2. Consider the following utility function: u(x, y) = x² + y. (a) Derive the optimal utility maximizing demands for x as a function of prices and income. (b) Find the formula for price elasticity of demand for x. (c) Find the formula for the income elasticity of demand for x.

2. Consider the following utility function: u(x, y) = x² + y. (a) Derive the optimal utility maximizing demands for x as a function of prices and income. (b) Find the formula for price elasticity of demand for x. (c) Find the formula for the income elasticity of demand for x.

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter6: Consumer Choices

Section: Chapter Questions

Problem 15CTQ: Income Effects depend on the income elasticity of demand for each good limit you buy. If one of the...

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Income Effects depend on the income elasticity of demand for each good limit you buy. If one of the goods you buy has a negative income elasticity, that is, it is an inferior good, what must be true of the income elasticity of the other good you buy?
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a) A consumer has a utility function given by U = x025 y0.75 He has an income of £100, the price of good x is £5 and the price of good y is £10. How much of the 2 goods x and y does the consumer buy? Take a picture of your workings and upload with your answer, or type out your workings. b) For the utility function above, what is the cross-price elasticity of demand for good x with respect to the price of good y? Take a picture of your workings and upload with your answer, or type out your workings. c) For the utility function above, what is the elasticity of demand of good x with respect to its own price? Take a picture of your workings and upload with your answer, or type out your workings.
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What is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income elasticity of demand for X? Does this hold only for the given type of utility function or all well behaved utility functions? What does this mean?
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