101 Concepts for the Level I Exam
Concept 17: Price, Income and Cross-Price Elasticities of Demand
Elasticity of demand is measured as a ratio of percentage change in quantity demanded to a percentage change in other variables.
Own-price elasticity
![Rendered by QuickLaTeX.com $Own\ price\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ own\ price}}$](https://ift.world/wp-content/ql-cache/quicklatex.com-b8b953f4a156d73d2639fa43c23e79c7_l3.png)
- Own-price elasticity of demand is usually always negative.
- If |own price elasticity| > 1, then demand is elastic.
- If |own price elasticity| < 1, then demand is inelastic.
- If own price elasticity = -1, then demand is unit, or unitary, elastic.
Income elasticity
![Rendered by QuickLaTeX.com $Income\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ income}}$](https://ift.world/wp-content/ql-cache/quicklatex.com-e112425754b560051e352a6265b6ed59_l3.png)
- If income elasticity > 0, then the good is a normal good.
- If income elasticity < 0, then the good is an inferior good.
Cross price elasticity
![Rendered by QuickLaTeX.com $Cross\ price\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ \ price\ of\ related\ good}}$](https://ift.world/wp-content/ql-cache/quicklatex.com-514e454fc8f9b5a1a0b1670ba6c87bf2_l3.png)
- If cross price elasticity > 0, then the related good is a substitute.
- If cross price elasticity < 0, then the related good is a complement.
A demand function for chairs is as follows:
![Rendered by QuickLaTeX.com $$Q_{chairs}=200-2P_{chairs}+0.05Income-0.8P_{tables}+{1.2P}_{stools}$$](https://ift.world/wp-content/ql-cache/quicklatex.com-776e60aec5c886ee3c7973bdada84451_l3.png)
At current average prices, a chair costs $50, a table costs $100 and a stool costs $30. Average income is $5,000. Calculate the income elasticity of demand for chairs.
Solution:
Substitute current values for the independent variables (except income)
![Rendered by QuickLaTeX.com $$Q_{chairs}=200-2(50)+0.05Income-0.8(100)+1.2(30)$$](https://ift.world/wp-content/ql-cache/quicklatex.com-1e7c1e2d93317aad18aeadccc174aff0_l3.png)
![Rendered by QuickLaTeX.com $$Q_{chairs}=56+0.05Income$$](https://ift.world/wp-content/ql-cache/quicklatex.com-9bdb22a1857e8b2eb22f50d64957716d_l3.png)
The slope of income is 0.05
For an income of $5,000; Qchairs = 306
![Rendered by QuickLaTeX.com $$Income\ elasticity={{I_0}\over {Q_0}}\times {{\italic{\Delta}Q}\over {\italic{\Delta}I}}={{5,000}\over {306}}\times 0.05=0.82$$](https://ift.world/wp-content/ql-cache/quicklatex.com-f05925922ad061b8e18953690ebc3575_l3.png)
Factors impacting the own price elasticity of demand for a product include:
- Substitutes: If the number of substitutes for this product is high, then elasticity will be high.
- Portion of total budget: If the portion of total budget spent on this product is high, then elasticity will be high.
- Time horizon: If the time horizon we consider is long, then elasticity will be high. This is because consumers will have enough time to respond to changes in the price of this product.
- Discretionary (optional) versus non-discretionary (necessary): If the product is discretionary rather than non-discretionary, then the elasticity will be high.
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