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Showing papers on "Limit price published in 2004"


Journal ArticleDOI
Barry Nalebuff1
TL;DR: In this paper, the authors show that bundling is a particularly effective entry-deterrent strategy in an oligopolistic environment, where a company that has market power in two goods, A and B, can, by bundling them together, make it harder for a rival with only one product to enter the market.
Abstract: In this paper we look at the case for bundling in an oligopolistic environment. We show that bundling is a particularly effective entry-deterrent strategy. A company that has market power in two goods, A and B, can, by bundling them together, make it harder for a rival with only one of these goods to enter the market. Bundling allows an incumbent to credibly defend both products without having to price low in each. The traditional explanation for bundling that economists have given is that it serves as an effective tool of price discrimination by a monopolist. Although price discrimination provides a reason to bundle, the gains are small compared with the gains from the entry-deterrent effect. I. INTRODUCTION In this paper we look at the case for bundling in an oligopolistic environment. We show that bundling is a particularly effective entry-deterrent strategy. A company that has market power in two goods, A and B, can, by bundling them together, make it harder for a rival with only one of these goods to enter the market. Bundling allows an incumbent to defend both products without having to price low in each. While it is still possible to compete by offering a rival bundle, a monopolist can significantly lower the potential profits of a one-product entrant without having to engage in limit pricing prior to entry. We also show that bundling continues to be an effective pricing tool even if entry deterrence fails (or if there is already an existing one-product rival). A company with a monopoly in product A and a duopoly in product B makes higher profits by selling an A‐B bundle than by selling A and B independently. Leveraging market power from A into B and accepting some one-product competition against the bundle is better than using the monopoly power in good A all by itself. Since bundling mitigates the impact of competition on the incumbent, an entrant can expect the bundling strategy to persist, even without any commitment. The traditional explanation for bundling that economists have given is that it serves as an effective tool of price discrimination by a monopolist (see Stigler [1968], Adams and Yellen

504 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined four million daily price observations for more than 1,000 consumer electronics products on the price comparison site http://shopper.com and found little support for the notion that prices on the Internet are converging to the law of one price.
Abstract: This paper examines four million daily price observations for more than 1,000 consumer electronics products on the price comparison site http://Shopper.com. We find little support for the notion that prices on the Internet are converging to the ‘law of one price.’ In addition, observed levels of price dispersion vary systematically with the number of firms listing prices. The difference between the two lowest prices (the ‘gap’) averages 23 per cent when two firms list prices, and falls to 3.5 per cent in markets where 17 firms list prices. These empirical results are an implication of a general ‘clearinghouse’ model of equilibrium price dispersion.

496 citations


Journal ArticleDOI
TL;DR: In this paper, the cause of large fluctuations in prices on the London Stock Exchange is studied at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell, and it is shown that price fluctuations caused by individual market orders are essentially independent of the volume of orders.
Abstract: We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are essentially independent of the volume of orders. Instead, large price fluctuations are driven by liquidity fluctuations, variations in the market's ability to absorb new orders. Even for the most liquid stocks there can be substantial gaps in the order book, corresponding to a block of adjacent price levels containing no quotes. When such a gap exists next to the best price, a new order can remove the best quote, triggering a large midpoint price change. Thus, the distribution of large price changes merely reflects the distribution of gaps in the limit order book. This is a finite size effect, caused by the granularity of order flow: in a market where participants place many small orders uniformly across prices, such large...

352 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider an inÞnitely repeated Bertrand game, in which prices are publicly observed and each broker receives a privately observed, i.i.d. cost shock in each period.
Abstract: We consider an inÞnitely repeated Bertrand game, in which prices are publicly observed and each Þrm receives a privately observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any “punishments” are borne equally by all Þrms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each Þrm is strictly increasing in its cost level: such “fully sorting” schemes offer efficiency beneÞts, as they ensure that the lowest-cost Þrm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost Þrm must be deterred from mimicking a lower-cost Þrm by charging a lower price. A rigid-pricing scheme, where a Þrm’s collusive price is independent of its current cost position, sacriÞces efficiency beneÞts but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i). the absence of equilibrium-path price wars and (ii). a rigid price. If Þrms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost Þrms may be distorted downward, in order to diminish the incentive to cheat. When the model is modiÞed to include i.i.d. public demand shocks, the downward pricing distortion that accompanies a Þrm’s lower-cost realization may occur only when current demand is high.

332 citations


Posted Content
TL;DR: In this paper, the authors characterize institutional trading in international stocks from 37 countries during 1997 to 1998 and 2001 and find that the underlying market condition is a major determinant of the price impact and, more importantly, of the asymmetry between price impacts of institutional buy and sell orders.
Abstract: This study characterizes institutional trading in international stocks from 37 countries during 1997 to 1998 and 2001. We find that the underlying market condition is a major determinant of the price impact and, more importantly, of the asymmetry between price impacts of institutional buy and sell orders. In bullish markets, institutional purchases have a bigger price impact than sells; however, in the bearish markets, sells have a higher price impact. This differs from previous findings on price impact asymmetry. Our study further suggests that price impact varies depending on order characteristics, firm-specific factors, and cross-country differences.

274 citations


Journal ArticleDOI
TL;DR: In this article, a model of price discrimination that includes both second-degree and third-degree price discrimination is described, and it is shown that the observed price discrimination may improve the firm's profit by approximately 5%, relative to uniform pricing, while the difference for aggregate consumer welfare is negligible.
Abstract: A common thread in the theory literature on price discrimination has been the ambiguous welfare effects for consumers and the rise in profit for firms, relative to uniform pricing. In this study I resolve the ambiguity for consumers and quantify the benefit for a firm. I describe a model of price discrimination that includes both second-degree and third-degree price discrimination. Using data from a Broadway play, I estimate the structural model and conduct various experiments to investigate the implications of alternative pricing policies. The observed price discrimination may improve the firm's profit by approximately 5%, relative to uniform pricing, while the difference for aggregate consumer welfare is negligible. Also, I show that the gain from changing prices in the face of fluctuating demand is small under the observed price discrimination.

264 citations


Journal ArticleDOI
TL;DR: In this article, a variety of models provide differing predictions regarding the effect of an increase in the number of competitors in a market (seller density) on prices and price dispersion.

221 citations


Patent
11 Feb 2004
TL;DR: In this paper, a set of demand-based claims, each of which can be a vanilla option or a digital option, approximate or replicate the contingent claim into a vanilla replicating basis or a Digital Replicating basis, and the order for the contingent claims is then evaluated or processed in the demand based auction, where the equilibrium price and/or the payout for the derivatives strategy are determined as a function of the demandbased valuation of each replicating claim in the replication set.
Abstract: Methods and systems for trading and replicating contingent claims, such as derivatives strategies, in a demand-based auction are described. In one embodiment, a set of demand-based claims, each of which can be a vanilla option or a digital option, approximate or replicate the contingent claim into a vanilla replicating basis or a digital replicating basis, and the order for the contingent claim is then evaluated or processed in the demand-based auction. In another embodiment, a plurality of strikes and a plurality of replicating claims are established for a demand-based auction on an event, one or more replicating claims striking at each of the strikes in the auction. A contingent claim, such as derivatives strategy, is replicated with a replication set that includes one or more of the replicating claims in the auction. The equilibrium price and/or the payout for the derivatives strategy is determined as a function of the demand-based valuation of each of the replicating claims in the replication set. For a customer order requesting a number of a certain derivatives strategy in the demand-based auction and a limit price per derivatives strategy, the premium of the customer order is determined as a product of the equilibrium price for the derivatives strategy and a filled number of derivatives strategies for the order, each determined as a function of the demand-based valuation of each of the replicating claims in the demand-based auction.

203 citations


01 Sep 2004
TL;DR: In this article, the authors present a new theoretical model of asymmetric adjustment that empirically matches observed retail gasoline price behavior better than previously suggested explanations, and develop a "reference price" consumer search model that assumes consumers' expectations of prices are based on prices observed during previous purchases.
Abstract: It has been documented that retail gasoline prices respond more quickly to increases in wholesale price than to decreases. However, there is very little theoretical or empirical evidence identifying the market characteristics responsible for this behavior. This paper presents a new theoretical model of asymmetric adjustment that empirically matches observed retail gasoline price behavior better than previously suggested explanations. I develop a “reference price” consumer search model that assumes consumers’ expectations of prices are based on prices observed during previous purchases. The model predicts that consumers search less when prices are falling. This reduced search results in higher profit margins and a slower price response to cost changes than when margins are low and prices are increasing. Following the predictions of the theory, I use a panel of gas station prices to estimate the response pattern of prices to a change in costs. Unlike previous empirical studies I focus on how profit margins (in addition to the direction of the cost change) affect the speed of price response. Estimates are consistent with the predictions of the reference price search model, and appear to contradict previously suggested explanations of asymmetric adjustment.

202 citations


Posted Content
TL;DR: In this article, the authors investigated the effects of different forms of price regulation on airport efficiency and found that the effect of ROR regulation may lead to over investment in capacity, while price-cap regulation is prone to under-investment.
Abstract: This paper investigates the effects of different forms of price regulation on airport efficiency Our investigation takes into account the interaction between concession profits and price regulations Our results show that while ROR regulation may lead to over investment in capacity, price-cap regulation is prone to under-investment The extent of the under-investment is found to be less under the dual-till price cap than under the single-till price cap Our empirical investigation of capital input productivity and total factor productivity confirm the analytical findings In particular, the total factor productivity is greater under the dual-till price cap than under either the single-till price cap or single-till ROR Our analysis appears to support the argument made by several economists that dual till regulation would be better than the single-till regulation in terms of economic efficiency, especially for large and busy airports

201 citations


Journal ArticleDOI
TL;DR: In this paper, the average duration of prices in the sectors covered by the database (65% of the French CPI) is found to be around 8 months, and a strong heterogeneity across sectors both in the average length of prices and in the pattern of price setting is reported.
Abstract: Based upon a large fraction of the price records used for computing the French CPI, we document consumer price rigidity in France. We first provide a methodological discussion of issues involved in estimating average price duration with micro-data. The average duration of prices in the sectors covered by the database (65% of the CPI) is then found to be around 8 months. A strong heterogeneity across sectors both in the average duration of prices and in the pattern of price setting is reported. There is no clear evidence of downward nominal rigidity, since price cuts are almost as frequent as price rises. Moreover, the average size of a change in price is quite large in both cases. Overall, while our results do not entail a clear conclusion about the existence of menu costs, there is evidence of both time-dependent and state-dependent price setting behaviors by retailers.

Journal ArticleDOI
TL;DR: This paper examined retail price variation across a range of goods and regions of the United States and found that the typical grocery product has a regular price and stays at that price at least 50% of the time, and that most deviations from that regular price are downward.
Abstract: We examine retail price variation across a range of goods and regions of the United States. We find that the typical grocery product has a regular price and stays at that price at least 50% of the time, and that most deviations from that regular price are downward. Temporary discounts or sales, while infrequent, account for 20% to 50% of the annual variation in retail prices for most product categories. Although existing models of retail sales yield predictions consistent with some aspects of the retail pricing distributions, all of these models fail to explain other important aspects of retail pricing identified here.

Journal ArticleDOI
TL;DR: In this paper, the effects of changing search costs on prices both when product differentiation is fixed and when it is endogenously determined in equilibrium were investigated through a model of buyer and seller behavior, and the overall effect of lower buyer search costs for price may even lead to higher prices, lower social welfare and higher industry profits.
Abstract: Buyer search costs for price are changing in many markets. Through a model of buyer and seller behavior, I consider the effects of changing search costs on prices both when product differentiation is fixed and when it is endogenously determined in equilibrium. If firms cannot change product design, lower buyer search costs for price lead to increased price competition. However, if product design is a decision variable, lower search costs for price may also lead to higher product differentiation, which decreases price competition. In this case, the overall effect of lower buyer search costs for price may even be higher prices, lower social welfare, and higher industry profits. The result is especially interesting because recent technological changes, such as Internet shopping, can affect the market structure through lowering buyer search costs.

Journal ArticleDOI
TL;DR: The results of a survey conducted by the Banque de France during winter 2003-2004 to investigate the price-setting behavior of French manufacturing companies are reported in this paper. Prices are found to adjust infrequently; the median firm modifies its price only once a year.
Abstract: This paper reports the results of a survey conducted by the Banque de France during winter 2003-2004 to investigate the price-setting behavior of French manufacturing companies. Prices are found to adjust infrequently; the median firm modifies its price only once a year. Price reviews are more frequent than price changes; the median firm reviews its price quarterly. Firms are found to follow either time-dependent, state-dependent or both pricing rules. Moreover, the chosen interval of price reviews depends on the probability that changes in the firms' environment occur. Coordination failure and nominal contracts (either written or implicit) are the most important sources of price stickiness, while pricing thresholds and physical menu costs appear to be totally unimportant. Asymmetries in price stickiness are found to be different for cost shocks compared to demand shocks: prices are more rigid downward than upward for cost shocks, while the reverse is true for demand shocks.

Journal ArticleDOI
TL;DR: In this paper, a large unpublished data set about the prices by store of 381 products collected by the Israeli Bureau of Statistics during 1991-1992 in the process of computing the CPI was used.

ReportDOI
TL;DR: The authors argue that price stickiness arises from strategic considerations of how customers and competitors will react to price changes, and they find that this prediction is broadly consistent with the behavior of nine Philadelphia gasoline wholesalers.
Abstract: The menu-cost interpretation of sticky prices implies that the probability of a price change should depend on the past history of prices and fundamentals only through the gap between the current price and the frictionless price. We find that this prediction is broadly consistent with the behavior of nine Philadelphia gasoline wholesalers. Nevertheless, we reject the menu-cost model as a literal description of these firms' behavior, arguing instead that price stickiness arises from strategic considerations of how customers and competitors will react to price changes.

Posted Content
TL;DR: In this paper, the authors examined price setting behavior of Italian firms on the basis of survey data and found that prices are mostly fixed following mark-up rules, although customer-specific characteristics have a role in some sectors.
Abstract: This study examines price setting behaviour of Italian firms on the basis of survey data. Prices are mostly fixed following mark-up rules, although customer-specific characteristics have a role in some sectors. Rival prices mostly affect price strategies of industrial firms. In reviewing their prices, firms follow either state-dependent rules or a combination of time and state-dependent ones. A considerable degree of price stickiness emerges; in 2002 most firms changed their price only once. Three explanations are ranked highest: explicit contracts, tacit collusive behaviour and the temporary nature of the shock. Prices respond asymmetrically to shocks, depending on the direction of the required adjustment and the source of the shock. Real rigidities play an important role in determining this asymmetry. Cost shocks impact more when prices have to be raised than when they have to be reduced; demand decreases are more likely to induce a price change than demand increases.

Journal ArticleDOI
TL;DR: In this article, the authors show that appropriate online price partitioning may enhance consumers' purchase intentions, perceived value, and price satisfaction, and reduce further information search intentions, but when multiple surcharges are added to partition the price further, these positive effects may decline leading to an inverted “U” shape function of partitioning on price perceptions.

Journal ArticleDOI
TL;DR: In this paper, the authors found significant variation in the identity of the low-price firm and the level of the lowest price for 36 of the best selling consumer electronics products sold at Shopper.com between November 1999 and May 2001.

Journal ArticleDOI
TL;DR: In this paper, the effectiveness of a price-matching guarantee as a signal of low store prices depends on individuals' beliefs about the degree to which other consumers in the market engage in price search, enforce pricematching guarantees, or both.

Journal ArticleDOI
01 Jul 2004
TL;DR: This paper proves the existence and uniqueness of the pure-strategy Nash equilibrium, a horizontal market of multiple firms that face stochastic price-dependent demand that exhibits a bias toward under-pricing caused by competition.
Abstract: This paper considers a horizontal market of multiple firms that face stochastic price-dependent demand. The firms make joint pricing/inventory decisions and use price to compete for market demand. With fairly general demand models that are price-dependent, stochastic, and substitutable among firms, we prove the existence and uniqueness of the pure-strategy Nash equilibrium. The market at the equilibrium exhibits a bias toward under-pricing caused by competition; specifically, raising prices at any equilibrium of the game increases the total system profit, and at any joint-optimal set of pricing levels each self-interested firm has an incentive to lower its price. This result closely parallels that obtained in the inventory competition games in which prices are fixed and the bias is toward overstocking.

Posted Content
TL;DR: In this paper, the authors identify the basic features of the price setting mechanism in the Spanish economy, using a large dataset that contains over 1.1 million price records and covers around 70% of the expenditure on the CPI basket.
Abstract: This paper identifies the basic features of the price setting mechanism in the Spanish economy, using a large dataset that contains over 1.1 million price records and covers around 70% of the expenditure on the CPI basket. In particular, the paper identifies differences in the frequency and size of price adjustments across types of products and explores how these general features are affected by certain specific factors: seasonality, the level of inflation, changes in indirect taxation and the practice of using psychological and round prices. We find that prices do not change often but do so by a large amount, although there is a marked heterogeneity across products. Moreover, the high frequency of price reductions suggests that there is no strong downward rigidity. Our evidence also supports the use of time and state-dependent pricing strategies. JEL Classification: E31, D40, C25

Journal ArticleDOI
TL;DR: In this paper, a model of price transmission where both oligopoly and oligopsony power co-exist and where industry technology is assumed to be characterised by variable input proportions is presented.
Abstract: Several studies in the literature have argued that price transmission in vertically-related markets is imperfect, i.e. that farm input price changes are not fully passed-through to the final product price. Market power, notably oligopoly, is presumed to be the principal source of imperfect price transmission. To date, the impact of oligopsony (buyer) power on the degree of price transmission has not been evaluated using a formal theoretical model. Moreover, neither has the combination of oligopoly and oligopsony despite the fact that its influence has been formally acknowledged in both the UK and some European food markets. This paper makes a contribution to the literature by developing a model of price transmission where both oligopoly and oligopsony power co-exist and where industry technology is assumed to be characterised by variable input proportions. It shows that taking the degree of price transmission in a perfectly competitive market as a benchmark, oligopoly and oligopsony power do not necessarily lead to imperfect price transmission, although they can. Indeed, they may counteract each other's impact on the degree of price transmission. The key to these outcomes is to be found in the functional forms for retail demand and farm supply.

Journal ArticleDOI
TL;DR: In this paper, the authors show that if the probability of obtaining the high price is not too high, sellers profit from using contingent pricing while economic efficiency increases, and that the optimal contingent pricing structure depends on the buyer's risk attitude.
Abstract: The price for a product may be set too low, causing the seller to leave money on the table, or too high, driving away potential buyers. Contingent pricing can be useful in mitigating these problems. In contingent pricing arrangements, price is contingent on whether the seller succeeds in obtaining a higher price within a specified period. We show that if the probability of obtaining the high price is not too high, sellers profit from using contingent pricing while economic efficiency increases. The optimal contingent pricing structure depends on the buyer's risk attitude-a deep discount is most profitable if buyers are risk prone. A consolation reward is most profitable if buyers are risk averse. To motivate buyers to participate in a contingent pricing arrangement, the seller must provide sufficient incentives. Consequently, buyers also benefit from contingent pricing. In addition, because the buyers with the highest willingness-to-pay get the product, contingent pricing increases the efficiency of resource allocation.

Patent
16 Oct 2004
TL;DR: In this article, an apparatus determines a current price of a product for sale by the vending machine and then determines, for the product, a price increment, a predetermined price, and a demand threshold, that are defined by data stored in at least one data table.
Abstract: According to one embodiment of the disclosed invention, an apparatus determines a current price of a product for sale by the vending machine. It then determines, for the product, a price increment, a predetermined price, and a demand threshold, that are defined by data stored in at least one data table. A rate of units of the product that are sold are determined. The rate is compared with the demand threshold. Based on the comparison of the rate with the demand data, it is determined whether the new price should be greater than or less than the current price. The new price is set to the predetermined price if the new price should be greater than the current price. If the new price should be less than the current price, a price increment amount is subtracted from the current price to yield the new price. The determined new price is displayed.

Journal ArticleDOI
TL;DR: In this paper, a reduced-form model of price transmission in a vertical sector was developed, allowing for refined asymmetric, contemporaneous and lagged, own and cross-price effects under time-varying volatility.
Abstract: We develop a reduced-form model of price transmission in a vertical sector, allowing for refined asymmetric, contemporaneous and lagged, own and cross-price effects under time-varying volatility. The model is used to investigate the wholesale-retail price dynamics in the U.S. butter market. The analysis documents the nature of nonlinear price dynamics in a vertical sector. It finds strong evidence of asymmetric retail price responses, both in the short term and the longer term, but only weak evidence of asymmetric wholesale price responses. Asymmetric retail responses play a major role in generating a skewed distribution of butter prices. The empirical results indicate the presence of imperfect competition at the retail level.

Journal ArticleDOI
TL;DR: In this article, the authors identify a theoretical explanation for these patterns of pricing behavior, and look for evidence consistent with the theory by examining market structure, conduct, and spatial pricing patterns in different retail gasoline markets in Canada.
Abstract: Retail gasoline markets have been found to exhibit either price volatility and price dispersion or price rigidity and uniformity across large metropolitan areas. The purpose of this paper is to identify a theoretical explanation for these patterns of pricing behavior, and to look for evidence consistent with the theory by examining market structure, conduct, and spatial pricing patterns in different retail gasoline markets in Canada. The study utilizes a novel source of price data: price observations reported to internet data collection sites. The firm and station specific price data are consistent with the presence of tacitly collusive behavior in one retail gasoline market and the presence of maverick retailers that prevent tacit collusion in the other retail market.

Book
04 Feb 2004
TL;DR: This chapter discusses the three Levels of Price Management and discusses how to bring these levels together to create a Pricing Architecture that works for the modern marketplace.
Abstract: Preface.Acknowledgments.PART ONE: PRICING FUNDAMENTALS.Chapter 1. Introduction.Chapter 2. The Three Levels of Price Management.PART TWO: EXPLORING THE LEVELS.Chapter 3. Transaction.Chapter 4. Product/Market Strategy.Chapter 5. Industry Strategy.PART THREE: SPECIAL TOPICS.Chapter 6. New Product Pricing.Chapter 7. Solutions, Bundles, and Other Packaged Offerings.PART FOUR: UNIQUE EVENTS.Chapter 8. Postmerger Pricing.Chapter 9. Price Wars.PART FIVE: EXPANDING THE BOUNDARIES.Chapter 10. Technology-Enabled Pricing.Chapter 11. Legal Issues.PART SIX: BRINGING IT TOGETHER.Chapter 12. Pricing Architecture.Chapter 13. Driving Pricing Change.Chapter 14. The Monarch Battery Case.Chapter 15. Epilogue.Appendix 1: Sample Pocket Price and Pocket Margin Waterfalls.Appendix 2: Antitrust Issues.Appendix 3: List of Acronyms.About the Authors.Index.

Patent
08 Mar 2004
TL;DR: In this paper, the price of a derivative product order (bid or offer) is updated based on changes in the prices of a related underlying product, such as delta and gamma.
Abstract: Methods and systems for an exchange to handle variable derivative product order prices are disclosed. The price of a derivative product order (bid or offer) is updated based on changes in the price of a related underlying product. Price determination variable(s), such as delta and gamma, are used to determine the price of the order. The exchange may periodically recalculate the price without requiring the trader to transmit additional information to the exchange.

Patent
16 Apr 2004
TL;DR: In this article, the authors present a method and computer program product for forecasting the retail price of electricity for a customer in a deregulated market and for providing probabilistic valuation of costs and risks.
Abstract: A method and computer program product for forecasting the retail price of electricity for a customer in a deregulated market and for providing probabilistic valuation of costs and risks. The method includes the steps of performing a digital simulation of marginal clearing prices and hourly customer load to derive expected and probabilistic forecasts of load-weighted wholesale prices and costs for a customer; determining a supplier risk premium to be added to the forecasted retail price based on an expected wholesale price volatility, an expected variability of customer load, and a set of contractual conditions governing price structure, volume flexibility, and financial options embedded within a contract; performing a supply price analysis; and presenting the results of the supply price analysis to the customer. The method can also include the steps of performing a cash flow at risk analysis and/or performing a price duration analysis and/or financial valuation of options embedded in supply contracts such as collars (caps/floors) and contract extension options from the supplier or the end-user and combining the results with the results of the supply price analysis.