For some related questions with solutions see additional questions III.

Question 1 Assume a consumer has the following preferences over consumption bundles (x₁,x₂).

If x₁>=x₂, then in order to leave the consumer indifferent, a reduction of 1 unit of good 2 must be compensated by an increase of 2 units of good 1. In contrast, If x₁=<x₂, then in order to leave the consumer indifferent, a reduction of 1 unit of good 1 must be compensated by an increase of 2 units of good 2.

Graph the indifference curves through (2,2), (4,4) and (6,6). Indicate by using arrows the direction of the @quot;at least as good set@quot; (e.g., the set of all consumption bundles that are at least as good as (2,2).)

Question 2: Determine the marginal rate of substitution MRS for the following utility functions:
Click here for information on how to find the MRS.

• u(x₁,x₂) = x₁+4x₂.
• u(x₁,x₂) = x₁²+x₂
• u(x₁,x₂) = x₁-(1/x₂)
• u(x₁,x₂) = x₁^1/2+x₂^1/2

Question 3: Solve Question 4.7 in the workbook.

Question 4:

• Graph some indifference curves for the utility function
  u(x₁,x₂) = min{x₁,3x₂}.

• Assume the consumer has 5 units of each good. Would the consumer be willing to give up 1 unit of good 2 for 1/100 of a unit of good 1?
• Again assume the consumer has 5 units of each good. Would the consumer be willing to give up 1/100 unit of good 1 for 1 of a unit of good 2?

Question 5: Solve Question 4.5 in the workbook.

Question 6: Solve Question 4.9 in the workbook.

Question 7: Solve Question 4.10 in the workbook.

Question 8: Solve Question 4.11 in the workbook.

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