Consider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual,Plot the indifference curve giving a utility level of 6.Calculate her MRS at consumption bundle (x1,x2), does MRS depend on the value of (x1,x2)?Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=2.Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=4.Calculate the income and substitution effects resulting from the change in price of Good 2 (on the level of Good 2 consumption!)Calculate her demand function X1* (P1, P2,m)Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?

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12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.8P

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Consider an individual whose preferences are represented by the utility function U(x₁,x₂) = min {3x₁+x₂ , x₁+3x₂}. For this individual,

Plot the indifference curve giving a utility level of 6.
Calculate her MRS at consumption bundle (x₁,x₂), does MRS depend on the value of (x₁,x₂)?
Calculate her optimal consumption bundle when she has an income of 24, and P₁=1, P₂=2.
Calculate her optimal consumption bundle when she has an income of 24, and P₁=1, P₂=4.
Calculate the income and substitution effects resulting from the change in price of Good 2 (on the level of Good 2 consumption!)
Calculate her demand function X₁^* (P₁, P₂,m)
Calculate her own price, cross price, and income elasticities at X₁^*(1, 2, 24) and at X₁^*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?