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Logan has preferences over olives (x₁) and ice creams (x₂). He prefers to eat them separately not together, which is represented by: U(x1, x₂) = x² + x². Also suppose his income is $200 and the prices of olives and ice creames are p×₁ $1 and

Logan has preferences over olives (x₁) and ice creams (x₂). He prefers to eat them separately not together, which is represented by: U(x1, x₂) = x² + x². Also suppose his income is $200 and the prices of olives and ice creames are p×₁ $1 and

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.7P
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Answer subpart 4,5,6 only.

Question 7: Logan has preferences over olives (x₁) and ice creams (x₂). He prefers to eat them separately but not together, which is represented by: U(x₁, x₂) = x² + x². Also suppose his income is $200 and the prices of olives and ice creames are px₁ = $1 and Px₂ = $2, respectively. 1. Is this convex preferences or concave preferences? 2. Solve for the bundle that satisfis the tangency condition. 3. What's the level of utility using the bundle you just solved in Q7.2? 4. Consider spending all of your income on olives (x₁). What's the utility from this bundle? 5. Which bundle does Logan prefer between the bundle in Q7.2 and Q7.4? Does the tangency condition lead to the optimal bundle? 6. What's the optimal bundle when price of olives is $3.
Transcribed Image Text:Question 7: Logan has preferences over olives (x₁) and ice creams (x₂). He prefers to eat them separately but not together, which is represented by: U(x₁, x₂) = x² + x². Also suppose his income is $200 and the prices of olives and ice creames are px₁ = $1 and Px₂ = $2, respectively. 1. Is this convex preferences or concave preferences? 2. Solve for the bundle that satisfis the tangency condition. 3. What's the level of utility using the bundle you just solved in Q7.2? 4. Consider spending all of your income on olives (x₁). What's the utility from this bundle? 5. Which bundle does Logan prefer between the bundle in Q7.2 and Q7.4? Does the tangency condition lead to the optimal bundle? 6. What's the optimal bundle when price of olives is $3.
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