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Choice Continued

Choice Continued. At Z: At Y:. Interpretation. Consumer Demand. Consumer’s demanded bundle : optimal choice of goods 1 and 2 for given prices and income. Consumer’s demand functions :. Demand function for good 1: Demand function for good 2:. Cobb-Douglas. Demand function for good 1:

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Choice Continued

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  1. Choice Continued

  2. At Z: At Y: Interpretation

  3. Consumer Demand • Consumer’s demanded bundle: optimal choice of goods 1 and 2 for given prices and income. • Consumer’s demand functions:

  4. Demand function for good 1: Demand function for good 2: Cobb-Douglas

  5. Demand function for good 1: if if if Perfect Substitutes

  6. Optimal choice: Budget line: Demand function for goods 1 and 2: Perfect Complements

  7. Example: Choosing a Tax Q: Suppose that the government wants to raise a certain amount of revenue. Is it better to raise it via a quantity tax or an income tax?

  8. Budget line: Well-behaved preferences Consumer chooses: Before the Tax

  9. Budget line with quantity tax: Tax revenues: Quantity Tax

  10. Income Tax New budget line: where

  11. Questions • Q1: What is the slope of the budget line with the income tax? • Q2: Which kind of tax is this income tax? • Q3: Can the consumer afford when he is paying the income tax?

  12. Answers • A1: Slope of the budget line with income tax is: • A2: Lump-sum.

  13. A3: Yes. Is still Affordable • Budget line with income tax: • Substitute : • Rearrange: Evaluate at : Rearrange:

  14. Budget line with income tax: Budget line with quantity tax: On the Graph

  15. Q: Is Optimal with the Income Tax?

  16. The budget line is not tangent to indifference curve at . Optimal choice: A: No, it is not.

  17. Q: Which Tax Does the Consumer Prefer?

  18. A: Income Tax Gives Higher Utility to the Consumer Caution: • A uniform income tax for all consumers is not necessarily better than a uniform quantity tax. • Assumption that income tax is lump-sum is key.

  19. Another Question • Suppose that the government can use a uniform value tax on goods 1 and 2 to raise revenue (e.g. a sales tax). Does the consumer still prefer an income tax?

  20. Answer • With a uniform value tax, the budget consumer line reads • Rearranging:

  21. Answer Continued • Rearranging: • Budget line with income tax:

  22. Answer Continued • Budget line with income tax: • Same as budget line under value tax:

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