Joe consumes crawfish and shrimp. His utility function exhibits diminishing marginal utility of crawfish but the marginal utility of shrimp is constant. Will Joe's indifference curves be convex?
What will be an ideal response?
Yes, Joe has quasi-linear utility—linear in shrimp but diminishing in crawfish. This implies d2u/dC2 < 0. U(C,S) = u(C) + S where u(C) is an increasing, concave function. The slope of the indifference curve (MRS) is -du/dC. Differentiating again gives -d2u/dC2, which is positive by the assumption of diminishing marginal utility of crawfish.
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