Elasticity Essay, Research Paper


Elasticity is the responsiveness of demand or supply to the changes in prices or income. There are various formulas and guidelines to follow when trying to calculate these responses. For instance, when the percentage of change of the quantity demanded is greater then the percentage change in price, the demand is known to be price elastic. On the other hand, if the percentage change in demand is less than then the percentage change in price,

Like that of demand, supply works in a similar way. When the percentage change of quantity supplied is greater than the percentage change in price, supply is know to be elastic. When the percentage change of quantity supplied is less then the percentage change in price, then the supply then demand is known to be price inelastic.

The following text is real world examples of these economic principles. They have been provided to build a bridge between current economic situations and economic principles of elasticity.

The Demand for Lotto: The Role of Conscious Selection

In this article is a discussion about the elasticity of demand for lottery tickets. Time series data was used in a way in which the expected value of the lottery ticket would vary due to rollovers (Farrel 1). It was found that there are far more rollovers than expected given the lottery design (Farrel 1). There was also some strong evidence found that supported that individuals did not pick their numbers in a uniform matter. The inverse supply function was found by using estimates that enabled them to identify the demand elasticity (Farrel 1).

This analysis was based on the U.K. National Lottery that came about November 1994. With this in mind we realize that because game designs are similar throughout the world, these findings are more widely relevant (Farrel 1).

The price elasticity of demand for lottery tickets shows that demand varies depending on the expected return from a winning ticket (Farrel 1). From this we deduce that this elasticity is relevant to the design of the lottery (Farrel 1). The way that the demand elasticity is derived is by comparing the rollover weeks with the non-rollover weeks. By doing this, the normal demand is recorded during the non-rollover weeks to see what level the demand is usually at. Then from there they can see how the demand increases as the lottery rolls over.

Depending on rollovers for this study poses a problem. Rollovers should occur infrequently leaving the chance of not having enough variance in the data to create a reliable estimate (Farrel 2). However, one of the surprising details of the data is that rollovers occurred more regularly then if it was generated by “statistical chance” (Farrel 2). What this means to the U.K. lottery is that when ticket sales are at their mean level of 65 million with a 6-ball lottery; there is a one percent chance of rollover. Being that a high rollover rate is common in to all lotto games, the U.K. lottery yielded 19 rollovers from the 116 draws that were studied (Farrel 2).

The reason for this high rate of rollovers is that the people that are choosing the numbers are choosing them in a non-uniform way. This means that they cover a smaller range of combinations with their numbers. This also helps in explaining why when someone does win there is usually more than one winner (Farrel 2).

The Elasticity of Demand for Lotto Tickets

And the Corresponding Welfare Effects

This article did a study using the first 254 weeks of the Florida Lottery. The study shows evidence of the Florida Lottery price elasticity being near unity. This happens when employing a measure of lotto ticket price that is superior to that used by others (Mason 1). From these results it may be, in comparison to other states, that Florida has room to increase the odds to increase the price elasticity of demand to the revenue-maximizing level (Mason 1).

Price Elasticity of Demand and an Optimal

Cash Discount Rate in Credit Policy

The provision of a cash discount in setting up credit terms is equivalent to a reduction in price. Generally, it is assumed that when a cash discount is administered it will result in a higher level of sales. This assumption is only consistent with price elastic demand (Rashid 1). If the demand of a product is deemed price inelastic, then a cash discount will lower sales (Rashid 1). “Frantz Viscione (1976), in a survey of over 100 U.S. manufacturing firms, show that the introduction (and in some cases the elimination) of a cash discount led to more (or less) profits for some firms, less (or more) profits for some other firms and no change in profitability for the remaining firms. These findings are consistent with the differential effects of the cash discount in situations of elastic, inelastic, and unitary elastic demand (Rashid 1).”

When looking at the case of either elastic or inelastic demand, the provision a cash discount adds another benefit (cost) to be considered during the analysis of the determination of an optimal cash discount rate (Rashid 1). Regardless, there is still a level of inelasticity where all the marginal gains from a cash discount are exactly outweighed (Rashid 1).

Price elasticity may differ from one geographical location to the next. Hotch, Kim, Montgomery, and Rossi (1995) did a study that estimated the “store specific price elasticities of demand” for a chain of nearly 85 supermarkets (Rashid 1).

Among the findings of this study was that they found eleven demographic and competitive variables. These eleven variables helped to explain around sixty seven percent of the variations in elasticity (Rashid 2). From these it finding it is said that if a store is having different price elasticities for a product in different locations, that it should set different cash discounts accordingly.

Estimating Price Elasticities with Theory-Based Priors

Price elasticity can be improved in demand systems that involve multiple brands and multiple stores. “They treat these demand models in a hierarchical Bayesian framework (Montgomery 1).” Montgomery uses prior information based on the restrictions imposed by additive utility models. To explain additive utility approaches further, price elasticities are driven by a general substitution parameter as well as brand-specific expenditure elasticities (Montgomery 1). Along with the additive utility approach, Montgomery also used a differential shrinkage approach. Differential shrinkage is when the price elasticities are held close to restrictions of the additive utility theory and “store-to-store variation is accommodated through differences in expenditure elasticities.” After applying these new methods, Montgomery found that there were drastic improvements over the existing Bayesian and non-Bayesian methods (Montgomery 1).

The Detailed scanner data and pricing conditions have been made available for nearly every type of consumer-packaged good and all major retail formats. What does this do? It makes it possible to analyze and study the market structure, brand competition, and elasticity-based approaches to optimal pricing. (Montgomery 1). After analyses on the estimation of a demand system and the associated price elasticities, individual stores or groups of stores can exhibit micro-pricing. This is when the individual stores or the groups of stores charge different prices to exploit differences in consumer price sensitivity (Montgomery 2).

Regardless of the attempts of a quantitative demand-based approach to pricing issues, it is still distant from fully calculating the price that creates the best demand elasticity. This is because it is difficult to get reasonable price elasticity estimates.


There are many different types of elasticities. They can be found in just about every retail store. With this in mind, we note that there are new and old methodologies to study, analyze, and estimate relevant price elasticities.

This paper was an gateway to seeing how some studies and economic research has been taking place and where. I found some of the studies to be trivial. This meaning that the authors used creative techniques to figure and estimate some of the elasticities. I also found it interesting how I could relate to the real life situations such as the Lottery. For example, when the lottery starts rolling over it creates a hype, and the demand goes up. I was always aware of this phenomenon but never realized what it actually was.


Work Cited

Farrell, Lisa; Hartley, Roger; Lanot, Gauthier; Walker, Ian

The Demand for Lotto: The Role of Conscious Selection, Journal of Business & Economic Statistics, Apr2000, Vol. 18 Issue 2.

Mason, Paul M.; Steagall, Jeffrey W., The elasticity of

demand for lotto tickets and the corresponding welfare effects., Public Finance Review, Sep97, Vol. 25, Issue 5.

Rashid, Muhammad; Mitra, Devashis, Price Elasticity of

Demand and an Optimal Cash Discount Rate in Credit Policy, Financial Review, Aug99, Vol. 34 Issue.

Montgomery, Alan L.; Rossi, Peter E., Estimating Price

Elasticities with Theory-Based Priors, Journal of Marketing Research, Nov99, Vol. 36 Issue 4.

Table of Contents

Introduction 1

The Demand for Lotto: The

Role of Conscious Selection 1

The Elasticity of Demand

for Lotto Tickets And the

Corresponding Welfare Effects 3

Demand and an Optimal Cash Discount

Rate in Credit Policy 4

Estimating Price Elasticities

with Theory-Based Priors 5

Conclusion/Summary 7

Work Cited 8

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