University of Louisville

Department of Economics

Economics 201

The chart below shows the price and sales data of good A
for three months. Assume that there is no inflation during this
period and that very small shifts in Supply, along the Demand
curve, have caused the changes below.

January | February | March | |

Price | |||

Sales (in millions) |

Between February and March, consumer income
rose by 2%.

**Calculate the (own) price elasticity of demand (January - February)****Calculate the income elasticity (February - March)**

1. Measuring (demand) elasticity necessitates
the calculation of changes in physical quantities, not dollar
sales. Therefore, the first step is to make sure that we are working
with the proper variables. Sales is transformed into quantity
sold if we divide sales by price. Correspondingly, our table changes
as follows:

January | February | March | |

Price | |||

Sales (in millions) | |||

Quantity sold (in thousands) |

2. There are three different versions of demand elasticity:
the (own) price elasticity of demand, the income elasticity of demand, and the
cross price elasticity of demand.
Those equations are listed (respectively) below.

In each case, we find the percentage change in the quantity of good A (denoted by the superscript) and divide it by the percentage change in some other variable (the price of good A, consumer income and the price of good B respectively).

In this example, I calculated each percentage change by dividing a subtraction problem (e.g. the difference between two quantities) by an "average" (e.g. one quantity added to another quantity, and then that divided by two). It's possible to calculate percentage changes using other approaches.

To answer the two (boldfaced) questions above, we only need the first two
equations. This is because the first question relates good A's price to the quantity demanded of good A, and the second question relates consumer income to the quantity demanded of good A.

3. Calculate each elasticity by plugging the
appropriate values from the table into the relevant equation.

Note that the answer is a negative number.
With (own) price elasticity of demand, this is always true as
long as the demand curve is negatively sloped. Therefore, we often
state this elasticity measure in terms of absolute value (we don't
do this with the other two measures though). Since the solution
is greater than one in absolute value, we say that this is an
elastic good. If it was less than one in absolute value, it would
be called an inelastic good.

To find the income elasticity, we simply need
to calculate the percentage change in quantity - since the percentage
change in income is already given as 2% (which we write in the
denominator as .02)

Unlike the (own) price elasticity, this income
elasticity is a positive number. However, this is not necessarily
always the case. Sometimes income elasticity is negative too.
A positive income elasticity means that the good we're looking
at is a normal good. If it's negative, then it's an inferior good.