Elasticity

Factors affecting the the magnitude of the own price elasticity of a good

Available substitutes, time, and expenditure share.

Elasticity concept

Conceptually, the quantity consumed of a good is relatively responsive to a change in the price of the good when demand is elastic and relatively unresponsive to changes in price when demand in inelastic. This means that price increases will reduce consumption very little when demand is inelastic. However, when demand is elastic, a price increase will reduce consumption considerably.

Elastic demand

Demand is elastic if the absolute value of the own price elasticity is greater than 1 |EQx,Px|>1 (When demand is elastic and increase in price leads to a reduction in total revenue) (When demand is elastic a price cut results in a greater than proportional increase in sales and thus increases the firms total revenues) (When demand is elastic, marginal revenue is positive)

Time (in reference to elasticity)

Demand tends to be more inelastic in the short term than in the long term. The more time consumers have to react to a price change, the more elastic the demand for the good. Conceptually, time allows the consumer to seek out available substitutes. For example, if a consumer has 30 minutes to catch a flight, he is much less sensitive to the price charged for a taxi ride to the airport than would be the case if the flight were several hours later.

Linear demand function

In a linear demand function, demand is elastic at high prices and inelastic at lower prices. Not that when Px=0, |EQx,Px|=|Ax•0/Qx|=0<1. In other words, for prices near zero, demand is inelastic. On the other hand, when prices rise, Qd decreases and the absolute value of the elasticity increases.

Available substitutes

Intuitively, the more substitutes available for the good, the more elastic the demand for it. In these circumstances a price increase leads consumers to substitute towards another product, thus reducing considerably the quantity demanded of the good. When there are few close substitutes for a good, demand tends to be relatively inelastic. This is because consumers can not readily switch to a close substitute when the price increases. The demand for food (a broad commodity) is more inelastic than the demand for beef. Short of starvation, there are no close substitutes for food, and thus the quantity demanded of food is much less sensitive to price changes than is a particular type of food.

Own price elasticity

Measures the responsiveness of quantity demanded to a change in price of that good; the percentage change in quantity demanded divided by the percentage change in the price of the good. EQx,Px=%change In Qdx/% change in Px

Cross-price elasticity

A measure of the responsiveness of the demand for a good to changes in the price of a related good; the percentage change in the quantity demanded of one good divided by the percentage change in the price of a related good. EQx,Px=%change in Qdx/% change in Py EQx,Py>0 whenever goods X and Y are substitutes, and an increase in the price of Y leads to an increase in the demand for good X. EQx,Py<0 whenever goods X and Y are complements, an increase in the price of Y leads to a decrease in the demand for X.

Own advertising elasticity of demand

The ratio of the percentage change in the consumption of good X to the percentage change in advertising spent on X. Cross-advertising elasticity between goods X and Y would measure the percentage change in the consumption of X that results from a 1% change in advertising directed toward Y.

Important aspects of an elasticity

1) whether it is positive or negative and 2) whether it is greater than 1 or less that 1 in absolute value. The sign of the elasticity determines the relationship between G and S. If the elasticity is positive, an increase in S leads to an increase in G(S:study,G:grade). If the elasticity is negative, and increase in S leads to a decrease in G. Whether the absolute value of the elasticity is greater or less than 1 determines how responsive G is to changes in S. If the absolute value of the elasticity is greater than 1, the numerator is larger than the denominator in the elasticity formula, and we know that a small percentage change in S will lead to a relatively large percentage change in G. If the absolute value of the elasticity is less than 1, the numerator is smaller than the denominator. In this instance, a given percentage change in S will lead to a relatively small percentage change in G.

Income elasticity

A measure of the responsiveness of consumers demand to changes in income. EQx,M=%change in Qdx/%change in M When good X is a normal good, an increase in income leads to an increase in the consumption of X. Thus EQx,M>0 when X is a normal good. When X is an inferior good, an increase in income leads to a decrease in the consumption of X. Thus, EQx,M<0 when X is an inferior good.

Elasticity

A measure of the responsiveness of one variable to changes in another variable; the percentage change in one variable that arises due to a given percentage change in another variable. (Eg. The elasticity of your grade with respect to studying, denoted Eg,s, is the percentage change in your grade (%change in G) that will result from a given percentage change in the time you spend studying (%change in S). In other words, Eg,s=%change in G/%change in S or Eg,s=(change in G/change in S) Change in G/ change in S represents the slope of the functional relation between G and S; it tells the change in G that results from a given a given change in S.

Inelastic demand

Demand is inelastic if the absolute value of the own price elasticity is less than 1 |EQx,Px|<1 (When demand is inelastic an increase in price increases total revenue) (The more inelastic the demand for a product, the greater the decline in revenue that results from a price cut, despite the increased quantity demanded) (When demand is inelastic the marginal revenue is negative)

Perfectly elastic demand

Demand is perfectly elastic if the own price elasticity is infinite in absolute value. In this case the demand curve is horizontal. When demand is perfectly elastic a manager who raises prices even slightly will find that none of the good is purchased. Generic products such as aspirin may face demand curves that are perfectly elastic

Perfectly inelastic demand

Demand is perfectly inelastic if the own price elasticity is zero. In this case the demand curve is vertical. When demand is perfectly inelastic, consumers do not respond at all to changes in price. (Life-saving drugs are seen to have a perfectly inelastic demand)

Unitary elastic demand

Demand is unitary elastic if the absolute value of the own price elasticity is equal to 1 |EQx,Px|=1 ( total revenue is maximized when demand is unitary elastic) (When demand is unitary elastic marginal revenue is zero)

Expenditure share

Goods that comprise a relatively small share of consumers budgets tend to be more inelastic than good for which consumers spend a sizable portion of their incomes. In the extreme case, where a consumer spends their entire budget on a good, the consumer must decrease consumption when the price rises. In essence, there is nothing to give up but the food itself. When goods comprise only a small portion of the budget, the consumer can reduce the consumption of other goods when the price of the good increases. For example, most consumers spend very little on slat; a small increase in the price of salt would reduce quantity demanded very little, since salt constitutes a small fraction of consumers' total budgets.

Total revenue test

If demand is elastic, an increase in price will lead to a decrease in total revenue. If demand is inelastic, an increase in price will lead to an increase in total revenue. Finally, total revenue is maximized at the point where demand is unitary elastic.

Marginal revenue

The change in total revenue due to a change in output, and that to maximize profits a firm should produce where marginal revenue equals marginal cost. The marginal revenue curve is less than the price for each unit sold. If the original price were $5/unit then for another unit to be purchased the price will have to drop to $4 now the firms revenue has changed from $5 to $8 because the drop in price created another purchase of a unit. So In turn, total revenue increases but marginal revenue is gathered by, $8-$5=$3. MR=P[1+E/E]