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Understanding Exponential Demand Functions and Their Elasticities

This document explores exponential demand functions, specifically showcasing their characteristics such as constant elasticities. It outlines market demand for a good (X) as a sum of individual demands from four participants: Pauper, Broke, Average, and Rich. The text delves into different types of elasticities: price elasticity, cross-price elasticity, and income elasticity. It emphasizes the importance of understanding how changes in income or price impact demand and offers scenarios to illustrate these concepts further, including government taxation effects.

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Understanding Exponential Demand Functions and Their Elasticities

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  1. Exponential Demand Functions The following demand function is an exponential demand function:

  2. Exponential Demand Functions This exponential demand function exhibits constant elasticities:

  3. Problem 7.1, page 188 a. The market demand function for X is the sum of the demands of the four participants: For i= 1 (Pauper),2 (Broke),3 (Average), and 4 (Rich).

  4. Price Elasticity of Demand

  5. Cross Price Elasticity of Demand

  6. Income Elasticity of Demand We can not compute the income elasticity of demand for good X without knowing whose income has changed.

  7. If price of X doubles:

  8. If Mr. Pauper loses his job and his income falls by 50%:

  9. If Ms. Rich’s income drops by 50%:

  10. If the government imposes a 100 percent tax on Y:

  11. If IP=IB=IA=IR=25:

  12. If IP=IB=IA=IR=25 and PX doubles:

  13. If IP or IR drops by 50%:

  14. If Ms. Rich finds Z a necessary complement to X:

  15. Price Elasticity of Demand, ex, Px

  16. Cross Price Elasticity of Demand

  17. Cross Price Elasticity of Demand

  18. Cross Price Elasticity of Demand

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