# 3.3: Computing Demand Elasticities

- Page ID
- 45347

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## The Point Formula for Demand Elasticities

Type | Formula |
---|---|

Own-price elasticity | \(\epsilon_{ii} = \dfrac{\Delta Q_{i}}{\Delta P_{i}} \times \dfrac{P_{i}}{Q_{i}}\) |

Cross-price elasticity | \(\epsilon_{ij}= \dfrac{\Delta Q_{i}}{\Delta P_{j}} \times \dfrac{P_{j}}{Q_{i}}, i \neq j\) |

Income elasticity | \(\epsilon_{iM} = \dfrac{\Delta Q_{i}}{\Delta M} \times \dfrac{M}{Q_{i}}\) |

Elasticity for other demand shift variable \(X\) | \(\epsilon_{iX} = \dfrac{\Delta Q_{i}}{\Delta X} \times \dfrac{X}{Q_{i}}\) |

Type | Data Point 0 | Data Point 1 |
---|---|---|

Own-price elasticity | \(\epsilon_{11} = -4 \times \dfrac{60}{160} = -1.5\) | \(\epsilon_{11}= -4 \times \dfrac{50}{200} = 1.0\) |

Cross-price elasticity | \(\epsilon_{12} = 2 \times \dfrac{20}{160} = 0.25\) | \(\epsilon_{12} = 2 \times \dfrac{20}{200} = 0.20\) |

Income elasticity | \(\epsilon_{1M} = 0.01 \times \dfrac{30000}{160} = 1.875\) | \(\epsilon_{1M} = 0.01 \times \dfrac{30000}{200} = 1.5\) |

Advertising elasticity | \(\epsilon_{1A} = 1.5 \times \dfrac{40}{160} = 0.375\) | \(\epsilon_{1A} = 1.5 \times \dfrac{40}{200} = 0.30\) |

## The Arc Formula for Elasticities

Type | Formula |
---|---|

Own-price elasticity | \(\epsilon_{ii} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{P_{i}^{1} - P_{i}^{0}} \times \dfrac{P_{i}^{1} + P_{i}^{0}}{Q_{i}^{1} + Q_{i}^{0}}\) |

Cross-price elasticity | \(\epsilon_{ij} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{P_{j}^{1} - P_{j}^{0}} \times \dfrac{P_{j}^{1} + P_{j}^{0}}{Q_{i}^{1} + Q_{i}^{0}}, i \neq j\) |

Income elasticity | \(\epsilon_{iM} = \dfrac{Q_{i}^{1}-Q_{i}^{0}}{M^{1}-M^{0}} \times \dfrac{M^{1} + M^{0}}{Q_{i}^{1} + Q_{i}^{0}}\) |

Elasticity for other demand shift variable \(X\) | \(\epsilon_{iX} = \dfrac{Q_{i}^{1}- Q_{i}^{0}}{X^{1}-X^{0}} \times \dfrac{X^{1} + X^{0}}{Q_{i}^{1} + Q_{i}^{0}}\) |