cross elastic demand

uni/mmme/3049_engineering_management_2/xed.md

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+---
+author: Akbar Rahman
+date: \today
+title: Cross Elastic Demand (XED)
+tags: []
+uuid: d6b6e3dd-1bba-466a-aad8-9e39c68280ab
+---
+
+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:
+
+$$\text{XED}
+= \frac{\frac{q_{A,2}-q_{A,1}}{q_{A,1}}}{\frac{p_{B,2}-p_{B,1}}{p_{B,1}}}
+= \frac{\text{percentage change in quantity of A}}{\text{percentage change in price of B}}
+$$
+
+## 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 $revenue = price \times quantity$:
+
+$$quantity_1 = \frac{2\,250\,000}{11\,000} = 205$$
+$$quantity_2 = \frac{4\,850\,000}{11\,000} = 441$$
+
+$$\text{percentage change in quantity of A} = \frac{441-205}{205} = 1.156$$
+$$\text{percentage change in price of B} = \frac{2600-6800}{6800} = -0.618$$
+
+$$\text{XED} = \frac{1.156}{-0.618} = -1.871$$