Definitions and Formulas

Elasticity can be best thought of as a measure of responsiveness. It is a very generic term defined as a ratio of two percentage changes. When we talk about demand elasticity we are talking about how some factor affects demand and the percentage change in quantity demand will be in the numerator.  Similarly, when we are talking about supply elasticity we are talking about how some factor affects supply, and the percentage change in quantity supplied will be in the numerator. 

For example the income elasticity of demand would be used as a measure of the responsiveness of demand to changes in income.  From your study of demand you know an increase in income will generally increase demand.  Income elasticity is simply a precise measure of this relationship - it is defined as the ratio of the percentage change in demand to the percentage change in income. If you knew the income elasticity of demand wad 2, then you would expect demand would increase by 20 percent as income expanded by 10 percent. 

When would this information be important?  Income elasticity can be important if you are interested in the cyclical or secular properties of demand.   For example, we would expect the income elasticity of demand for automobiles to be rather high, while the income elasticity of demand for food to be rather low.  As an economy went into a recession and income fell, you would expect demand for automobiles to fall more than demand for food. As we will discuss in the section on determinants of elasticity, even in the recession you can be expected to eat, although you may postpone the purchase of that car.  This is why you are more likely to hear about auto worker layoffs than you are to hear about unemployment on the farms during recessions. 

If we take the long view, meanwhile, we would expect to see demand for autos rise more than demand for food as a country grows.  This is why you hear so much about the growth in auto demand in the world's poorer countries that are growing rapidly - why environmentalists are terrified about the prospect of hundreds of millions on Chinese turning in their bicycles for cars as income in the nation continues to grow rapidly. 

As important as income elasticity may be, attention is usually focused on the own-price elasticity of demand, or in its shortened version, the price elasticity of demand, or the even shorter version, elasticity of demand. The price elasticity of demand is a measure of how demand responds to price changes and it would be calculated by dividing the percentage change in demand by the percentage change in price. As we will see later, the size of the resulting number will matter when we look at the relationship between revenue and price. If demand is unresponsive, we would talk about inelastic demand while a responsive demand would be referred to as elastic demand.

The formulas for demand and supply elasticities are:

• Income elasticity of demand
  • definition: responsiveness of demand to income change
  • formula: e_y = %DQ/%DY
• Cross-price elasticity of demand
  • definition: responsiveness of demand (good A) to change in price of another good (price of B)
  • formula: e_c = %DQ_A/%DP_B
• Own-Price elasticity of demand
  • definition: responsiveness of demand to price change
  • formula: e_p = %DQ/%DP
  • possibilities
    • inelastic: unresponsive = | e_p | < 1
    • elastic: responsive | e_p | > 1
    • unitary elastic: | e_p | = 1
• Own-Price elasticity of supply
  • definition: responsiveness of supply to price change
  • formula: e_ps = %DQ_s/%DP

Now that you have looked at the formulas, what are you to do with them?  A suggestion is to think of the formulas as an equation with three unknowns where you are given two of the unknowns and you must solve for the third.   As an example, consider the following question which is very similar to review question number 5.

If the price elasticity of demand is -2 and you wanted the output sold by a company to increases 10 percent, what would you suggest as a price strategy?

You need to start by recognizing we are talking about the relationship between price and quantity demanded - we are talking about own-price elasticity.   The formula is:   e_p = %DQ/%DP.  In this problem we have the figure for elasticity (2) and for the desired change in Q (6).  If you now plug this into the equation you get:

e_p = %DQ/%DP

-2 = 10/(%DP )  

where you need to solve for %DP.  With the help of some algebra you can get %DP   = 10/-2 = -5.   If you are to increase demand by 6 percent, you will need to decrease the price by 5 percent. 

To try one more, assume that in the last recession you observed that when income went down by 6 percent, demand went down by 3 percent.   What is the income elasticity of demand? 

You need to start by recognizing that we are talking about the relationship between income and quantity demanded - we are talking about income elasticity.   The formula is:   e_y = %DQ/%DY .  In this problem we have the figure for percentage change in income (-6) and for the percentage change in  demand (-3).  If you now plug this into the equation you get:

e_y = %DQ/%DY

e_y = -6/-3  =  2

where you need to solve for e_y.    The solution is that the income elasticity is 2.