## Calculating PED

You will be expected to calculate and use elasticity, and to interpret given data. This may happen in any of the papers that are taken. As we have seen price elasticity of demand is calculated and defined as:

Where Qd = Quantity demanded

and P = Price

So, to calculate the value of the price elasticity, we simply need to substitute the appropriate values in this equation. Let's look at this calculation through some examples.

### Example 1 - price elasticity of demand

A product sells for $100 per unit, and the demand at that price is 10,000 units per week. The firm increases its price to $110 each and sales fall to 8,000 units per week. What is the price elasticity of demand for the product, and what effect will the price rise have on the firm's revenue?

P1 | $100 | Q1 | 10,000 |
---|---|---|---|

P2 | $110 | Q2 | 8,000 |

Change in price | +10 | Change in quantity demanded | -2,000 |

Percentage change in price | +10% | Percentage change in quantity demanded | -20% |

Price elasticity of demand = % change in quantity demand / % change in price = -20 / +10 = **-2**

Demand in this case is elastic, i.e. the numerical value is greater than 1.

Sales revenue was $100 x 10,000 = $1,000,000 and became $110 x 8,000 = $880,000

Revenue has fallen.

Remember, if demand for a good or service is price elastic then an increase in price will decrease both sales and sales revenue. However, a price cut will increase both sales and revenue.

### Example 2 - price elasticity of demand

A product has a PED (price elasticity of demand) of 0.8. At present it sells for $10 and sales have reached 100,000 per month. The firm is planning a price increase to $12 each. What can it expect to happen to sales and revenue if it goes ahead with the rise?

First remember that price elasticity is negative, and then use the formula that you know.

P1 = $10 | P2 = $12 | Change in P = $2 (+20%) |

PED = 0.8

Cross-multiply and find:

% change in quantity = -0.8 x 20 = - 16%

New sales = 84% (100,000) = 84,000

Price would go up and sales would fall, as expected.

Revenue was $10 x 100,000 = $1,000,000

Would become $12 x 84,000 = 1,008,000

Revenue, on the other hand, would increase by $8,000.

### Measuring elasticity

Price elasticity is based on the demand curve. In fact, the elasticity is the gradient of the demand curve at a particular point. i.e mathematicians will note that it is the differential of the demand function, in fact. This means it is a static measure, since it is based on static, or equilibrium data.

In the real world elasticity is very difficult to measure. There are far too many variables, and these change all the time. Quantitative data is rare, but qualitative data can be useful.

It is useful to remember that essentials tend to be price inelastic, as are addictive products. This is one of the reasons behind the taxing of alcohol and tobacco by many governments.