# 3.5: Elasticities of Supply

- Page ID
- 45349

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## Ranges for Supply Elasticities

Type | Range | Implication |
---|---|---|

Own-price | \(\phi_{ii} >1\) | Supply for good \(i\) is elastic |

Own-price | \(\phi_{ii} = 1\) | Supply for good \(i\) is unitary elastic |

Own-price | \(0 \leq \phi_{ii} <1\) | Supply for good \(i\) is inelastic |

Cross-price | \(\phi_{ij} > 0, i \neq j\) | Good \(j\) is a joint product for good \(i\) |

Cross-price | \(\phi_{ij} < 0, i \neq j\) | Good \(j\) is a competing product for good \(i\) |

Input price | \(\phi_{iW} \leq 0\) | Input price elasticities are non-positive |

## Calculating Supply Elasticities

Type | Point Formula | Arc Formula |
---|---|---|

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

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

Input-price elasticity | \(\phi_{iW} = \dfrac{\Delta Q_{i}}{\Delta W} \times \dfrac{W}{Q_{i}}\) | \(\phi_{iW} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{W^{1} - W^{0}} \times \dfrac{W^{1} + W^{0}}{Q_{i}^{1} + Q_{i}^{0}}\) |

Elasticity for other supply shift variable \(Z\) | \(\phi_{iZ} = \dfrac{\Delta Q_{i}}{\Delta Z} \times \dfrac{Z}{Q_{i}}\) | \(\epsilon_{iZ} = \dfrac{Q_{i}^{1}-Q_{i}^{0}}{Z^{1} - Z^{0}} \times \dfrac{Z^{1} + Z^{0}}{Q_{i}^{1} + Q_{i}^{0}}\) |