Theory of Elasticity

Elasticity:

Chapter Summary:

The elasticity of demand evaluates the responsiveness of demand to modifications in a factor that influences demand. Elasticity can be estimated for income, price, prices of correlated products, and advertising expenses. The own-price elasticity is the ratio of percentage change in the quantity demanded to percentage change in price, and is a negative number. Demand is price elastic if a 1 percentage raise in price leads to more than a 1 percentage drop in quantity demanded and inelastic when it leads to less than a 1prcentage drop in quantity demanded.

The own-price elasticity can be employed to forecast the consequences of price changes on quantity demanded and buyer expenses. Elasticity can be employed to forecast the consequences on demand of concurrent changes in multiple factors. All elasticity differs with adjustment time. The long-run demand is usually more elastic than the short-run demand in case of nondurables, however not essentially for durables.

Elasticity can be predicted from records of precedent experience or test markets by the statistical method of multiple regressions.

Key Concepts:

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General Chapter Objectives:

A) Elucidate the concept of elasticity.

B) Illustrate the arc approach and the point approach if deriving the own-price elasticity of demand and talk about the properties of own-price elasticity.

C) Talk about the intuitive determinants of the price elasticity.

D) Mention the relationship between own-price elasticity and total revenue if there is a price modification for an elastic and an inelastic item.

E) Explain the application of cross-price elasticity, income elasticity and advertising elasticity, as and also forecasting the consequences of multiple factors on demand.

F) Elucidate the significance of time on elasticity.

G) State the statistical estimation of elasticity.
 
Notes:

1) Elasticity of demand:

(i) Definition: the awareness of demand to changes (that is, decrease or increase) in an underlying factor (example: price of the product itself, income, prices of correlated products and advertising).

(ii) Modifications in any of such factors will lead to a movement all along or shift of the demand curve.

(iii) There is an elasticity equivalent to every factor (that is, measuring the responsiveness of demand to modify in each factor) which affects demand.

(iv) Elasticity based on the time accessible for adjustment.

(v) With elasticity, managers can predict the consequence of single or multiple modifications in the factors underlying demand.

(vi) Construction: The two ways of computing the elasticity of demand with respect to all factors which affect demand as:

  • Arc approach: Evaluates the percentage change in the quantity demanded divided by percentage change in underlying factor. This approach computes the elasticity among two points on demand curve.
  • Point approach: Computes the coefficient from a mathematical equation, in which the quantity demanded is the function of underlying factor being inspected and other variables.  This approach computes the elasticity at a particular point on the demand curve.
  • For an infinitesimally short arc, the arc and point approaches generate similar numbers.    

2) Own-price elasticity of demand (that is, price or demand elasticity).

(i) Definition:

  • Percentage by which the quantity demanded will modify when the price of the item increases by 1percentage.
  • Percentage (or proportionate) change in the quantity demanded divided by percentage (or proportionate) change in price.

(ii) Every demand curve (comprising the market demand curve, individual demand curve, and the demand curve faced by an individual seller) has corresponding own-price elasticity.

(iii) Construction:

  • Arc approach: computes the percentage change in quantity demanded (that is, change in quantity demanded or average quantity demanded) divided by the percentage change in price (that is, change in price or average price).
  • Point approach: computes the coefficient from a mathematical equation, in which the quantity demanded, is the function of the price and other variables. The own-price elasticity is a coefficient of price.
  • For an infinitesimally small modification in price, the arc predicts equals the point elasticity.

(iv) Properties:

  • This is a negative number (at times reported as an absolute number)
  • This is a ratio of two proportionate modifications, and therefore a pure number independent of units of measurement. 
  • It ranges from 0 (where a large percentage change in price causes no change in the quantity demanded) to negative infinity (where an infinitesimal percentage change in the price causes a big change in the quantity demanded).
  • The demand is considered as price inelastic when a 1percent increase in price leads to less than a 1percent drop in the quantity demanded;  
  • The demand is considered as price elastic when a 1percent increase in price leads to a greater than 1percent drop in the quantity demanded.

(v) Intuitive factors influencing own-price elasticity.

(a) The accessibility of indirect or direct substitutes influences the elasticity of demand.

  • Fewer substitutes are accessible, the less elastic the demand.
  • The more particularly defined the item (that is, a particular brand of cigarettes), the more elastic will be its demand. The product category (cigarettes as an entire) will be relatively less elastic.

(b) The buyer's previous commitments.

(c) Cost relative to the advantage from searching for better prices (that is, buyers have restricted time therefore they focus on items which account for relatively bigger expenditures).

Note: The balance between the cost and benefit of economizing as well depends on a possible divide between the person who incurs the cost of economizing and the person who gains.

(d) Modifications in any of the other factors influencing demand.

(vi) Own-price elasticity of the demand and slope of a demand curve.

  • Own-price elasticity explains the shape of only one part of the demand curve.
  • Whether the demand curve is a curved or straight line, the own-price elasticity can differ with modifications in the price of item.
  • Even whenever the slope remains steady, the proportional modifications in price and quantity demanded all along the demand curve signify the own-price elasticity will differ.
  • The steeper is the demand curve; the less elastic is demand, and vice-versa.

(vii) Predicting quantity demanded and expenses.

a) Given the own-price elasticity of demand, a seller (that is, both an individual seller and the whole market) can predict the result of price changes on:

  • Quantity demanded (that is, sales from the point of view of an individual seller); and 
  • Expenditure (that is, quantity demanded x price) (or revenue from the view-point of an individual seller).

b) When demand is price inelastic, a seller can raise profit by the raising price:

  • A price raise causes the drop in quantity demanded (that is, the fall in sales) to be proportionally smaller than the raise in price; 
  • Expenses (and revenue) will raise; and
  • As production is decreased, costs are lowered and gain increased.

c) When demand is price elastic and a seller increases the price:

  • The fall in quantity demanded will be proportionally bigger than the raise in price; and
  • Expenses will be decreased.

d) Accordingly, this is in the best interest of a seller to increase the price till the demand becomes price elastic.

(viii) Forecasting the consequence of price modifications on quantity demanded and expenses: accuracy.

a) Use of demand curve: more exact forecasts.

b) Utilization of own-price elasticity.

  • Not as precise as employing the full demand curve as own-price elasticity might vary all along a demand curve.
  • Does not give as much information as full demand curve.
  • Usually, the error in forecast, based on the own-price elasticity will be bigger for bigger changes in the price and the other factors which affect demand.
  • However managers seldom recognize the whole demand curve, as their information is very limited to the quantity demanded about the present values of the factors which affect the demand.
  • Elasticity gives enough information for most business decisions.

3) Income elasticity of demand:

A) Definition: The percentage by which the quantity demanded will modify if the buyer's income increases by 1percent.

B) Construction: Arc approach, Point approach.

C) Properties:

i) With properties identical to those of own-price elasticity, however the difference in that income elasticity can be a positive number.

ii) This is a ratio of two proportionate changes, and therefore a pure number independent of units of measurement

iii) It ranges from negative infinity to the positive infinity.

  • Normal products (or positive income elasticity): when income increases, demand increases.
  • Inferior products (or negative income elasticity): when income increases, demand drops.

D) Demand is considered as income inelastic if 1percent increase in income leads to less than a 1percent change in the quantity demanded;

E) Demand is considered as income elastic if 1percent increase in income leads to a greater than 1percent change in the quantity demanded.

F) Factors affecting own-price elasticity:

  • Demand for requirements tends to be comparatively less income elastic than the demand for discretionary items.
  • Modifications in any of other factors (comprising price) affecting demand.

G) Forecasting quantity demanded and expenses. The main difference between income and some other variables which affect demand like price and advertising is that, usually, sellers contain no control over buyer's income.
 
4) Cross-price elasticity of demand:

a) Definition:

  • It is a percentage by which the demand of first item will modify if the price of a second item (that is, a related product) increases by 1percent.
  • Other things equivalent (comprising the own price of first item).

b) Properties:

i) It ranges from negative infinity to the positive infinity.

  • Substitutes (or positive cross-price elasticity): a raise in the price of one will raise the demand for the other. The more two items are substitutable, the greater their cross price elasticity.
  • Complements (or negative cross-price elasticity): a raise in the price of one will decrease the demand for the other.

ii) The demand is considered inelastic with respect to price of a second item if a 1percent increase in the price of the second item leads to a less than 1percent change in the demand of first item.

iii) Demand is considered as elastic with respect to price of a second item when a 1percent raise in the price of second item leads to more than 1percent change in the demand of first item.
 
5) Advertising elasticity:

a) Definition: It is a percentage by which the demand will modify when the seller’s advertising expenses increase by 1percent.

b) Most of the advertising is undertaken by individual sellers to encourage their own business. By drawing buyers away from the competitors, advertising has a much stronger result on the sales of an individual seller than market demand.

Advertising elasticity of the demand faced by an individual seller tends to be bigger than the advertising elasticity of market demand. 
 
6) Factors affecting all elasticity:

a) Buyers require time to adjust: Adjustment time is a factor which affects all elasticity (example: own-price elasticity).

  • Differentiate between long run and short run.
  • Short run for the buyer: the time horizon in which a buyer can’t adjust at least one item of consumption or usage.
  • Long run for the buyer: the time horizon long adequate to adjust all items of usage or consumption.
  • The long run demand is usually more elastic than the short run demand for in the situation of nondurables, however not necessarily for durables.

b) Substitution frequency effect: It affects all elasticity. For illustration, with respect to income elasticity,

  • Short run: a fall in income will cause demand to go down more sharply in short run. 
  • Long run: the consequences on sales will be muted.

c) Nondurables (comprising services and goods, example: commuter train services): the longer the time which buyers have to adjust, the greater will be the response to a price change, and thus the relatively more elastic the demand in long run.

d) Durables (example: automobiles): the main difference between short and long-run elasticity of demand based on a balance between the requirement for time to adjust and the substitution frequency effect.

e) Just as short-run elasticity can be employed to forecast the consequence of multiple (short-run) modifications in the factors which affect demand, we can as well apply similar technique to forecast the consequence of long-run changes, employing long-run elasticity in place of short-run elasticity.
 
7) Forecasting the consequence of multiple factors. We can forecast the percentage change in demand due to modifications in multiple factors (at times pushing in various directions) by just summing the percentage modifications due to each separate factor, employing elasticity.
 
8) Estimating elasticity: Elasticity can be predicted from records of past experience or test markets through statistical method of multiple regressions.

a) Businesses sell various products and or cater to distinct buyers, and face various demand curves.

b) Data:

i) Types of data:

  • Time series: a record of modifications over time in one market, obtained by focusing on a specific group of buyers and observing how their demand modifies as the factors influencing demand differ over time.
  • Cross section: It is a record of data at one time over some markets, obtained by comparing quantities purchased in the markets with distinct values of the factors influencing demand.

ii) Compilation of data:

  • Past experience (example: statistics and records, private or public).
  • Surveys and experiments (example; test markets on genuine buyers making real purchases).

(c) Specification:

i) Dependent variable: the variable whose modifications are to be described.

ii) Independent variable: a factor influencing the dependent variable.

d) Multiple regressions: a statistical method to predict the separate consequence of each and every independent variable on dependent variable.

i) Aims to predict values for constant and coefficients of independent variables.
ii) Estimated coefficients diminish the sum of squares of the residuals (residual = difference between real value of dependent variable and predicted value).

(e)  Interpretation:

i) Employ estimated coefficients to compute corresponding elasticity.  
ii) R-squared and F-statistic measure overall importance of equation.
iii) t-statistic measures importance of specific independent variable.

Question-Answer:

There is an expert report in the litigation between the recording industry and Napster. It is concluded that: “the evidence recommends that exchanges facilitated by the Napster and others stimulate overall demand for recorded music”. One piece of proof cited was that, between the initial quarters of 1999 and 2000, U.S. CD sales grew by 6.7percent as compared with a 5percent increase in the real gross domestic product (or GDP) over similar period.

a) How would the raised penetration of computer systems equipped with fast CD drives and high-quality speakers have influenced the demand for music CDs?

b) The income-elasticity of demand for music CDs has been predicted to be 0.8. Employing this elasticity, compute by how much the real GDP growth would have increased CD sales.

c) How would you utilize the price-elasticity of demand for music CDs and the change in an average CD price to predict the impact of price modifications on the demand for CDs?

d) Provide a formula which incorporates (a)-(c) above to appropriately measure Napster’s impact on music CD sales.

Answer:

a) These computers are complement to the music CDs. The raised penetration would have increased the demand for music CDs.

b) The real GDP growth would have increased CD sales by 0.8 x 5% = 4%.

c) The consequence would be price-elasticity of demand times, the average modification in the CD price.

d) The change in CD sales, 6.7% = 4% + impact of computer penetration + impact of price change + impact of Napster. 
Therefore, Napster’s impact = 2.7% - impact of price change - impact of computer penetration.

 

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