## Calculating PED

## Syllabus: Calculate PED between two designated points on a demand curve using the PED equation.

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.

Letīs Do Some Economics

### 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? (Revenue is just price times quantity)

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 because demand is elastic: Elastic is when the proportionate change in demand is greater than the proportionate change in price

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.

Thinking
time: In example 1 the price increase and revenue fell but in example 2
the price increase and revenue increased - can you say why? |