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As we have noted, elasticity can be roughly compared by looking at the relative steepness or flatness of a supply or demand curve. Thus, it makes sense that the formula for calculating elasticity is similar to the formula used for calculating slope. Instead of relating the actual prices and quantities of goods, however, elasticity shows the relationship between changes in price and quantity. To calculate the coefficient for elasticity, divide the percent change in quantity by the percent change in price:
\(\text{Elasticity} = \text{% Change in Quantity}/\text{% Change in Price}\)
To find percent change, you divide the amount of change in a variable by the initial level of the variable:
\(\text{% Change} = \text{Amount of Change}/\text{Initial Level}\)
(Technically you should multiply by 100 to make it a proper percent, but since the 100 cancels out in the elasticity formula, we will ignore that extra step here.) Let's apply this by solving for elasticity in the market for ping pong balls. When ping pong balls cost $1 each, Alice is willing to buy 10 balls, and Joe is willing to sell 10 balls. When the balls cost $1.50 each, Alice is willing to buy 6, and Joe is willing to sell 20. First, let's solve for Alice's price elasticity of demand:
\(\text{% Change in Quantity} = (6-10)/10 = -0.4 = -40\%\)
\(\text{% Change in Price} = (1.50-1)/1 = 0.5 = 50\%\)
\(-40\% / 50\% = -0.8\)
\(\text{Elasticity of Demand} = -0.8\).
Now, we use the same process to find Joe's price elasticity of supply:
\(\text{% Change in Quantity} = (20-10)/10 = 1 = 100\%\)
\(\text{% Change in Price} = (1.50-1)/1 = 0.5 = 50\%\)
\(\text{Elasticity of Supply} = 100\%/50\% = 2\)
