A consumer has a utility function of the form U(x, y) =x a + y b, where both a and b are nonnegative. What additional restrictions on the values of the parameters a and b are imposed by each of the following assumptions?
a. Preferences are quasilinear and convex, and x is a normal good.
b. Preferences are homothetic.
c. Preferences are homothetic and convex.
d. Goods x and y are perfect substitutes.
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