a) Derive his demand functions of good x and good y. b) Look at the demands of good x and good y you found in part (a). Explain how an increase in income would affect the quantity of x and the quantity of y David optimally consumes. [Hint: You can do a visual check or take the partial derivative of the demand of each good with respect to income and check whether this partial derivative is positive or negative] • Is good x a normal good? Is good y a normal good? ●
a) Derive his demand functions of good x and good y. b) Look at the demands of good x and good y you found in part (a). Explain how an increase in income would affect the quantity of x and the quantity of y David optimally consumes. [Hint: You can do a visual check or take the partial derivative of the demand of each good with respect to income and check whether this partial derivative is positive or negative] • Is good x a normal good? Is good y a normal good? ●
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Show full work and explanation to part b)
![**Exercise 4**
David is a consumer whose preferences over goods x and y are represented by the quasilinear utility function \( u(x, y) = x^{1/2} + y \).
a) **Derive his demand functions** of good x and good y.
b) Look at the demands of good x and good y you found in part (a). **Explain** how an **increase in income** would affect the quantity of x and the quantity of y David optimally consumes.
*[Hint: You can do a visual check or take the partial derivative of the demand of each good with respect to income and check whether this partial derivative is positive or negative]*
- Is good **x** a normal good?
- Is good **y** a normal good?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0128e8-6553-498c-afa0-dd14e88e258d%2F152abb7d-988d-45b1-9285-723ed68be195%2Fy6mt4wg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 4**
David is a consumer whose preferences over goods x and y are represented by the quasilinear utility function \( u(x, y) = x^{1/2} + y \).
a) **Derive his demand functions** of good x and good y.
b) Look at the demands of good x and good y you found in part (a). **Explain** how an **increase in income** would affect the quantity of x and the quantity of y David optimally consumes.
*[Hint: You can do a visual check or take the partial derivative of the demand of each good with respect to income and check whether this partial derivative is positive or negative]*
- Is good **x** a normal good?
- Is good **y** a normal good?
Expert Solution
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Step 1: Explaining utility maximization problem
Utility maximization problem: With the given prices and the income, a consumer chooses his consumption bundle at a point where his utility gets maximized within his budget.
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Solved in 4 steps
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