Monopoly, Pareto and Ramsey Mark-ups

Monopoly prices are too high. It is a price level problem, in the sense that the relative mark-ups have Ramsey optimal proportions, at least for independent constant elasticity demands. I show that this feature of monopoly prices breaks down the moment one demand is replaced by the textbook linear demand or, even within the constant elasticity framework, dependence is introduced. The analysis provides a single Generalized Inverse Elasticity Rule for the problems of monopoly, Pareto and Ramsey.      

INFLATION AND THE TIMING OF PRICE CHANGES (*)

Consider an oligopolistic industry in which the firms produce perfect substitutes and incur transaction costs of changing price. Under constant inflation, there is an equilibrium in which the firms change their nominal prices at equally spaced time-points. Increasing the inflation rate increases the size of price changes, increases the frequency of price changes, and increases the average real price paid by buyers. The analysis derives its significance from its implications for the welfare costs of inflation: the inflation-induced distortions in relative prices are larger the more sticky nominal prices are; and are larger the greater the tendency for firms to stagger (rather than synchronize) their price changes.     

A Simplified Quadrature Approach for Computing Bermudan Option Prices

We examine a simple quadrature approach to compute the prices of Bermudan options when the value of the corresponding European claim can be computed in closed form, one period before maturity. Using a constant grid of stock prices at early exercise time points, the known value of the European option is used as a smoothing device to enable efficient numerical integ ration with quadrature approaches. Examples with the geometric Brownian motion context and the lognormal jump‐diffusion context are provided.     

A cointegrated commodity pricing model

We propose a commodity pricing model that extends the Gibson–Schwartz two‐factor model to incorporate the effect of linear relations among commodity spot prices, and provide a condition under which such linear relations represent cointegration. We derive futures and call option prices for the proposed model, and indicate that, unlike in Duan and Pliska (2004), the linear relations among commodity prices should affect commodity derivative prices, even when the volatilities of commodity returns are constant. Using crude oil and heating oil market data, we estimate the model and apply the results to the hedging of long‐term futures using short‐term ones.     

WORLD IMBALANCES AND MACROECONOMIC ADJUSTMENTS: A THREE‐COUNTRY STOCK‐FLOW CONSISTENT MODEL WITH FIXED OR FLEXIBLE PRICES

World macroeconomic adjustments are analysed with a three‐country Stock‐Flow Consistent (SFC) models. Three SFC models are considered, the first one with a fixed dollar–yuan parity including a version with Chinese foreign reserves' diversification, the second with a flexible dollar–yuan parity which can be freely floating or following a more managed float, the third one being a generalization of the two others with flexible prices instead of constant prices. The fixity of the dollar–yuan parity limits the adjustments facing shocks and world imbalances while a more flexible dollar–yuan exchange rate appears as a powerful adjustment mechanism to reduce these imbalances.     

ANALYTIC APPROXIMATIONS FOR MULTI‐ASSET OPTION PRICING

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi‐ or single‐asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi‐asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single‐asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi‐asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi‐asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi‐asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.     

The effects of informative and non‐informative price patterns on consumer price judgments

Converging evidence from laboratory experiments and empirical models of scanner data suggests that product price evaluations are often based on a comparison to an internal reference price. Research indicates that the reference price may reflect various characteristics of previously encountered prices including the mean, the range, and the last price encountered. In this research, the authors test whether, for prices purportedly sampled over time, the reference price reflects temporal patterns of the price sequence (ascending and descending prices). In four studies, participants viewed prices purportedly sampled at one time point or at multiple time points and then evaluated a target price. Price distributions differed only in their temporal pattern, whereas the mean, the range, and in some conditions, the last price, were held constant. The results reveal that the price pattern does not affect price judgments when prices are purportedly sampled at one time point. However, for ascending and descending price sequences purportedly sampled over time, the price pattern affects price judgments. Based on these findings the authors propose that consumers flexibly select the internal reference price used for price evaluations. © 2006 Wiley Periodicals, Inc.     

Production,liquidity, and futures price dynamics

This study examines the optimal design of a futures hedge program for the competitive firm under output price uncertainty. All futures contracts are unbiased and marked to market in that they require interim cash settlement of gains and losses. The futures price dynamics follows a first-order autoregression with a random walk serving as a special case. The firm's futures hedge program is constituted of an endogenous provision for premature termination, which depends on how the futures prices are autocorrelated. Succinctly, the firm voluntarily commits to premature liquidation of its futures position on which the interim loss incurred exceeds a predetermined threshold level if the futures prices are positively autocorrelated. In this case, the liquidity constrained firm optimally opts for an over-hedge if its preferences exhibit either constant or increasing absolute risk aversion. If the futures prices are uncorrelated or negatively autocorrelated, the firm prefers to be liquidity unconstrained and thus adopts a full-hedge to completely eliminate the output price risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:749–762, 2008     

Expectations,monetary policy rules,and macroeconomic stability: Analysis of an open economy with flexible exchange rates

This paper makes use of a dynamic model of an open economy with flexible exchange rates to examine the dynamic characteristics of the system for different specifications of monetary authority behavior. The model contains dynamic adjustment equations for both output and prices. Two policy rules are examined: (a) maintaining a constant nominal money supply growth, and (b) maintaining a constant nominal interest rate. With the former the system is found to be self-equilibrating. The latter, however, could easily give rise to self-perpetuating disequilibrium situations. In both cases expectations play a crucial role in the adjustment process.     

Option Pricing For Jump Diffusions: Approximations and Their Interpretation

We derive a computable approximation for the value of a European call option when prices satisfy a jump-diffusion model with the coefficients depending explicitly on time. This is achieved by approximating the original coefficients with functions that are piecewise constant in time. We give an interpretation of the approximating option values, in particular in the context of a discrete-time model associated with the approximating continuous-time model.     

Efficient Universal Portfolios for Past-Dependent Target Classes

We present a new universal portfolio algorithm that achieves almost the same level of wealth as could be achieved by knowing stock prices ahead of time. Specifically the algorithm tracks the best in hindsight wealth achievable within target classes of linearly parameterized portfolio sequences. The target classes considered are more general than the standard constant rebalanced portfolio class and permit portfolio sequences to exhibit a continuous form of dependence on past prices or other side information. A primary advantage of the algorithm is that it is easily computable in a polynomial number of steps by way of simple closed-form expressions. This provides an edge over other universal algorithms that require both an exponential number of computations and numerical approximation.     

Demand Analysis of Meat in Malaysia

One distinct change in Malaysians' food consumption behavior has been the preference toward meat products. Thus it is meaningful to gain insight of meat consumption patterns. As the market becomes increasingly market-led, information on current meat consumption patterns is required to assess how they are likely to change as prices and incomes change. This study attempts to provide a better understanding of demand for meat products in Malaysia. By utilizing data from Household Expenditure Survey 2004/2005, Engel curve analysis was conducted to derive income elasticities of meat products from QUAIDS model. The estimated income elasticities show that current food consumption patterns are showing signs of convergence toward a Western diet, exhibiting tendency for preference toward red meats (mutton and beef) over white meats (poultry and pork). The estimated elastic own-price elasticities indicate that Malaysian consumers are sensitive to the change in prices of the meat products, with other things remain constant.     

Distributional Effects of Lower Food Prices in a Rich Country

Controlling for differences in taxes and transportation costs, the Nordic Competition Authorities claims, in a report from 2005, that food prices are 11% higher in Sweden compared to the EU-15 countries. One explanation for this put forward in the report is the limited competition on this market which suggests there to be a potential for lower food prices. This paper focuses on distributional effects of a price decrease on food. Based on a simple model of household utility, the households demand for food is derived and estimated. Price and income elasticities for different income groups are then calculated based on these parameter estimates. Our results suggest that food is a normal good with an average income elasticity of approximately 0.18 and a price elasticity of 0.45. In addition, and of importance from a policy perspective, the results indicate the income elasticity to differ across income groups while price elasticities are constant.     

Black‐Scholes‐Merton revisited under stochastic dividend yields

European options are priced in a framework à la Black‐Scholes‐Merton, which is extended to incorporate stochastic dividend yield under a stochastic mean–reverting market price of risk. Explicit formulas are obtained for call and put prices and their Greek parameters. Some well‐known properties of the Black‐Scholes‐Merton formula fail to hold in this setting. For example, the delta of the call can be negative and even greater than one in absolute terms. Moreover, call prices can be a decreasing function of the underlying volatility although the latter is constant. Finally, and most importantly, option prices highly depend on the features of the market price of risk, which does not need to be specified at all in the standard Black‐Scholes‐Merton setting. The results are simulated in order to assess the economic impact of assuming that the dividend yield is deterministic when it is actually stochastic, as well as to assess the economic importance of the features of the market price of risk. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:703–732, 2006     

An Empirical Model of Automobile Engine Variant Pricing

This paper estimates a random-coefficients structural model of the demand for car model engine variants. It uses a new identification approach that assumes the mean unobserved quality is the same for all engine variants within a model. The demand estimates imply that absolute markups increase in horsepower within a car model, while percentage markups are constant or falling in horsepower. The estimated results–as well as simulations of a simple theory model–show that prices are not typically cost-plus-fixed-fee, and absolute markups may increase in quality.     

Überlegungen zur Bedeutung Unverbindlicher Preisempfehlungen und ihrer Kontrolle durch das Bundeskartellamt Ein Kommentar zu den Beiträgen von Reich und Schultes in ZVP, 1, 1977/3 bzw. 1977/4

Reflections on the importance of recommended prices and their control by the Cartel Office. A comment on the papers by Reich (JCP, 1, 1977/3) and Schultes (JCP, 1, 1977/4). The The comment deals with two previous articles on recommended prices. Both Reich and Schultes refer to the 1977 report of the German Federal Government on recommended prices, which was intended to show the consequences of price recommendations and to give a better base for further decisions of the legislative assembly. The two authors evaluate the information in this report very differently and draw opposite conclusions. Reich pleads in the interest of the consumer for an unlimited prohibition of the institute of recommended prices. His thesis is based on three arguments:

1. Article 38 a of the Law Against Restraints of Competition implies that manufacturers often find themselves in a dilemma. Either they respect the character of the price as recommended, not binding, whereby the often emerging wide retail price range activates the Cartel Office which calls for the abolition of the recommended price since it is “unrealistic”, or manufacturers require that the recommended price is adhered to, which leads to accusations of price fixing. In practice, therefore, the institute of recommended prices is on the decrease except in connection with selective distribution systems where it is used increasingly and functions as vertical price fixing.
2. Prices which are recommended and available to retailers only are devices for concerted vertical pricing and in reality work like price fixing.
3. An abolition of recommended prices would strengthen traders' and consumers' resistance to high prices.

Schultes, on the other hand, adopts the view that the present Law together with some minor improvements is sufficient to protect the consumer against misuses of recommended prices. His view is based on the argument that the control by the Cartel Office has been successful, considering the great number of eliminated price recommendations, and that in the case of an unlimited prohibition of recommended prices on would have to reckon with the development of uncontrollable surrogates. A critical examination of these arguments shows that neither position is well-founded. The theoretical considerations of both authors contain contradictions and are not based on empirical findings. Schultes' paper suggests that the control of recommended prices by the Cartel Office leads to a continuous decimation of recommended prices and therefore, in the long run, either to the same result as Reich's demand or to a treatment which discriminates against certain firms or trades. It is very doubtful if the development of surrogates is prevented through this control. The statement of Schultes that the Cartel Office's control activity has been sucessful up to now also seems very questionable, since the number of eliminated price recommendations is not sufficient proof; a more sophisticated cost-benefit analysis is called for. The analysis of Reich's arguments indicates the following:

1. It is quite correct that Article 38 a of the Law contains conflicting aims. This conflict arises from the choice of criteria for declaring recommendations unlawful. There are two possible solutions to the conflict: the total abolition of recommended prices or a change in the criteria for misuses of the institute. Reich favours the first solution without considering that the second possibility may perhaps offer a better solution. Further considerations show that the conflict arises above all from prohibiting actual prices from being much lower than recommended prices. This rule seems very questionable because it eliminates price competition. Furthermore it is very doubtful that consumers are really misled by a large difference between the recommended price and that charged.
2. Prices which are recommended to retailers only certainly work like vertical price fixing sometimes, but not always. Apart from this objection, the least plausible of Reich's theses is that a prohibition of recommended prices would eliminate concerted pricing behaviour. This would be true only if the recommendations were the main cause of such behaviour. This view must be questioned because the development and the practice of concerted pricing is linked with specific market structures which cannot be eliminated by the prohibition of recommended prices.
3. Therefore, by prohibiting recommended prices one cannot expect greater retailer resistance to high prices. In addition, there seems to be no chance to strengthen price resistance of consumers by an abolition of the institute. This would suppose a very intensive comparing of prices, which is not be expected in the case of low price products. On the other hand, the consumer will compare prices if he wants to buy a very expensive or long-lasting article. In this case recommended prices are very helpful, because they indicate the highest possible price of a product, and it facilitates price bargaining if the consumer knows both recommended and actual selling prices of several traders.

The author's discussion shows that the dispute about the importance of recommended prices suffers above all from not differentiating between products which are bought and consumed daily and durable goods. Furthermore, the previous articles are one-sided in that they concentrate almost entirely on prices. If one takes product quality into consideration as well, one will find that the present Law offers a good chance to ensure that products are supplied in a constant or improved quality. Recommended prices should therefore only be allowed if the manufacturer submits to recurrent quality controls of his products. The advantages of recommended prices pointed out in the article adhere only to price recommendations which are made known to all consumers; therefore, recommendations intended for retailers only should be prohibited.     

EQUITY CORRELATIONS IMPLIED BY INDEX OPTIONS: ESTIMATION AND MODEL UNCERTAINTY ANALYSIS

We propose a method for constructing an arbitrage‐free multiasset pricing model which is consistent with a set of observed single‐ and multiasset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained by solving a well‐posed convex optimization problem. Application of this method to equity and index options shows that, whereas multivariate diffusion models with constant correlation fail to match the prices of index and component options simultaneously, a jump‐diffusion model with a common jump component affecting all stocks enables to do so. Furthermore, we show that even within a parametric model class, there is a wide range of correlation patterns compatible with observed prices of index options. Our method allows, as a by product, to quantify this model uncertainty with no further computational effort and propose static hedging strategies for reducing the exposure of multiasset derivatives to model uncertainty.     

Dynamics of Stock Prices and Exchange Rates Relationship: Evidence From Five Sub-Saharan African Financial Markets

This article examines the dynamic relationship between stock prices and exchange rates for five Sub-Saharan African financial markets: Ghana, Kenya, Mauritius, Nigeria and South Africa. It uses weekly data, covering the floating exchange rate regime from January 14, 2000, to December 31, 2009, and applies both the Vector Autoregression and the Dynamic Conditional Correlation models. Results from the Vector Autoregression model suggest no evidence of cointegration between stock prices and real exchange rates for all the five countries in the sample. Results from the dynamic conditional correlation show that the correlation coefficients are not constant for the period under study, and the estimates largely show a negative time-varying correlation for all the countries except Ghana that indicates a positive correlation.     

Cost share‐induced technological change and Kaldor’s stylized facts

This paper presents a theory of induced technological change in which firms pursue a random, local, and bounded search for productivity‐enhancing innovations. Firms implement profitable innovations at fixed prices, which then spread through the economy. After diffusion, all firms adjust prices and wages. The model is consistent with a variety of price‐setting behaviors, which determine equilibrium positions characterized by constant cost shares and productivity growth rates. A fixed mark‐up can yield Marx‐biased technological change. Target‐return pricing yields Harrod‐neutral technological change with a fixed wage share as a stable equilibrium, consistent with Kaldor's stylized facts, while allowing for deviations from equilibrium, as observed in the longer historical record.     

The promise and peril of dynamic targeted pricing

Dynamic pricing is widely adopted in many industries, such as travel and insurance. These industries are also gaining extensive capabilities in identifying and segmenting customers, partly fueled by the increasing availability of data. It is natural to ask whether firms should take advantage of such developments by charging different prices to different customer segments. If so, under what conditions? We seek answers to these highly managerially relevant questions.We consider a market with two customer segments served by a monopolist. The monopolist can choose among a set of pricing strategies to exploit consumers’ inter-temporal preferences and/or inter-segment variations. At one end of the spectrum, the firm can charge a constant price to all customers, which is called static pricing. At the other end of the spectrum, the firm can charge different prices to different customer segments and vary these prices over time, which is referred to as dynamic targeted pricing. We systematically compare these alternative pricing strategies. We show that dynamic pricing without targeting can be more effective than static targeted pricing when customers are not very forward looking, which corroborates the findings in the empirical literature. Interestingly, we find that the monopolist can be worse off when she adopts targeting in addition to dynamic pricing. We conduct laboratory experiments to test several key model predictions. The studies show that individuals behave in a manner consistent with the predictions of our model.