notes/uni/mmme/3049_engineering_management_2/xed.md

---
author: Akbar Rahman
date: \today
title: Cross Elastic Demand (XED)
tags: []
uuid: d6b6e3dd-1bba-466a-aad8-9e39c68280ab
---

# Cross Elastic Demand (XED)

The equation given in the lecture slides is:

$$\text{XED} = \frac{\frac{\Delta q_A}{q_A}}{\frac{\Delta p_B}{p_B}}$$

But that's a bit ambiguous, so it's better write as:

$$\text{XED}
= \frac{\frac{q_{A,2}-q_{A,1}}{q_{A,1}}}{\frac{p_{B,2}-p_{B,1}}{p_{B,1}}}
= \frac{\text{percentage change in quantity of A}}{\text{percentage change in price of B}}
$$

If XED is positive, the two goods A and B are substitutes for each other.
If XED is negative, the two goods are complimentary.

## Example

![A question from the book (page 91)](./images/xed_question.png)

Here, product A is the CNC machining system and product B is the control software.

Quantity of product A sold can be found using $revenue = price \times quantity$:

$$quantity_1 = \frac{2\,250\,000}{11\,000} = 205$$
$$quantity_2 = \frac{4\,850\,000}{11\,000} = 441$$

$$\text{percentage change in quantity of A} = \frac{441-205}{205} = 1.156$$
$$\text{percentage change in price of B} = \frac{2600-6800}{6800} = -0.618$$

$$\text{XED} = \frac{1.156}{-0.618} = -1.871$$