Barry Haworth
University of Louisville
Department of Economics
Economics 201

### Calculating Elasticity

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 \$5000 \$6000 \$6000 Sales (in millions) \$500 \$300 \$360

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 \$5000 \$6000 \$6000 Sales (in millions) \$500 \$300 \$360 Quantity sold (in thousands) 100 50 60

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.