Elasticity of demand


Income elasticity of demand
Introduction
Income elasticity of demand measures the relationship between a change in quantity demanded and a change in income. The basic formula for calculating the coefficient of income elasticity is:

% change in quantity demanded of good X
% change in real consumers' income



Normal Goods


Normal goods have a positive income elasticity of demand so as income rise more is demand at each price level. We make a distinction between normal necessities and normal luxuries (both have a positive coefficient of income elasticity).
Necessities have an income elasticity of demand of between 0 and +1. Demand rises with income, but less than proportionately. Often this is because we have a limited need to consume additional quantities of necessary goods as our real living standards rise. The class examples of this would be the demand for fresh vegetables, toothpaste and newspapers.
Luxuries on the other hand are said to have an income elasticity of demand > +1. Luxuries are items we can (and often do) manage to do without during periods of below average income and falling consumer confidence. When incomes are rising strongly and consumers have the confidence to go ahead with “big-ticket” items of spending, so the demand for luxury goods will grow.


Inferior Goods


Inferior goods have a negative income elasticity of demand. Demand falls as income rises. In a recession the demand for inferior products might actually grow (depending on the severity of any change in income and also the absolute co-efficient of income elasticity of demand). For example if we find that the income elasticity of demand for cigarettes is -0.3, then a 5% fall in the average real incomes of consumers might lead to a 1.5% fall in the total demand for cigarettes (ceteris paribus).

Price Elasticity


Price elasticity of demand is an elasticity that measures the nature and degree of the relationship between changes in quantity demanded of a good and changes in its price. For example, if, in response to a 10 % fall in the price of a good, the quantity demanded increases by 20 %, the price elasticity of demand would be 20 %/(− 10 %) = −2.
In general, a fall in the price of a good is expected to increase the quantity demanded, so the price elasticity of demand is negative as above. The demand for a good is considered inelastic when the quantity demanded does not change much with the price. Neccesities have highly inelastic demand curves (approaching vertical lines). For instance, antibiotics may cure a person who would otherwise die. The sick person will likely pay anything for the neccesary medication to keep himself alive. By constrast, elastic goods face large changes in quantity demanded with relatively small changes in price. Elastic goods have demand curves that approach horizontal lines. Elastic goods are usually those with very similar substitutes. For example, if you might buy a twenty sticks of generic chewing gum a week at $.05 a stick. If the price goes up to $.06, you switch over to another generic brand of gum. Your weekly quantity demanded has shifted from twenty to zero. A sharp decrease for only a slight change in price.

Mathematical Definition

The formula used to calculate the coefficient of price elasticity of demand is

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Elasticity and Revenue

When the price elasticity of demand for a good is inelastic (|Ed| < 1), the percentage change in quantity is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa.
When the price elasticity of demand for a good is elastic (|Ed| > 1), the percentage change in quantity is greater than that in price. Hence, when the price is raised, the total revenue of producers falls, and vice versa.
When the price elasticity of demand for a good is unit elastic (or unitary elastic) (|Ed| = 1), the percentage change in quantity is equal to that in price. Hence, when the price is raised, the total revenue remains unchanged. The demand curve is a rectangular hyperbola.
When the price elasticity of demand for a good is perfectly elastic (Ed is undefined), any increase in the price, no matter how small, will cause demand for the good to drop to zero. Hence, when the price is raised, the total revenue of producers falls to zero. The demand curve is a horizontal straght line. A ten-dollar banknote is an example of a perfectly elastic good; nobody would pay $10.01, yet everyone will pay $9.99 for it.
When the price elasticity of demand for a good is perfectly inelastic (Ed = 0), changes in the price do not affect the quantity demanded for the good. The demand curve is a vertical straight line; this violates the law of demand. An example of a perfectly inelastic good is a human heart for someone who needs a transplant; nobody would buy more than the exact amount of hearts demanded, no matter how low the price is.

Point Elasticity

The price elasticity of demand can be calculated at a specific price and quantity. This is called the point price elasticity and is different at every price. To calculate point price elasticity uses the formula:

Point Elasticity = (% change in Quantity)/(% change in Price)

The slope of the demand function P1 is the original price Q1 is the original quantity The Total-Revenue Test The test for demand elasticity is based on the relationship between price and elasticity. As it turns out, there is a direct mathematical link between price, revenue, and elasticity. There is a relationship between the change in revenue and the change in price that brought it about. This relationship will depend on the elasticity of demand. The total-revenue test is a straightforward application of this result: dR/dP Q(1 - Ed). If demand is elastic, Ed > 1, then dR/dP < 0: price and total revenue move in opposite directions. If demand is inelastic, Ed < 1, then dR/dP > 0: price and total revenue move in the same direction. Finally, if demand is unit elastic, Ed1, then dR/dP = 0: an increase in price leaves total revenue unchanged.


Sources:
http://en.wikipedia.org/wiki/Price_elasticity_of_demand
www.tutor2u.net/economics/content/topics/**elasticity**/income_**elasticity**.htm - 18k
http://www.mintercreek.com/micro/revenue.html
http://www.mhhe.com/economics/mcconnell15e/graphics/mcconnell15eco/common/dothemath/totalrevenuetest.html
http://www.idbsu.edu/econ/lreynol/web/PDF/Elasticity.pdf
Santerre and Neun, Health Economics, Edition 4, copyright 2007

Sample Questions:


1) We know that the demand for a good or service is inelastic if?
a. When price rises, quantity demanded falls
b. When price rises, total revenue falls
c. When price rises, total revenue rises
d. When price rises, quantity demanded rises
If prices rise and demand stays the same then total revenue will increase.

2) The local hospital discovered that when it charged $50 for a flu shot, they had 500 patients, but on the first day of the month when the price was discounted to $40 for a shot there were 650 people who received the shot. This implies that the elasticity of demand for the flu shot is?
a. Unit elastic
b. Perfectly elastic
c. Price inelastic
d. Price elastic
Its elastic because when the price decreased the demand increased.

3) A pharmacy reduces its handling fees by 10% and finds that the demand for prescription deliveries rises by only 3%. Which of the following would describe the price elasticity of demand?
a. It is elastic
b. It is inelastic
c. It is perfectly inelastic
d. It is perfectly elastic
If it was more elastic there would have been a greater demand for the decrease in the handling fees.

4) The quantity of healthcare consumed falls by 14% if the price a of healthcare services increases by 9% then the health care services demand would be
a. 1.6
b. .64
c. .012
d. none of the above
Price Elasticity = (% change in Quantity)/(% change in Price)