mark-up over the manufacturer's price in the regular periods. The manufacturer takes advantage of the retailer's softer pricing by increasing its regular wholesale price. As long as such trade spends are used to finance advertising, the total profits of each firm increase. Using fixed trade spends, where the manufacturer allocates a fixed amount for the retailer, does not lead to an increase in profits.     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

On how size and composition of customer bases affect equilibrium in a duopoly with switching costs

Switching costs may facilitate monopoly pricing in a market with price competition between two suppliers of a homogenous good, provided the switching cost is above some critical level. It is also well known that asymmetric size of customer bases makes monopoly pricing more difficult. Adding consumer heterogeneity to the model we demonstrate that also composition of each firms customer base affects pricing, and this composition may aggravate or ease the incentives to break out of the monopoly pricing equilibrium.Received: 16 August 2001, Accepted: 27 September 2004, JEL Classification: D43, L10, L13This research has been sponsored by Telenor, through the Foundation for Research in Economics and Business Administration. We thank participants at the 2002 EARIE conference in Madrid, Matthew Jackson and an anonymous referee for helpful and constructive comments to an earlier version. The usual disclaimer applies.     

Variable pricing business solutions in a decomposed business environment

Evolving business models and technology advances have facilitated the creation of innovative pricing strategies. Variable pricing represents the ability to configure a pricing schedule from a set of pricing options such as fixed cost, usage, shared benefit, and performance. The objective of variable pricing is to improve a pricing schedule for the mutual benefits of the provider and consumer, based on an evaluation of criteria that results in the setting of a price as a function of the expected value to be derived, as well as the time and materials used. In this paper, we focus on the variable pricing of ‘business solutions’, which is abstractly defined as the capabilities that enable or add value to the purposes of an enterprise. In a decomposed business environment, the structure of a business is partitioned into discrete business components that are assigned specific purposes and are endowed with resources to meet them. Business components interact to achieve business goals, and do so by exposing their capabilities through business services they offer. Business services have suitable levels of granularity offering constituent units of function, which, when selectively chosen and composed, form business solutions. We assert that business services are also suitable units for variable pricing, the implication being that pricing for a given business solution is an evaluation of the variable pricing of its assemblage of business services. The benefits of this ‘variable price composition’ approach offer greater accuracy for the pricing plan, coupled with increased flexibility to compose, modify, calculate and articulate pricing for business solutions.     

Franchise bidding,regulation and investment costs

This paper analyzes the design of an optimal monopoly franchise policy when firms incur investment costs. We show how this policy depends on the timing of entry. When the investment cost is a fixed cost or a sunk cost paid after knowing the marginal cost parameter, the optimal policy consists of a Baron-Myerson type pricing rule and a lowest cost awarding rule. When the investment cost is a sunk cost paid before knowing the marginal cost parameter, auctioning the right to serve the market eliminates the need for an incentive regulation: the price is given by the complete information Ramsey formula and the subsidy is a Loeb-Magat type subsidy, while an entry fee yields first best entry.     

Fixed margin price undercutting: An adequate entry strategy in a market with switching costs?

Purpose We try to determine the best strategy for entering a market with switching costs that is initially served by a monopolistic incumbent. Findings We show that an offer to undercut the incumbent by a fixed margin (FM) dominates traditional entry with a binding price offer (BO) as this conditional pricing strategy restrains the ability of the incumbent to block entry by limit pricing. Combining FM with a price ceiling (PC) insures customers against future price increases and turns out to be optimal for markets with elastic demand as long as cost uncertainty is not an issue. Conclusion Using a more elaborate entry strategy may facilitate entry in markets with switching costs. However, as these strategies may decrease welfare, they should be closely monitored by antitrust authorities.     

Costs and goals of the multiproduct firm

A profit-maximizing multiproduct firm's optimum production and pricing decision rules are different if the firm's fixed resources are fully employed than if they are underutilized. If they are fully employed, the opportunity cost of using a fixed input affects the firm's pricing decisions. The way for a multiproduct firm to maximize profit is to lose money on a product if large volume and low price of that product increases sales or reduces cost for other products sufficiently. Decision rules are different for a revenue-maximizing firm than for a profit-maximizing one.     

Entry and price dynamics in a perfect foresight model

This paper studies firms' entry and price dynamics in a model that combines the assumptions of free entry and perfect foresight with the hypothesis of consumer's loyalty postulated by Phelps and Winter. The analysis of the transition to long-run equilibrium reveals that, in such a model, the entry of firms is related to the difference between current prices and costs. In relation to the growth of the firms' output, it is shown that the model is consistent with Gibrat's Law. Finally, it is shown that the size distribution of firms approaches asymptotically a Pareto distribution.     

Bargains Followed by Bargains: When Switching Costs Make Markets More Competitive

In markets where consumers have switching costs and firms cannot price‐discriminate, firms have two conflicting strategies. A firm can either offer a low price to attract new consumers and build future market share or a firm can offer a high price to exploit the partial lock‐in of their existing consumers. This paper develops a theory of competition when overlapping generations of consumers have switching costs and firms produce differentiated products. Competition takes place over an infinite horizon with any number of firms. This paper shows that the relationship between the level of switching costs, firms' discount rate, and the number of firms determines whether firms offer low or high prices. Similar to previous duopoly studies, switching costs are likely to facilitate lower (higher) equilibrium prices when switching costs are small (large) or when a firm's discount rate is large (small). Unlike previous studies, this paper demonstrates that the number of firms also determines whether switching costs are pro‐ or anticompetitive, and with a sufficiently large (small) number of firms switching costs are pro‐ (anti‐) competitive.     

Optimal Two‐Part Pricing under Demand Uncertainty

This paper examines the pricing behavior of a risk‐averse monopolistic firm under demand uncertainty. The firm produces a single good at a constant marginal cost. To facilitate sales, the firm uses a two‐part pricing contract that includes a membership fee and a selling price per unit. The good is sold to a continuum of heterogeneous consumers who are subject to a common demand shock. We show that the global and marginal effects of risk aversion are to push the unit price closer to the constant marginal cost and to shrink the market coverage so as to limit the firm’s risk exposure to the demand uncertainty. The more risk‐averse firm as such charges a higher membership fee to consumers. We further show that an increase in the fixed cost of production induces the firm to lower (raise) the unit price, to raise (lower) the membership fee, and to shrink (enlarge) the market coverage under decreasing (increasing) absolute risk aversion. The firm’s optimal two‐part pricing contract, however, is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving‐spread increase in the demand uncertainty induces the firm to lower the unit price, to raise the membership fee, and to shrink the market coverage under either decreasing or constant absolute risk aversion. The firm’s risk preferences as such play a pivotal role in determining the optimal two‐part pricing under demand uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.     

Transport improvements,commuting costs,and residential location

This paper develops a theoretical framework for evaluating one of the long-run or secondary effects of a transport improvement. The familiar model of residential location is manipulated to derive an estimating equation relating changes in travel costs to changes in the household's preferred location. When estimated for a particular transport situation the major finding is the importance of the price effect. Although direct cost savings are important, especially in the short-run, in the long-run and especially for innovations with substantially increased speed or reduced operating costs the price effect may completely dwarf the income effect.     

城市垃圾按量收费的经济分析

本文从理论上分析了城市垃圾按量收费制度下的单位定价问题和其对居民行为的影响。研究表明,在考虑环境成本的情况下,城市垃圾处理的边际成本不但要包括垃圾收集和处理的边际成本,还要包括边际环境成本。以此为基础进行按量收费的单位定价会促使以减少环境容污能力为代价的最终处理方式的成本不断提高,而分类回收的成本却趋于下降。所以处理厂商在垃圾处理方式的选择上会朝着资源化的方向变化。按量收费制度会促使居民减少垃圾的排放量,增加垃圾的分类回收量,因此具有显著的减量效果。同时,政府的宣传教育和政策法规的制定也具有重要的作用。     

The demand for computer services: A disaggregate decision model

Pricing schedules for computer resources have traditionally been based on ‘cost-recovery’ principles. While economists have begun to address pricing based on marginal congestion costs, most models take demand to be exogenous and given. Discrete alternatives are inadequately treated, and aggregation of data precludes any assessment of the impact of transaction size on consumers' decisions. Using disaggregated data, this paper derives empirical results confirming that consumers are strongly influenced by transaction sizes. Simulation experiments demonstrate that price incentives designed to modify the use of computer resources are considerably more effective if the distribution of demand is weighted towards large transactions.     

Residual value forecasting using asymmetric cost functions

Leasing is a popular channel for marketing new cars. However, the pricing of leases is complicated because the leasing rate must embody an expectation of the car’s residual value after contract expiration. This paper develops resale price forecasting models in order to aid pricing decisions. One feature of the leasing business is that different forecast errors entail different costs. The primary objective of this paper is to identify effective ways of addressing cost asymmetry. Specifically, this paper contributes to the literature by (i) consolidating prior work in forecasting on asymmetric functions of the cost of errors; (ii) systematically evaluating previous approaches and comparing them to a new approach; and (iii) demonstrating that forecasting using asymmetric cost of error functions improves the quality of decision support in car leasing. For example, if the costs of overestimating resale prices are twice those of underestimating them, incorporating cost asymmetry into forecast model development reduces costs by about 8%.     

Can boundedly rational sellers learn to play Nash?

How does Nash pricing compare to pricing with adaptive sellers using reinforcement learning (RL)? We consider a market game similar to Varian’s model (Am Econ Rev 70:651–659, 1980) with two types of consumers differing by the size of their fixed sample search rule and derive the Nash search equilibrium (NSE) strategy (the density, the mean and the variance of the posted price distribution). Our findings are twofold. First, we find that the RL price distribution does not converge in a statistical sense to the NSE one except when competition is à la Bertrand. Second, we show that the qualitative properties of the NSE with respect to a change in buyers‘ search behavior are still valid for the RL distribution. The average price and the variance of both price distributions exhibit similar variations to a change in buyers’ search.     

Should Firms Employ Personalized Pricing?

This paper theoretically considers a duopoly model in which all firms do not always employ personalized pricing. Our model incorporates the fact that firms engage in marginal cost‐reducing activities after they decide whether to employ personalized pricing. When the ex ante cost difference between the firms is large, the less‐efficient firm does not employ personalized pricing even when the fixed cost to do so is zero. This is because employing personalized pricing induces the rival firm to engage more in reducing its costs, which is more likely to harm the less‐efficient firm.     

Planning horizons for master production scheduling

Production and operations planning in organizations quite often is a multi-level sequential process, involving aggregate planning, master production scheduling, and detailed operations planning and scheduling. To obtain good planning results, it is desirable to have a proper planning horizon for each level of planning. There have been a considerable number of studies dealing with planning horizons for aggregate planning or production smoothing problems. There are also many planning horizon studies for single-item lot sizing problems. No study has addressed the issues associated with the planning horizons for master production schedules (which is a multi-item lot sizing problem in nature), particularly with respect to the relationship to the aggregate plan.This study addresses the issue of planning horizons for companies employing a make-to-stock competitive strategy facing a seasonal demand for their products. We formulate the aggregate planning problem and the master scheduling problem as two separate mathematical programs to approximate the two-stage process that typically takes place in practice. Rolling planning horizons are used to approximate the periodic updates of the plans commonly done in practice. The models also incorporate resource requirements planning concepts to estimate loads on the critical work centers.The planning process is simulated as a single pass procedure where the results of aggregate planning are passed to the master production scheduling model once per month and the results of the master scheduling model (i.e., the portion of the master schedule actually implemented) are passed back to the aggregate planning model for the next planning session.The experimental results show that when the planner faces extreme cost structures such as high smoothing costs/high setup costs or low smoothing costs/low setup costs, the planning horizon effects are reduced to a minimum. Master schedule planning horizons need not be as long as aggregate planning horizons. Alternatively, non-extreme cost structures such as high smoothing costs/low setup costs and low smoothing costs/high setup costs should be handled with equal planning horizons for both aggregate planning and master scheduling.It is also found that the firm's cost structure has an impact on the appropriate planning horizon for both aggregate planning and master scheduling. Some cost conditions allow for smaller master schedule horizons. The best horizon choice seems to be equal planning horizons for both aggregate planning and master scheduling, even though the cost savings is slight in some cases.Finally, the proper length of the planning horizon for master scheduling is affected by the planning horizon of the aggregate plans.