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Question 1:A utility function is given by u(x₁,x₂) = x₁²+x₂². Then which of the following statements are true and which are false.

• (2,1) is at least as good as (1,2).
• (4,0) is at least as good as (2,2).
• (2,0) is at least as good as (1,1).
• (3,3) is strictly prefered but not at least as good as (2,2).
• Given a choice among (2,2),(0,2),(1,1) the consumer would choose (0,2).

Question 2: A utility function is given by u(x₁,x₂) = x₁-4x₂. Graph the indifference curves through (2,2), (0,4) and (4,0).

Question 3: Which of the following utility functions describes monotone preferences?

• u(x₁,x₂) = x₁-4x₂.
• u(x₁,x₂) = x₁x₂^1/2
• u(x₁,x₂) = x₁-(1/x₂)
• u(x₁,x₂) = x₁+3x₂.

Question 4: Determine the marginal rate of substitution MRS for the following utility functions:

• u(x₁,x₂) = x₁+3x₂.
• u(x₁,x₂) = 3x₁-x₂.
• u(x₁,x₂) =x₁^1/4+2x₂
• u(x₁,x₂) =x₁^1/4+x₂^1/4.
• u(x₁,x₂) = x₁+(1/x₂²).
• u(x₁,x₂) =10x₁+x₂
• u(x₁,x₂) =4x₁+5x₂

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