40 lines
1.2 KiB
Markdown
Executable File
40 lines
1.2 KiB
Markdown
Executable File
---
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author: Akbar Rahman
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date: \today
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title: Cross Elastic Demand (XED)
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tags: []
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uuid: d6b6e3dd-1bba-466a-aad8-9e39c68280ab
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---
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# Cross Elastic Demand (XED)
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The equation given in the lecture slides is:
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$$\text{XED} = \frac{\frac{\Delta q_A}{q_A}}{\frac{\Delta p_B}{p_B}}$$
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But that's a bit ambiguous, so it's better write as:
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$$\text{XED}
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= \frac{\frac{q_{A,2}-q_{A,1}}{q_{A,1}}}{\frac{p_{B,2}-p_{B,1}}{p_{B,1}}}
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= \frac{\text{percentage change in quantity of A}}{\text{percentage change in price of B}}
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$$
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If XED is positive, the two goods A and B are substitutes for each other.
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If XED is negative, the two goods are complimentary.
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## Example
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Here, product A is the CNC machining system and product B is the control software.
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Quantity of product A sold can be found using $revenue = price \times quantity$:
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$$quantity_1 = \frac{2\,250\,000}{11\,000} = 205$$
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$$quantity_2 = \frac{4\,850\,000}{11\,000} = 441$$
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$$\text{percentage change in quantity of A} = \frac{441-205}{205} = 1.156$$
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$$\text{percentage change in price of B} = \frac{2600-6800}{6800} = -0.618$$
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$$\text{XED} = \frac{1.156}{-0.618} = -1.871$$
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