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.

Question
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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