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22. A class of utility functions we have not yet discussed are quasilinear utility functions. In particular, quasilinear utility functions have the form U (x1,

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22. A class of utility functions we have not yet discussed are quasilinear utility functions. In particular, quasilinear utility functions have the form U (x1, x2) = f (170+be where b is a constant and f(x1) is some increasing fUHCTiOI'I Of xlor U (36],)C2)=bxI + f (x) where b is a constant and f (x2) is some increasing function of x2. Economic studies have shown that quasilinear utility functions oftentimes reasonably approximate consumer behavior. For this question, consider the specific quasilinear utility function U (xv x2) : x1 +3x22. A. What is the marginal rate of substitution between good 1 land good 2 ( MRthle at the points (3,4), (4,4), and (5,4)? B. What is the marginal rate of substitution between good 1 and good 2 ( MRthxz) at the points (3,1), (4,1), and (5,1)? C. With good 1 on the x-axis and good y on the y-axis, draw three indifference curves for these preferences. Be very precise, making sure to label the utility of each indifference curve, and include mathematically accurate points that you label. D. At each point on your indifference curves where the individual consumes 0 units of good 1 , what is the MRS ? What can we conclude from this finding? xi J2

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